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Research Article

An improved genetic algorithm and its application in neural network adversarial attack

Contributed equally to this work with: Dingming Yang, Zeyu Yu, Hongqiang Yuan

Roles Conceptualization, Data curation, Formal analysis, Methodology, Software, Validation, Writing – original draft, Writing – review & editing

Affiliation School of Computer Science, Yangtze University, Jingzhou, China

Roles Funding acquisition, Supervision, Validation, Writing – review & editing

Affiliation School of Electronic & Information, Yangtze University, Jingzhou, China

Roles Funding acquisition, Resources, Writing – review & editing

Affiliation School of Urban Construction, Yangtze University, Jingzhou, China

Roles Conceptualization, Project administration, Resources, Supervision, Writing – review & editing

* E-mail: [email protected]

• Dingming Yang, 
• Zeyu Yu, 
• Hongqiang Yuan, 
• Yanrong Cui

• Published: May 5, 2022
• https://doi.org/10.1371/journal.pone.0267970
• Reader Comments

The choice of crossover and mutation strategies plays a crucial role in the searchability, convergence efficiency and precision of genetic algorithms. In this paper, a novel improved genetic algorithm is proposed by improving the crossover and mutation operation of the simple genetic algorithm, and it is verified by 15 test functions. The qualitative results show that, compared with three other mainstream swarm intelligence optimization algorithms, the algorithm can not only improve the global search ability, convergence efficiency and precision, but also increase the success rate of convergence to the optimal value under the same experimental conditions. The quantitative results show that the algorithm performs superiorly in 13 of the 15 tested functions. The Wilcoxon rank-sum test was used for statistical evaluation, showing the significant advantage of the algorithm at 95% confidence intervals. Finally, the algorithm is applied to neural network adversarial attacks. The applied results show that the method does not need the structure and parameter information inside the neural network model, and it can obtain the adversarial samples with high confidence in a brief time just by the classification and confidence information output from the neural network.

Citation: Yang D, Yu Z, Yuan H, Cui Y (2022) An improved genetic algorithm and its application in neural network adversarial attack. PLoS ONE 17(5): e0267970. https://doi.org/10.1371/journal.pone.0267970

Editor: Mohd Nadhir Ab Wahab, Universiti Sains Malaysia, MALAYSIA

Received: November 24, 2021; Accepted: April 19, 2022; Published: May 5, 2022

Copyright: © 2022 Yang et al. This is an open access article distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Data Availability: All relevant data are within the paper and its Supporting information files.

Funding: D.Y., Z.Y., H.Y. and Y.C.; This work was supported by the Major Technology Innovation of Hubei Province [2019AAA011]. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

Competing interests: The authors have declared that no competing interests exist.

1 Introduction

In real life, optimization problems such as shortest path, path planning, task scheduling, parameter tuning, etc. are becoming more and more complex and have complex features such as nonlinear, multi-constrained, high-dimensional, and discontinuous [ 1 ]. Although a series of artificial intelligence algorithms represented by deep learning can solve some optimization problems, they lack mathematical interpretability due to the existence of a large number of nonlinear functions and parameters inside their models, so they are difficult to be widely used in the field of information security. Traditional optimization algorithms and artificial intelligence algorithms can hardly solve complex optimization problems with high dimensionality and nonlinearity in the field of information security.

Therefore, it is necessary to find an effective optimization algorithm to solve such problems. In this background, various swarm intelligence optimization algorithms have been proposed one after another, such as Particle Swarm Optimization(PSO) [ 2 , 3 ], Grey Wolf Optimizer(GWO) [ 4 ], etc. Subsequently, a variety of improved optimization algorithms also have been proposed one after another. For example, the improved genetic algorithm for cloud environment task scheduling [ 5 ], the improved genetic algorithm for flexible job shop scheduling [ 6 ], the improved genetic algorithm for green fresh food logistics [ 7 ], etc.

However, these improved optimization algorithms are improved for domain-specific optimization problems and do not improve the accuracy, convergence efficiency and generalization of the algorithms themselves. In this paper, the crossover operator and mutation operator of the genetic algorithm are improved to improve the convergence efficiency and precision of the algorithm without affecting the effectiveness of the improved genetic algorithm on most optimization problems. The effectiveness of the improved genetic algorithm is also verified through many comparison experiments and applications in the field of neural network adversarial attacks.

• By improving the single-point crossover link of SGA, the fitness function is used as an evaluation index for selecting children after crossover, thus reducing the number of iterations and accelerating the convergence speed.
• By improving the basic bitwise mutation of the SGA, traversing each gene of the offspring and performing selective mutation on them, setting different mutation rates for two parts of a chromosome, thus improving the global search in the stable case of local optimum.
• The improved genetic algorithm is applied to the field of neural network adversarial attack, which increases the speed of adversarial sample generation and improves the robustness of the neural network model.

2 Related works

2.1 genetic algorithm.

Genetic Algorithm is a series of simulation evolutionary algorithms proposed by Holland et al. [ 8 ], and later summarized by DeJong, Goldberg and others. The general flowchart of the Genetic Algorithm is shown in Fig 1 . The Genetic Algorithm first encodes the problem, then calculates the fitness, then selects the parent and the mother by roulette, and finally generates the children with high fitness by crossover and mutation, and finally generates the individuals with high fitness after many iterations, which is the satisfied solution or optimal solution of the problem. Simple Genetic Algorithm (SGA) uses single-point crossover and simple mutation to embody information exchange between individuals and local search, and does not rely on gradient information, so SGA can find the global optimal solution.

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https://doi.org/10.1371/journal.pone.0267970.g001

2.2 Other meta-heuristic algorithms

The meta-heuristic algorithm is problem-independent, does not exploit the specificity of the problem, and is a general solution. In general, it is not greedy, can explore more search space, and tends to obtain the global optimum. To be more specific, meta-heuristic have one of the most important ideas: a dynamic balance mechanism between diversification and intensification.

The PSO [ 2 , 3 ] algorithm is a swarm intelligence-based global stochastic search algorithm inspired by the results of artificial life research and by simulating the migration and flocking behavior of bird flocks during foraging, and its basic idea is inspired by the results of research on modeling and simulation of birds flock behavior. The GWO algorithm is a swarm intelligence optimization algorithm proposed by Mirjalili et al. [ 4 ]. The algorithm is inspired by the grey wolf prey hunting activity and developed as an optimization search algorithm, which has strong convergence performance, few parameters, and easy implementation. The Marine Predator Algorithm (MPA) [ 9 ] is mainly inspired by foraging strategies widely found in marine predators, namely Lévy and Brownian motion, and optimal encounter rate strategies in biological interactions between predators and prey. The Artificial Gorilla Troops Optimizer (GTO) [ 10 ] was inspired by the gorilla group life behavior. The GTO is characterized by fast search speed and high solution accuracy. The African Vulture Optimization Algorithm(AVOA) [ 11 ] was inspired by the foraging and navigation behavior of African vultures. this algorithm is fast and has high solution accuracy which is widely used in single-objective optimization. The Remora Optimization Algorithm (ROA) [ 12 ] first proposed an intelligent optimization algorithm inspired by the biological habits of the neutrals in nature, which has good solution accuracy and high engineering practical value in both function seeking to solve extreme values and typical engineering optimization problems.

2.3 Neural network adversarial attack

Szegedy et al. [ 13 ] first demonstrated that a highly accurate deep neural network can be misled to make a misclassification by adding a slight perturbation to an image that is imperceptible to the human eye, and also found that the robustness of deep neural networks can be improved by adversarial training. Such phenomena are far-reaching and have attracted many researchers in the area of adversarial attacks and deep learning security. Akhtar and Mian [ 14 ] surveyed 12 attack methods and 15 defense methods for neural networks adversarial attacks. The main attack methods are finding the minimum loss function additive term [ 13 ], increasing the loss function of the classifier [ 15 ], the method of limiting the l_0 norm [ 16 ], changing only one pixel value [ 17 ], etc.

Nguyen et al. [ 18 ] continued to explore the question of “what differences remain between computer and human vision” based on Szegedy et al. [ 13 ]. They used the Evolutionary Algorithm to generate high-confidence adversarial images by iterating over direct-encoded images and CPPN (Compositional Pattern-Producing Network) encoded images, respectively. They obtained high-confidence adversarial samples (fooling images) using the Evolutionary Algorithm on a LeNet model pre-trained on the MNIST dataset [ 19 ] and an AlexNet model pre-trained on the ILSVRC 2012 ImageNet dataset [ 20 , 21 ], respectively.

Neural network adversarial attacks are divided into black-box attacks and white-box attacks. Black-box attacks do not require the internal structure and parameters of the neural network, and the adversarial samples can be generated with optimization algorithms as long as the output classification and confidence information is known. The study of neural network adversarial attacks not only helps to understand the working principle of neural networks but also increases the robustness of neural networks by training with adversarial samples.

3 Approaches

This section improves the single-point crossover and simple mutation of SGA. The fitness function is used as the evaluation index of the crossover link, and the crossover points of the whole chromosome are traversed to improve the efficiency of the search for the best. A selective mutation is performed for each gene of the children’s chromosome, and the mutation rate of the latter half of the chromosome is set to twice that of the first half to improve the global search under the stable situation of local optimum.

3.1 Improved crossover operation

As shown in algorithm 1 is the Python pseudocode for the improved crossover algorithm. The single-point crossover of SGA is to generate a random number within the parental chromosome length range, and then intercept the first half of the father’s chromosome and the second half of the mother’s chromosome to cross-breed the children according to the generated random number. In this paper, the algorithm is improved by trying to cross genes within the parental chromosome length range one by one, calculating the fitness, and picking out the highest fitness children individuals. Experimental data show that such an improvement can reduce the number of iterations and speed up the convergence of fitness.

Algorithm 1 Crossover with fitness as evaluation.

Input : Father’s gene, mother’s gene, fitness function;

Output : Child’s gene;

1: function CROSSOVER( father , mother , fitness )

2:   best _ fitness = float . MIN _ VALUE ;

3:   best _ child = np . zeros ( father . size );

4:   for i = 0 → father . size do

5:    current _ child = np . zeros ( father . size );

6:    current _ child = np . append ( father [0: i ], mother [ i :]);

7:    current _ fitness = fitness ( current _ child );

8:    if current _ fitness > best _ fitness then

9:     best _ fitness = current _ fitness ;

10:     best _ child = current _ child . copy ();

11:    end if

12:   end for

13:   return best _ child

14: end function

3.2 Improved mutation operation

As shown in algorithm 2 is the pseudocode of the improved mutation algorithm. The simple mutation of SGA sets a relatively large mutation rate, and mutates any one gene of the incoming children’s chromosome when the generated random number is smaller than the mutation rate. In this paper, we improve the algorithm by setting a small mutation rate and then selectively mutating each gene of the incoming children’s chromosome. That is, when the generated random number is smaller than the mutation rate, the gene is mutated, and when the traversed gene position is larger than half of the chromosome length, the mutation rate is set to twice the original one (the second half of the gene has relatively less influence on the result). This ensures that the first half of the gene and the second half of the gene have an equal chance of mutation respectively, and can mutate at the same time. When the gene length is 784, the mutation rate of the whole chromosome is 1 − (1 − 0.025) 392 × (1 − 0.05) 392 , which greatly improves the species diversity and at the same time ensures the stability of the species (in the stable situation of the local optimum improves the global search ability), and experimental data show that it can improve the search capability.

Algorithm 2 Mutate child with alter each gene if rand number less than mutate rate.

Input : Child’s gene;

Output : Mutated child’s gene;

1: function MUTATE( child )

2:   mutate _ rate = 0.025;

3:   for i = 0 → child . size do

4:    if i > child . size //2 then

5:     mutate _ rate = 0.05;

6:    end if

7:    if random . random () < mutate _ rate then

8:     child [ i ] = ! child [ i ];//child[i] equals 0 or 1

9:    end if

10:   end for

11:   return child

12: end function

4 Numerical experiments and analysis

4.1 test functions.

In order to evaluate the optimization performance of the proposed improved genetic algorithm, 15 representative test functions from AVOA paper of Abdollahzadeh et al. [ 11 ] and Wikipedia [ 22 ] are selected in this paper. Since the proposed improved genetic algorithm is mainly used for the neural network adversarial attack problem, and the neural network has multi-dimensional parameters, the dimensions of the test functions will be tested on 30, 50, and 100, respectively. The details of the formula, dimensions, range, and minimum of the 15 test functions are shown in Tables 1 – 3 , where Table 1 are multi-dimensional test functions with unimodal, Table 2 are multi-dimensional test functions with multi-modal, and Table 3 for fixed-dimensional test functions.

https://doi.org/10.1371/journal.pone.0267970.t001

https://doi.org/10.1371/journal.pone.0267970.t002

https://doi.org/10.1371/journal.pone.0267970.t003

4.2 Experimental environment

The hardware environment of the experiment includes 8G of RAM, i7–4700MQ CPU; the software environment includes Windows 10 system, and the version of Python is 3.8.8. In order to compare the optimization performance of IGA, SGA (Simple Genetic Algorithm), PSO (Particle Swarm Optimization) and GWO (Grey Wolf Optimizer) are selected as the experimental objects for comparison experiments in this paper.

(a) Mutation rate. (b) Population size. (c) Max iteration.

https://doi.org/10.1371/journal.pone.0267970.g002

https://doi.org/10.1371/journal.pone.0267970.t004

4.3 Experimental results and analysis

4.3.1 qualitative result analysis..

(a) Parameter space. (b) Population distribution. (c) Best record. (d) Convergence curve.

https://doi.org/10.1371/journal.pone.0267970.g003

https://doi.org/10.1371/journal.pone.0267970.g004

https://doi.org/10.1371/journal.pone.0267970.g005

https://doi.org/10.1371/journal.pone.0267970.g006

4.3.2 Quantitative result analysis.

In order to make a quantitative comparison with the other three mainstream optimization algorithms, the four optimization algorithms are performed independently for 10 experiments on F1-F11 test functions in dimensions 30, 50, and 100, respectively. The purpose of performing the high-dimensional function test is to test the convergence superiority of IGA on the high-dimensional space for application in the field of neural network adversarial attack. Tables 5 – 7 are the test results of the test functions F1-F11 in 30, 50, and 100 dimensions, respectively. Table 8 shows the results of the four optimization algorithms tested on the test functions F12-F15. The best result, worst result, mean, median, standard deviation, and P-value are compared for 10 experiments. Where P-value is the result of the Wilcoxon rank-sum statistical test and P-value below 5% is significant.

https://doi.org/10.1371/journal.pone.0267970.t005

https://doi.org/10.1371/journal.pone.0267970.t006

https://doi.org/10.1371/journal.pone.0267970.t007

https://doi.org/10.1371/journal.pone.0267970.t008

In Table 5 , IGA achieves significantly superior performance in 9 test functions, PSO is better in F3, and SGA is slightly better in F8. In Tables 6 and 7 , IGA achieves significantly superior performance in 10 test functions, PSO performs better in F3. It can be seen that the performance loss of IGA with increasing dimensionality is not as large as the other three optimization algorithms. In Table 8 , IGA achieves significantly superior performance in 3 test functions, and PSO performs slightly better in F14.

In general, IGA has better iteration efficiency, global search capability, and convergence success rate than the other three optimization algorithms.

5 Application in neural network adversarial attack

5.1 mnst dataset.

The MNST dataset (Mixed National Institute of Standards and Technology database) [ 19 ] is one of the most well-known datasets in the field of machine learning and is used in applications from simple experiments to published paper research. It consists of handwritten digital images from 0–9. The MNIST image data is a single-channel grayscale map of 28 × 28 pixels, with each pixel taking values between 0 and 255, with 60,000 samples in the training set and 10,000 samples in the test set. The general usage of the MNIST dataset is to learn with the training set first and then use the learned model to measure how well the test set can be correctly classified [ 23 ].

5.2 Implementation

As shown in Fig 7(a) , the Deep Convolutional Neural Network (DCNN) pre-trained on the MNST dataset [ 19 ] is used as the experimental object in this paper, and the accuracy of the model is 99.35% with a Loss value of 0.9632. As shown in Fig 7(b) , the model of network adversarial attack is shown. The number of populations of a specific size (set to 100 in this paper) is first generated and then input to the neural network to obtain the confidence of the specified labels. To reduce the computational expense, the input is reduced to a binary image of 28 × 28 and the randomly generated binary image is iterated using the IGA proposed in this paper. Among the 100 individuals, the fathers and mothers with relatively high confidence are selected by roulette selection, and then the children are generated by using the improved crossover link in this paper, and the children from a new population by improving the mutation link until the specified number of iterations. Finally, the individual with the highest confidence is picked from the 100 individuals, which is the binary image with the highest confidence after passing through the neural network.

(a) The structure of DCNN for experiment. (b) The model of network adversarial attack.

https://doi.org/10.1371/journal.pone.0267970.g007

As shown in Fig 8 , the confidence after 99 iterations of DCNN is 99.98% for sample “2”. Sample “6” and sample “4” have the slowest convergence speed, and the confidence of sample “6” is 78.84% after 99 iterations, and the confidence of sample “4” is 78.84% after 99 iterations.

https://doi.org/10.1371/journal.pone.0267970.g008

The statistics of the experimental results are shown in Fig 9 . The binary image of sample “1” generated after 999 iterations has confidence of 99.94% after passing DCNN, which is much higher than the confidence of sample “1” in the MNIST test set in the DCNN control group. In the statistics of the results after initializing the population with the MNIST test set, because the overall confidence of the population initialized with the test set is higher, the increase in confidence during iteration is smaller. The confidence of the sample selected from the MNIST test set is 99.56%, and after 10 iterations the confidence of the sample is 99.80%, and the number “1” becomes vertical; after 89 iterations the confidence is 99.98%, and the number “1” has a tendency to “decompose” gradually.

https://doi.org/10.1371/journal.pone.0267970.g009

As shown in Fig 10 , the reason for this situation is probably that the confidence as a function of the image input is a multi-peak function, and the interval in which the test set images are distributed is not the highest peak of the confidence function. This causes the initial population of the test set to “stray” from some pixels in the images generated by the IGA.

https://doi.org/10.1371/journal.pone.0267970.g010

6 Conclusion

The comparison and simulation experiments show that the improved method proposed in this paper is effective and greatly improves the convergence efficiency, global search capability and convergence success rate. Applying IGA to the field of neural network adversarial attacks can also quickly obtain adversarial samples with high confidence, which is meaningful for the improvement of the robustness and security of neural network models.

In this paper, although the genetic algorithm has been improved to enhance the performance of the genetic algorithm, it is based on the genetic algorithm, so it cannot be completely separated from the general framework of the genetic algorithm, and the problem that the genetic algorithm is relatively slow in a single iteration cannot be solved. We hope to explore a new nature-inspired optimization algorithm in our future work. In addition, the reason why the neural network model has so many adversarial samples, we believe that it is a design flaw in the architecture of the neural network model. In future work, we will also try to explore a completely new way of the infrastructure of neural networks so as to compress the space of adversarial samples.

With the wide application of artificial intelligence and deep learning in the field of computer vision, face recognition has outstanding performance in access control systems and payment systems, which require a fast response to the input face image, but this has instead become a drawback to be hacked. For face recognition systems without in vivo detection, using the method in this paper only requires output labels and confidence information can obtain high confidence images quickly. In summary, neural networks have many pitfalls due to their uninterpretability and still need to be considered carefully for use in important areas.

Supporting information

https://doi.org/10.1371/journal.pone.0267970.s001

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Evolutionary algorithms and their applications to engineering problems

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• Volume 32 , pages 12363–12379, ( 2020 )

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The main focus of this paper is on the family of evolutionary algorithms and their real-life applications. We present the following algorithms: genetic algorithms, genetic programming, differential evolution, evolution strategies, and evolutionary programming. Each technique is presented in the pseudo-code form, which can be used for its easy implementation in any programming language. We present the main properties of each algorithm described in this paper. We also show many state-of-the-art practical applications and modifications of the early evolutionary methods. The open research issues are indicated for the family of evolutionary algorithms.

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Evolution Strategies and Evolutionary Programming

Evolutionary Algorithms

Avoid common mistakes on your manuscript.

1 Introduction

These days, in the area of soft computing research we can observe a strong pressure to search for new optimization techniques which are based on nature. Figure  1 presents some approaches in optimization techniques with a concentration on evolutionary approaches. Today, the whole family of evolutionary optimization algorithms is referred to as evolutionary computation (EC) algorithms. In the evolutionary computation domain, we can mention the following main algorithms: the genetic algorithm (GA) [ 1 ], genetic programming (GP) [ 2 ], differential evolution (DE) [ 3 ], the evolution strategy (ES) [ 4 ], and evolutionary programming (EP) [ 5 ]. Each of these techniques has many different varieties and is used in many different industrial applications.

Taxonomy of nature-inspired methods

This paper is a state-of-the-art paper which topic is connected mainly with evolutionary algorithms (EAs) such as GA, GP, DE, ES, and EP. (In the other paper [ 6 ], we have presented swarm intelligence algorithms (SIAs) such as ant colony optimization (ACO), particle swarm optimization (PSO), and others in which social collaboration between agents exist.) The other nature-based methods, like family of physical algorithms (e.g., simulated annealing, extremal optimization, harmony search, cultural algorithm, gravitational search, river formation dynamics, black hole algorithm), or family of plant intelligence algorithms (e.g., flower pollination algorithm, invasive weed optimization, paddy field algorithm, artificial plant optimization algorithm, photosynthetic algorithm, plant growth optimization, rooted tree optimization), are not considered here due to their less popularity.

The aim of this paper is to present a short overview of the practical applications of evolutionary algorithms (EAs). The paper is the complement to [ 6 ] where a state of the art of industrial (real-life) applications of swarm intelligence is presented. The paper is organized as follows. In Sect.  2, we briefly present the main EAs, namely genetic algorithm , genetic programming , differential evolution , evolution strategies , and evolutionary programming . Section  3 describes the various uses of the considered methods in selected areas. Finally, recent advances and the current trends of the EAs are described.

2 Brief presentation of the EAs

2.1 genetic algorithms.

The genetic algorithm (GA) [ 1 ] is one of the oldest and most known optimization techniques, which are based on nature. In the GA, the search for solution space imitates the natural process which takes place in the environment, and the Darwinian theory of species evolution is taken into consideration. In GAs, we have a population of individuals; each, called a chromosome, represents a potential solution to the problem. The problem being solved is defined by the objective function. Depending on how “good” the given individual is fitted to the objective function, the value which represents its quality is attributed to it. This value is referred to as the fitness of the individual, and it is a main evaluating factor. Highly valued individuals have a better chance to be selected to the new generation of the population. In GAs, we have three operators: selection (a new population of individuals is created based on the fitness values of individuals from the previous generation), crossover (typically parts of individuals are exchanged between two individuals selected to the crossover), and mutation (the values of particular genes are changed randomly). Algorithm 1 presents the standard GA in the pseudo-code form (for more details see [ 7 ]).

Many modifications of the standard GA have been developed; some of them are listed in Table  1 .

2.2 Genetic programming

Genetic programming (GP) [ 2 ] is relatively new; it is a specialized form of a GA which operates on very specific types of solution, using modified genetic operators. The GP was developed by Koza [ 2 ] as an attempt to find the way for the automatic generation of the program codes when the evaluation criteria for their proper operation is known. Because the searched solution is a program, the evolved potential solutions are coded in the form of trees instead of linear chromosomes (of bits or numbers) widespread in GAs. As GP differs from GA the used coding schema, the main loop of GP is the same as in Algorithm 1. Of course, the genetic operators are specialized for working on trees, e.g., crossover as exchanging the subtrees, mutation as a change of node or leaf. Some modifications of the GP are shown in Table  1 .

2.3 Differential evolution algorithm

The differential evolution (DE) is a type of evolutionary algorithm useful mainly for the function optimization in continuous search space. Although a version of DE algorithm for combinatorial problems has also been discussed [ 51 ], the principal version of the DE algorithm was discussed by Storn and Price [ 3 ]. The main advantages of DE over a traditional GA are: It is easy to use, and it has efficient memory utilization, lower computational complexity (it scales better when handling large problems), and a lower computational effort (faster convergence) [ 52 ]. The standard DE procedure is shown in Algorithm 2. Presented there DE optimizes the problem with n decision variables. Parameter F scales the values added to the particular decision variables (mutation), and CR parameter represents the crossover rate [ 52 ] ( \(x_{i,j}\) is the value of j th decision variable stored in i th individual in the population). More detailed information on how the parameters should be tuned can be found in [ 53 ]. The main idea of the DE algorithm is connected with computing the difference between two individuals chosen randomly from the population. (The DE determines the function gradient within a given area—not at a single point.) Therefore, the DE algorithm prevents the solution of sticking at a local extreme of the optimized function [ 52 ]. Twenty years of DE development resulted in many modifications. Some of them are shortly presented in Table  1 .

2.4 Evolution strategies

The evolution strategies (ESs) are different when compared to the GAs, mainly in the selection procedure. In the GA, the next generation is created from the parental population by choosing individuals depending on their fitness value, keeping a constant size of the population. In the ES, a temporary population is created; it has the different size than the parental population (depending on the assumed parameters \(\lambda \) and \(\mu \) ). In this step, the fitness values are not important. Individuals in the temporary population undergo crossover and mutations. From such populations, an assumed number of the best individuals are selected to the next generation of the population (in a deterministic way). ESs operate on the vectors of the floating point numbers, while the classical GA operates on binary vectors. The primary types of ESs are ES( \(1+1\) ), ES( \(\mu +\lambda )\) , and ES( \(\mu ,\lambda \) ) [ 7 ].

2.4.1 Evolution strategy ES(1 + 1)

It is the oldest approach; only one individual x is evolved. The initial individual x is randomly generated. In each iteration, only one new individual y is created. The crossover operator does not exist, and the mutation operator creates the individual y by adding a randomly generated number to each gene of the individual x . The normal distribution N with a mean value equal to zero and a standard deviation equal to one is used. The value of i th gene in the individual y is computed as follows: \(y_{i}=x_{i}+\sigma \cdot {}N_{i}(0,1)\) , where \(\sigma \) is a parameter which determines the range of the mutation. Based on the fitness value of individuals x and y , the better one is selected for the new generation and becomes a new individual x . Parameter \(\sigma \) undergoes adaptation by the so-called rule of 1/5 successes. According to this rule, the best results are obtained when the relation R between successful mutations and all mutations is equal to 1/5. When during k successive generations, the relation R is higher than 1/5, then the value of the \(\sigma \) parameter is increased. When the relation R is lower than 1/5, then the value of the \(\sigma \) parameter is decreased. The \(\sigma \) parameter does not change when the relation R is equal to 1/5 [ 7 ].

2.4.2 Evolution strategy ES( \(\mu +\lambda \) )

This is an extension of the ES(1 + 1). The ES( \(\mu +\lambda \) ) has a self-adaptive mutation range, which replaces the 1/5 success rule implemented in ES(1 + 1). In the ES( \(\mu +\lambda \) ), each individual in the population contains additional chromosome \(\sigma \) , consisting of values of standard deviation for each gene. These values are used during mutation procedure. The crossover operator operates before the mutation. Both chromosomes (consisting of the value of variables, and of the value of \(\sigma \) parameters) undergo mutation and crossover processes [ 7 ]. Algorithm 3 presents the pseudo-code of the ES( \(\mu +\lambda \) ).

2.4.3 ES( \(\mu ,\lambda \) ) evolution strategy

This type of the ES is used more often than ES( \(\mu +\lambda \) ). The operation of both algorithms is almost identical. The only one difference is that in the ES( \(\mu ,\lambda \) ), the new population P ( t ) is created using only the best individuals from the “children” population M ( t ). In this case, \(\mu \) has to be greater than \(\lambda \) . Such selection gives the advantage of ES( \(\mu ,\lambda \) ) over the ES( \(\mu +\lambda \) ); in the latter, the population can be dominated by one individual which is much better than others and the values of standard deviations \(\sigma \) are not well tuned. The ES( \(\mu ,\lambda \) ) does not have this disadvantage because the individuals from the parental population \(P(t-1)\) are not copied to the new generation P ( t ) [ 7 ].

The pseudo-code of the ES( \(\mu ,\lambda \) ) is almost the same as Algorithm 3. The only one difference is line 10; here, it is: “10: select \(\mu \) the best individuals to population P ( t ) from the population M ( t ).”

Today, the covariance matrix adaptation evolution strategy (CMA-ES) is perceived as a state-of-the-art ES [ 54 , 55 ]. Several variants of CMA-ES were developed [ 55 ] to enhance the efficiency or robustness of the method by different techniques. In the CMA-ES algorithm, the adaptation of the population size or other parameters was presented in papers [ 56 ]. The CMA-ES algorithm employs global weighted recombination for both, strategy and object variables, adapts the full covariance matrix for mutation and, in general, is based on the scheme of the ES( \(\mu ,\lambda \) ). The CMA-ES algorithm can handle poorly scaled functions, and its performance remains invariant under rotation of the search space [ 54 ]. Some modifications of ESs are mentioned in Table  2 .

2.5 Evolutionary programming

Evolutionary programming (EP) was developed as a tool for discovering the grammar of the unknown language. However, EP became more popular when it was proposed as the numerical optimization technique. The EP is similar to the ES( \(\mu +\lambda \) ), but with one essential difference [ 7 ]. In EP, the new population of individuals is created by mutating every individual from the parental population, while in the ES( \(\mu +\lambda \) ), every individual has the same probability to be selected to the temporary population on which the genetic operations are performed. In the EP, the mutation is based on the random perturbation of the values of the particular genes of the mutated individual. The newly created and the parental populations are the same sizes ( \(\mu =\lambda \) ). Finally, the new generation of the population is created using the ranking selection of the individuals from both, the parental and the mutated populations. The pseudo-code of the standard EP method is presented in Algorithm 4. EP, like other evolutionary methods, has many modifications. Some of them are listed in Table  2 .

2.6 Evolutionary algorithms: problems and challenges

EAs are a very interesting research area. There are many open research problems such as: control of the balance between the exploration and exploitation properties; the self-adaptive (or adaptive) control of steering parameters; reducing the number of CMA-ES algorithm parameters; introducing new selection schemes; and increasing their effectiveness. The latter is important especially in the area of evolutionary design and in evolvable hardware. Also, new more efficient techniques for constraint handling are needed.

Additionally, more investigation into the application of EAs to dynamic optimization problems, to the optimization in noisy and non-stationary environments, and to multi-objective optimization problems (especially with a large number of decision variables) is required. Also, further research is needed in the population size adaptation in different optimization scenarios. Novel strategies should be developed to deal with expensive problems more competitively. Among these matters, there is the open question of constraint handling in EAs specifically to solve engineering optimization problems. As we know, the constraint handling methods can be classified into six main categories: penalty methods, methods evolving in the feasible region, methods using parallel population approaches, methods based on the assumption of superiority of feasible individuals, methods using multi-objective optimization techniques, and hybrid methods. Of course, each of these categories can be divided into several subcategories. The taxonomy of the constraint handling techniques with EAs can be found in the paper [ 77 ] by Petrowski et al. If we want to use the proper constraint handling method in EAs for real-world application, we should find the answer to the several questions such as is the objective function defined in the unfeasible domain (if not, the penalization methods cannot be used, for example): are there any active constraints at the optimum? (if not, the methods based on the search on the feasible region boundaries are irrelevant); what is the nature of the constraints? (if only one of the constraints is a nonlinear inequality, the methods for linear constraints are excluded). Moreover, in the real-world application of EAs with constraint handling techniques the effectiveness of a method is often dominated by two other decision criteria such as complexity and difficulty of implementation. Currently, penalty methods, feasibility rules, and stochastic ranking methods are used in real-world applications very often due to their simplicity [ 77 ]. Therefore, as we can see, there is no general approach for handling the constraints with EAs able to deal with any real-world problem, so the research on constraint handling techniques in EAs for real-world application is still a hot topic.

In EAs, there are many open research problems, which are discussed in more detail in [ 53 , 78 ].

Despite these weaknesses, we observe the growing popularity of EAs (please see Figs.  2 , 3 ). If we analyze the number of publications in the Web of Science (WoS) database (years 2000–2018) for particular EAs, we can see that their number is growing from year to year for the algorithms: GA, GP, DE, and ES. Only for EP algorithm, the number of published articles has been decreasing since the 2013 year. The total number of papers published in WoS database (years 2000–2018) which are related to these algorithms was equal to 98,596 for GA, 7038 for GP, 13,308 for DE, 1804 for ES, and 1585 for EP. Also, we have study the popularity of some EA methods in the selected scientific databases such as Google Scholar, Springer, IEEE Xplore, ACM, Scientific, Science Direct, Sage, Taylor, and Web of Science. The total number of the papers was equal to 1,304,205 for GA, 186,791 for GP, 119,668 for DE, 53,254 for ES, and 73,716 for EP.

Number of publications in the WoS database (years 2000–2018): GA ( a ), GP ( b ), DE ( c )

Number of publications in the WoS database (years 2000–2018): ES ( a ), EP ( b ), sum of publications for all listed algorithms GA, GP, DE, ES, EP ( c )

Also, many practical applications of EAs methods have been patented by such corporations like Caterpillar Inc., Yamaha Motor Co. Ltd., Fujitsu Limited, International Business Machines Corporation, Lsi Logic Corporation, Honda Research Institute Europe Gmbh, Prometheus Laboratories Inc., Siemens. The total number of patents registered in the Google Patents database (in years 2000–2018) for the particular EA methods was equal to 43,284 for GA, 2960 for GP, 2039 for DE, 1191 for ES, and 1583 for EP. More detailed information is presented in Table 3 .

We believe that over the next few years researchers will focus on the above areas.

3 Evolutionary algorithms in real-life problems

Similar to swarm intelligence algorithms [ 6 ], a major reason is a growing demand for smart optimization methods in many business and engineering activities. EAs are suitable mainly for optimization, scheduling, planning, design, and management problems. These kinds of problems are everywhere, in investments, production, distribution, and so forth. If we analyze, the results obtained from the WoS database (popularity of only ten first WoS categories for each method—for more detailed information see Table 4 ), we can see that the EAs methods are mainly used in the area such as:

Engineering electrical electronics,

Computer science artificial intelligence,

Computer science theory methods,

Computer science interdisciplinary applications,

Automation control system,

Computer science information systems,

Operations research management science.

When in WoS we will select a field Highly Cited in Field , we can see that the highly cited papers (in which EA methods are used) are from the following industry areas for the particular EA methods:

GA—energy fuels (EF), engineering electrical electronic (EEE), operations research management science (ORMS), engineering civil (EC),

GP—engineering civil (EC), water resources (WR), energy fuels (EF), automation control systems (ACS),

DE—energy fuels (EF), automation control systems (ACS), engineering electrical electronics (EEE), engineering civil (EC),

ES—construction building technology (CBT), energy fuels (EF), engineering civil (EC), engineering electrical electronic (EEE),

EP—construction building technology (CBT), engineering civil (EC), computer science software engineering (CSSE), transportation science technology (TST).

Therefore, in this paper, we will concentrate only on the real-world applications of particular EA methods in above areas of industry. In the next subsections, the abbreviation of industry area will be given in parenthesis after reference number to currently discussed paper.

3.1 Genetic algorithms in real-life problems

The GAs are a universal optimization tool. Using GAs, we can solve constrained optimization problems, multimodal optimization problems, continuous optimization problems, combinatorial optimization problems, and multi-objective optimization problems. Thus, there is a wide range of real-world applications of GAs. In this short section, we show only a few of them.

The paper [ 79 ] (EF) by Lv et al. presents the solar array layout optimization problem which is solved by GA. The presented numerical method is based on rotating model of a stratospheric airship to optimize the solar array layout. The results demonstrate that the proposed method is helpful in the preparation stage for installing large area flexible solar arrays. Also, it is shown that due to solar array optimization the output power of solar panel is significantly improved.

In paper [ 80 ] (EF) by Ma et al., the optimization model based on the GA, developed to reduce the energy consumption of high-sulfur natural gas purification process, is presented. A case study was performed in a high-sulfur natural gas purification plant with the capacity of \(300\cdot {}10^{4}\,\mathrm{N}\,\mathrm{m}^{3}/\mathrm{d}\) . The results demonstrate that the energy consumption of the purification plant was reduced by 12.7%.

In [ 81 ] (EEE), Yin et al. report a GA-inspired strategy designed and incorporated in the sequential evolutionary filter. Due to this strategy, the resampling used in most of existing particle filters is not necessary, and the particle diversity can be maintained. The experimental results show that the proposed sequential evolutionary filter offers better state estimation results than three other comparative filters.

The authors of [ 82 ] (EEE) investigate the pros and cons of hybridization of a GA and local search on the basis of a hard practical and up-to-date problem, namely the routing and spectrum allocation of multi-cast flows (RSA/M) in elastic optical networks (EONs). They proposed an efficient optimization method for solving the RSA/M problem in EONs. The proposed method outperformed all other competing methods. Additionally, introduction of Baldwin effects helped to preserve the population diversity in GA.

In the paper [ 83 ] (ORMS), the local-inventory-routing model for perishable products is presented. The proposed model integrates the three levels of a decision in the supply chain such as the number and location of required warehouses, the inventory level at each retailer, and the routes traveled by each vehicle. It is shown that the model developed in this paper is NP-hard; therefore, the authors develop a GA-based approach to solve this problem efficiently. It is shown that presented approach achieves a high-quality near-optimal solution in reasonable time.

The paper [ 84 ] (ORMS) by Ramos et al. presents new container loading algorithm with load balance, weight limit, and stability constraints which use a load distribution diagrams. This algorithm is based on multi-population biased random-key GA, with a new fitness function that takes static and loads balance into account. Due to incorporate weight balance goal with stability guaranteed by full base support and by the mechanical equilibrium conditions, the proposed approach is very effective.

In [ 85 ] (EC) by Yan et al., a framework to determine the investment plan to strengthen a railway system to earthquake hazard is proposed. This framework consists of four parts. In the third part, an investment optimization model is formulated, and in part four, this model is solved using GA. The proposed approach has been applied to the real Chinese railway system. The obtained results show that the presented framework is more responsive to the earthquake impact on railway system compared to topology-based methods.

In the paper [ 86 ] (EC) by Ascione et al., the multi-objective optimization of operating cost for space conditioning and thermal comfort to achieve a high level of building energy performance is presented. The main objective of proposed GA is to optimize the hourly set point temperatures with a day-ahead horizon, based on a forecast of weather conditions and occupancy profile. In comparison with the standard control strategy, the presented approach generates a reduction of operating cost up to 56%.

In [ 87 ] (EC) by Lin et al., a time-optimal train running reference curve is designed with least time-consuming, but highest energy consumption, and it is optimized by adding multi-point coasting control to realize energy saving with a relative rise in time. Multi-population GA is adopted to solve this multi-point combinatorial optimization problem. Simulation results, based on real line condition and train parameters of Shanghai line 7, demonstrate the advancement of multi-point coasting control with the proposed approach.

In [ 88 ] (EC), the application of GA to minimization of average delay for an urban signalized intersection under the oversaturated condition is presented. Relieving urban traffic congestion is an urgent call for traffic engineering. One of the key solutions to reduce congestion is the effectiveness of traffic signalization. The current traffic signal control system is not fully optimized for handling the oversaturated condition. Simulation results show that GA is able to control the traffic signals for minimizing the average delay to 55 s/vehicle.

Zhang et al. [ 89 ] (EEE) use the flexible GA for node placement problems. Node placement problems are encountered in various engineering fields, e.g., the deployment of radio-frequency identification systems or wireless sensor networks. The flexible GA with variable length encoding, subarea-swap crossover, and Gaussian mutation is able to adjust the number of nodes and their corresponding properties automatically. Experimental results show that the flexible GA offers higher performance than existing tools for solving node placement problems.

In the paper [ 90 ] (EF) by Reddy, the scheduling problem considering the hybrid generation system is presented. The new strategy based on GA for the optimal scheduling problem taking into account the impact of uncertainties in the wind, solar photovoltaic modules with batteries, and load demand forecast is proposed. From simulation results (for IEEE 30 and 300 bus test systems), it can be noticed that with a marginal increase in the cost of day-ahead generation schedule, a significant reduction in real-time mean adjustment cost is obtained.

3.2 Genetic programming in real-life problems

The GP possesses many practical applications.

In [ 91 ] (ACS) et al. the handwriting character recognition system for inertial-sensor-equipped pens is presented. In this system, the characteristic function is calculated for each character using a GP algorithm. The experimental results show that the performance of the proposed method is superior to that one of the state-of-the-art works in the area of recognizing Persian/Arabic handwriting characters.

Bagatur and Onen [ 92 ] (WR) propose novel models for the prediction of flood routing in natural channels using the gene expression programming (GEP) algorithm, which is one of the extensions of GP algorithm. The GEP method makes use of few hydrologic parameters such as inflow, outflow, and time. The performance of the proposed models is evaluated by two goodness-of-fit measures. The proposed GEP models are tested for the three datasets taken from the literature. It is proved that the GEP models show superior performance to the other solution techniques based on the Muskingum model.

In the paper [ 93 ] (EF) by Abkenar et al., an intelligent fuel cell (FC) power management strategy is proposed. The main objective of the proposed approach is to improve FC performance at different operating points without employing DC/DC interfacing converters. A hybrid all-electric ships (AES) driveline model using GP is utilized to formulate operating FC voltage based on the load current, FC air, and fuel flow rates. The proposed approach maintains FC performance and reduces fuel consumption, and therefore ensures the optimal power sharing between the FC and the lithium-ion battery in AES application.

The authors of [ 94 ] (EC) use GP algorithm to develop models to predict the deterioration of pavement distress of the urban road network. Five models for the prediction of pavement distress progression such as cracking, raveling, pothole, rutting, and roughness are created. In order to obtain a training dataset, and validation dataset, the real data from the roads of Patiala City, Punjab, India, have been collected. It was shown that GP models predict with high accuracy for pavement distress and help the decision makers for adequate and timely fund allocations for the preservation of the urban road network.

3.3 Differential evolution in real-life problems

The DE algorithm also found many real-world applications.

In [ 95 ] (EF), Ramli et al. present an application of multi-objective SaDE algorithm for optimal sizing of a photovoltaic (PV)/wind/diesel hybrid microgrid system (HMS) with battery storage. The multi-objective optimization is used to analyze the loss of power supply probability, the cost of electricity, and the renewable factor in relation to HMS cost and reliability. The proposed approach is tested using three case studies involving differing house numbers for the city Yanbu, Saudi Arabia. The results obtained are useful in investigating optimal scheduling of HMS components and can be used as a power reference for the economic operation of PV and wind turbine generators.

Yao et al. [ 96 ] (EF) use a multi-objective DE algorithm for optimizing a novel combined cooling, heating, and power-based compressed air energy storage system. The system combines a gas engine, ammonia–water absorption refrigeration system, and supplemental heat exchangers. The proposed optimization technique is used to find a trade-off between the overall exergy efficiency and the total specific cost of final product. The best trade-off solution which was selected possesses a total product unit cost of 20.54 cent/kWh and an overall exergy efficiency of 53.04%.

In the paper [ 97 ] (ACS) by Wang et al., the DE algorithm is applied for wind farm layout optimization with the aim of maximizing the power output. Due to a new encoding mechanism in DE, the dimension of the search space is reduced to two, and a crucial parameter (i.e., the population size) is eliminated. In comparison with seven other methods, the proposed approach is able to obtain the best overall performance, in terms of the power output and execution time.

The authors of [ 98 ] (EEE) investigate the problem of linear dipole array synthesis. Dynamic DE algorithm is proposed for synthesizing shaped power pattern by using element rotation and phase optimization for a linear dipole array. Based on two experiments for synthesizing flattop and cosecant squared pattern, the effectiveness and advantages of the proposed approach were verified in comparison with the phase-only optimization and the amplitude-phase joint optimization.

Tian et al. [ 99 ] (EC) use a multi-objective hybrid DE+PSO algorithm in order to create a set of Pareto solutions for the problem of dual-objective scheduling of rescue vehicles to distinguish forest fires. The novel multi-objective scheduling model to handle forest fires subject to limited rescue vehicles constraints, in which a fire spread model is introduced into this problem to better describe practical forestry fire is presented. Results show that the proposed approach is able to quickly produce satisfactory Pareto solutions in comparison with GA and PSO algorithms.

3.4 Evolution strategies in real-life problems

Studying the literature, we can find fewer papers with the real-life applications of ESs than those with GAs. Below we shortly present some of them.

The paper [ 100 ] (CBT) by Hasancebi presents ES integrated parallel optimization algorithm to minimize the total member weight in each test steel frame. Steel frames with various beam–column connection and bracing configuration are considered for comparative cost analyzes. Three multi-story buildings are chosen (10, 20, and 30-story buildings) as examples for numerical verification of proposed method. The results collected are utilized to reach certain recommendations regarding the selection of economically feasible frames for the design of multi-story steel buildings.

In [ 101 ] (EF), Fadda et al. consider the usage of electric batteries in order to mitigate it. In energy distribution systems, uncertainty is the single major cause of power outages; therefore, the authors propose intelligent battery able to maximize its lifetime while guaranteeing to satisfy all the electric demand peaks. The battery exploits a customized steady-state ES to dynamically adapt its recharge strategy to changing environments. Experimental results on both synthetic and real data demonstrate the efficacy of the proposed approach.

In the paper [ 102 ] (EC) by Ogidan et al., the enhanced non-dominated sorting ES algorithm that uses a specialized operator to guide the algorithm toward known sanitary sewer overflows (SSOs) locations is presented. The main objectives of the proposed method are the maximization of SSO reduction and minimization of rehabilitation cost. The proposed method was tested in an existing network in the eastern San Antonio Water System network. The presented approach improves the convergence rate by approximately 70% over the tested alternative algorithms.

The authors of [ 103 ] (EEE) investigate the problem of wireless sensor fault diagnosis based on fusion data analysis. The fault diagnosis model is proposed based on the hierarchical belief rule-based model, and the CMA-ES algorithm is used to optimize the initial parameters of the proposed model. In order to validation of presented approach, a case study based on Intel laboratory dataset of sensors is designed. The experiments prove the effectiveness of the proposed method in comparison with back propagation neural network model and the fuzzy expert system.

In the paper [ 104 ] (EEE), the problem of subsurface inverse profiling of a 2-D inhomogeneous buried dielectric target is presented and solved using proposed iterative optimization method which is based on CMA-ES algorithm. In relation to the results obtained using EP and PSO, the results obtained using CMA-ES significantly outperform the other two optimization techniques in the inhomogeneous imagining.

The paper [ 105 ] (EEE) by Emadi et al. presents CMA-ES algorithm for tasks scheduling in the cloud computing environment. The need for planning the scheduling of the user’s jobs is an important challenge in the field of cloud computing. The causes are manifold; the most important are: ever-increasing advancements of information technology, an increase in applications and user needs for these applications with high quality, also the popularity of cloud computing among user, and rapid growth of them during recent years. The results obtained indicate that presented algorithm, led to a reduction in execution time of all tasks, compared to the shortest processing time algorithm, longest processing time algorithm, and GA and PSO algorithms.

3.5 Evolutionary programming in real-life problems

In the literature, we can find the applications of EP in many different areas. However, in WoS the number of papers in which EP algorithm is used is decreasing since the 2013 year. Below we shortly present some of them.

The paper [ 106 ] (TST) by Yan et al. presents bi-subgroup self-adaptive EP algorithm for seeking the Pareto optimal solution of the multi-objective function of the hybrid electric vehicle (HEV) and the best degree of hybrid (DOH) for this vehicle. In the proposed algorithm, the evolution of Cauchy operator and Gauss operator are parallel performed with different mutation strategies. Moreover, the Gauss operator owns the ability of self-adaptation according to the variation of adaptability function. The simulation results show that the optimal DOH is equal to 0.311 for given HEV. Also, the validity of simulating method was proved, and the fuel saving effect was consistent with authors’ expectations.

In the paper [ 107 ] (CBT) by Gao, a new evolutionary neural network whose architecture and connection weights simultaneously evolve is proposed. This neural network is based on immunized EP algorithm and is used in the novel inverse back analysis for underground engineering. As a numerical example, an underground roadway of the Huainan coal mine in China is chosen for the verification of the accuracy of the presented inverse back analysis. The results obtained show that using the proposed method, the computed displacements agree with the measured ones. Therefore, it is demonstrated that the new inverse back analysis method is a high-performance method for usage in underground engineering.

Jiang et al. [ 108 ] (EC) use EP algorithm to find weights and the threshold value in the neural network which is applied to the traffic signal light control. According to the historical traffic flow data of a crossroad, the next node’s traffic flow data are predicted. Due to predicted data, the traffic signal light frequency can be re-adjusted in order to improve traffic congestion and other traffic problems. The results obtained show that the connection of EP algorithm with the neural network has a good effect on traffic signal light optimization.

The authors of [ 109 ] (CSSE) propose a novel approach to navigate over 3-D terrain using best viewpoints. The concept of viewpoint entropy is exploited for best view determination, and greedy n -best view selection is used for visibility calculation. In order to connect the calculated viewpoints, the authors use an EP algorithm for the traveling salesman problem. It was shown that the computed and planned viewpoints reduce human effort when used as starting points for scene tour. The proposed method was tested on real terrain and road network datasets.

3.6 Which EA should be used for a given problem?

What lesson for a potential user of evolutionary computation emerges from the above overview? The question is simple, but the answer is hard. All discussed methods are from the same family—evolutionary approaches to optimization problems. The principal question could be: Which of the discussed methods is suitable for the given problem? Expanding the answer to all heuristic methods in general, not just evolutionary algorithms, the best answer seems to be: take the method you know best, you can define your problem well in terms required by this method, you understand the sensitivity of this method to parameters, you can fine-tune this method. Let us see, for example, on energy fuels area. Numerous evolutionary approaches are applied within this scope. It is not possible to indicate one of them as the best for this particular subject. The similar situation is with other areas of industry.

As we can see, the literature on the evolutionary algorithms in general and in their industrial applications is plentiful, but very rarely this literature concerns applications that have been used in practice. Following [ 110 ], we can say that the theory does not support the practice; there is a big gap between theory and practice. Theoretical results on properties such as convergence, diversity, exploration, exploitation, deceptiveness, and epistasis are not useful enough for practice. Significant topics from the practice point of view are constraint and noise handling methods, robustness, or multi-objective optimization. The progress in the above matters is also observed; however, these methods are tested mainly on simple silo problems or standard sets of numerical functions, so their usefulness to practitioners working on EA-based software applications is very limited.

It is worth mentioning that the real usefulness of EAs could be not only in industry. The spectacular achievement of EA is presented in [ 111 ]. The artificial intelligence system, with the use of EA, the first time discovered a new theory, namely a mechanism of planar regeneration. The remarkable ability of these small worms to regenerate body parts made them a research model in human regenerative medicine.

4 Summary and future trends

As it is shown in this paper, the evolutionary algorithms are a popular research domain. Each year many new modifications of these algorithms are proposed. Some of these modifications are shortly described in Tables  1 and 2 . The EAs are applied to solve many industry problems. When we cannot use a dedicated algorithm for a given problem, one of the EAs will be a good choice. Of course, we must remember about specific issues the user can face when dealing with EAs. Here, we can mention two main problems. First of this problem is a premature convergence (the population converging to a suboptimal solution instead of an optimal one). We can solve this problem by introducing the mechanism which will provide a lower transfer rate of the genetic material between individuals—the whole population is divided into several subpopulations (so-called islands) and periodically migrate an individual between islands [ 15 ]. Another solution of the premature convergence problem is a cooperation of EAs with branch and bound algorithm endowed with interval propagation techniques, as it was shown in [ 112 ]. The second problem is related to the optimal trade-off between exploration and exploitation properties of EA. One of the solutions to this problem is control of the level of selection pressure [ 113 ]. We can do this by introducing specialized genetic operators which will guarantee high population diversity at the start of the algorithm operation (high exploration property–small exploitation property) and a low population diversity at the end of the algorithm operation (low exploration property–high exploitation property). A survey about exploration and exploitation in EAs can be found in [ 114 ].

As future trends in EAs, we can mention some main directions. The first of current trend is a hybridization of two or more algorithms to obtain better results. Currently, in the literature, we can find an increasing number of papers where hybrid algorithms are presented. Also, many researchers work on modifications of EAs to improve their computational performance. In many recently published papers, we can find modifications of GA [ 22 , 23 , 115 , 116 ], GP [ 31 , 32 , 117 , 118 ], DE [ 48 , 49 , 119 , 120 ], ES [ 64 , 65 ], and EP [ 74 , 75 ]. An interesting domain of future research in EAs is also memetic algorithms. The term memetic algorithm is widely used as a synergy of the evolutionary algorithm or any other population-based approach with separate local search techniques as the Nelder–Mead method. We can find very interesting information about future trends in EAs in the paper [ 121 ] written by Eiben et al. As one of the future trends in EAs, the authors point out the increasing interest in applying EAs to embodied or embedded systems, that is, employing evolution in populations for which the candidate solutions are controllers or drivers that implement the operational strategy for some situated entities, and are evaluated within the context of some rich, dynamic environment: not for what they are, but for what they do. Finally, there is another one important issue especially in the industrial application of EA methods. Very often in real-world problems, we must optimize a function in a high-dimensional domain. This process usually is very complex and takes a lot of computational time. Therefore, in real applications, the EAs designed for this type of problems should be designed to be implemented easily to run in parallel (or easy to run in GPU) to reduce their computational time. A greater effort in this feature should be in future proposals because this could be a crucial feature to decide whether an algorithm is useful in real applications. Some research in the area of EAs can be connected with the so-called surrogate models (computationally cheaper models of real-world problems) which can be used in the place of full fitness evaluation, and that refine those models through occasional full evaluations of individuals in the population [ 121 ]. Also, very often industry problems have many objectives. In tandem with algorithmic advances, the interactive evolutionary algorithms are used to increase the efficiency of EAs in multi-objective optimization [ 121 ]. As we know, each engineering problem is defined by the different objective function and has a different landscape of search space. The values of EAs parameters which are “good” in one problem cannot be sufficient in another one. Therefore, searching for new techniques in such area as automated tuning and adaptive parameter control is still a hot topic in EAs. Another important issue in the industrial application of EA methods is a proper definition of an objective function. The industrial problems are very complex. Therefore, a definition of a good mathematical model (good objective function for EAs) for a given industry process is also a very demanding task. The “quality” of the chosen objective function will have a great influence on the results obtained using EA methods. The next issue which we want to mention in discussing is repeatability of the EA methods. As we know, the EAs are stochastic techniques. Each time the EA method is run, a different result can be obtained. Therefore, the main focus should be on ensuring repeatability of the results generated by EA techniques. This issue is very important for application on EA methods in industry.

In summary, we believe that in the future, new evolutionary algorithms will be developed, and the research problems connected with evolutionary algorithms will always be a hot topic for researchers.

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Department of Electronics and Computer Science, Koszalin University of Technology, Sniadeckich 2 Street, 75-453, Koszalin, Poland

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Slowik, A., Kwasnicka, H. Evolutionary algorithms and their applications to engineering problems. Neural Comput & Applic 32 , 12363–12379 (2020). https://doi.org/10.1007/s00521-020-04832-8

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DOI : https://doi.org/10.1007/s00521-020-04832-8

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Genetic Algorithm: Review and Application

4 Pages Posted: 3 Mar 2020

Manoj Kumar

Dr. mohammad husain.

Azad Institute of Engineering and Technology; Islamic University of Madinah, KSA

Naveen Upreti

International Institute for Special Education

Deepti Gupta

Date Written: December 1, 2010

Genetic algorithms are considered as a search process used in computing to find exact or a approximate solution for optimization and search problems. There are also termed as global search heuristics. These techniques are inspired by evolutionary biology such as inheritance mutation, selection and cross over. These algorithms provide a technique for program to automatically improve their parameters. This paper is an introduction of genetic algorithm approach including various applications and described the integration of genetic algorithm with object oriented programming approaches.

Keywords: Genetic Algorithm, Chromosome, Evolutionary Algorithm, Selection, Mutation

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Islamic University of Madinah, KSA ( email )

Prince Naif Ibn Abdulaziz Road Al Jamiah Medina Saudi Arabia

International Institute for Special Education ( email )

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Computer Science > Neural and Evolutionary Computing

Title: genetic algorithm enhanced by deep reinforcement learning in parent selection mechanism and mutation : minimizing makespan in permutation flow shop scheduling problems.

Abstract: This paper introduces a reinforcement learning (RL) approach to address the challenges associated with configuring and optimizing genetic algorithms (GAs) for solving difficult combinatorial or non-linear problems. The proposed RL+GA method was specifically tested on the flow shop scheduling problem (FSP). The hybrid algorithm incorporates neural networks (NN) and uses the off-policy method Q-learning or the on-policy method Sarsa(0) to control two key genetic algorithm (GA) operators: parent selection mechanism and mutation. At each generation, the RL agent's action is determining the selection method, the probability of the parent selection and the probability of the offspring mutation. This allows the RL agent to dynamically adjust the selection and mutation based on its learned policy. The results of the study highlight the effectiveness of the RL+GA approach in improving the performance of the primitive GA. They also demonstrate its ability to learn and adapt from population diversity and solution improvements over time. This adaptability leads to improved scheduling solutions compared to static parameter configurations while maintaining population diversity throughout the evolutionary process.

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A review on genetic algorithm: past, present, and future

Affiliation.

• 1 Computer Science and Engineering Department, National Institute of Technology, Hamirpur, India.
• PMID: 33162782
• PMCID: PMC7599983
• DOI: 10.1007/s11042-020-10139-6

In this paper, the analysis of recent advances in genetic algorithms is discussed. The genetic algorithms of great interest in research community are selected for analysis. This review will help the new and demanding researchers to provide the wider vision of genetic algorithms. The well-known algorithms and their implementation are presented with their pros and cons. The genetic operators and their usages are discussed with the aim of facilitating new researchers. The different research domains involved in genetic algorithms are covered. The future research directions in the area of genetic operators, fitness function and hybrid algorithms are discussed. This structured review will be helpful for research and graduate teaching.

Keywords: Crossover; Evolution; Genetic algorithm; Metaheuristic; Mutation; Optimization; Selection.

© Springer Science+Business Media, LLC, part of Springer Nature 2020.

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Classification of metaheuristic Algorithms

Operators used in GA

Swapping genetic information after a…

Swapping genetic information after a crossover point

Swapping genetic information between crossover…

Swapping genetic information between crossover points

Swapping individual genes

Partially matched crossover (PMX) [117]

Cycle Crossover (CX) [140]

Local and global optima [149]

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• v.30(6); 2015 Nov

The Applications of Genetic Algorithms in Medicine

Ali ghaheri.

1 Department of Management and Economy, Science and Research Branch, Azad University, Tehran, Iran

Saeed Shoar

2 Department of Surgery, Shariati Hospital, Tehran University of Medical Sciences, Tehran, Iran

Mohammad Naderan

3 School of Medicine Tehran University of Medical Sciences, Tehran, Iran

Sayed Shahabuddin Hoseini

4 Hannover Medical School, Germany

A great wealth of information is hidden amid medical research data that in some cases cannot be easily analyzed, if at all, using classical statistical methods. Inspired by nature, metaheuristic algorithms have been developed to offer optimal or near-optimal solutions to complex data analysis and decision-making tasks in a reasonable time. Due to their powerful features, metaheuristic algorithms have frequently been used in other fields of sciences. In medicine, however, the use of these algorithms are not known by physicians who may well benefit by applying them to solve complex medical problems. Therefore, in this paper, we introduce the genetic algorithm and its applications in medicine. The use of the genetic algorithm has promising implications in various medical specialties including radiology, radiotherapy, oncology, pediatrics, cardiology, endocrinology, surgery, obstetrics and gynecology, pulmonology, infectious diseases, orthopedics, rehabilitation medicine, neurology, pharmacotherapy, and health care management. This review introduces the applications of the genetic algorithm in disease screening, diagnosis, treatment planning, pharmacovigilance, prognosis, and health care management, and enables physicians to envision possible applications of this metaheuristic method in their medical career.]

Introduction

There is no doubt that computers have revolutionized our everyday life. They are vastly used and have benefited nearly all fields of science from aerospace and astronomy to biology, chemistry, physics, mathematics, geography, archeology, engineering, and social sciences.

In medicine, electronic chips and computers are the backbones of a lot of imaging, diagnostic, monitoring, and therapeutic devices. These devices, which are composed of several different hardware components, are managed and controlled by software, which in turn are based on algorithms. An algorithm is a set of well-described rules and instructions that define a sequence of operations. Metaheuristic methods are algorithms that can more quickly solve complex problems, or they can find an approximate solution when classical methods are not able to find an exact one. 1

Several metaheuristic algorithms for finding an optimal or near-optimal solution exist. These include the ant colony (inspired by ants behavior), 2 artificial bee colony (based on bees behavior), 3 Grey Wolf Optimizer (inspired by grey wolves behavior), 4 artificial neural networks (derived from the neural systems), 5 simulated annealing, 6 river formation dynamics (based on the process of river formation), 7 artificial immune systems (based on immune system function), 8 and genetic algorithm (inspired by genetic mechanisms). 9 Metaheuristic approaches have been frequently used in other fields of science where complex problems need to be solved, or optimal decisions should be made. In medicine, although valuable work has been done, the power of these potent algorithms for offering solutions to the countless complex problems physicians encounter every day has not been fully exploited.

In this paper, we introduce the genetic algorithm (GA) as one of these metaheuristics and review some of its applications in medicine.

The genetic algorithm

A GA is a metaheuristic method, inspired by the laws of genetics, trying to find useful solutions to complex problems. In this method, first some random solutions (individuals) are generated each containing several properties (chromosomes). Based on the laws of genetics, cross-over and mutations occur in chromosomes to produce a second generation of individuals with more diverse properties.

Crossover and mutation are the two most central methods for diversifying individuals. In crossover, two chromosomes are chosen. Then a crossover point along each chromosome is chosen followed by the exchange of the values up to the crossover point between the two chromosomes [Figure 1]. These two newly-generated chromosomes produce new offspring. The process of crossover will be iterated over and over until the desired diversity of individuals (i.e. solutions) is made. The mutation also generates new configurations by applying random changes in different chromosomes. 10 One of the simplest mutation methods has been depicted in Figure 1.

Methods to induce diversity in the population of individuals (candidate solutions). (a) During crossover, one part of a chromosome is exchanged by another fragment of another chromosome. (b) During mutations, one or more datasets on a chromosome are converted to different ones. These alterations will generate new individuals whose fittest (more optimal solutions) will survive.

In a GA, the possibility of reproduction depends on the fitness of individuals. The better chromosomes they have (i.e., those with better characteristics), the more likely they are to be selected for breeding the next generation. There are several selection methods; however, the aim of all is to assign fitness values to individuals based on a fitness function and to select the fittest. Genetic alterations in chromosomes will happen via crossover and mutations to produce another generation. This iterative process will continue until the fittest individual (the optimal solution) is formed or the maximum number of generations is reached. 9 , 11

It is worth noting that GAs are different from the derivative-based, optimization algorithms. First of all, GAs search a population of points in the solution space in each iteration while classical derivative-based methods search only a single point. Moreover, GAs select the next population using probabilistic transition rules and random number generators while derivative-based algorithms use deterministic transition rules for selecting the next point in the sequence. 11 , 12

In the following, we introduce some of the applications of GAs in a variety of medical disciplines.

Imaging techniques in radiology generate a large amount of data that needs to be analyzed and interpreted by radiologists in a relatively short time. Computer-aided detection and diagnosis are rapidly growing interdisciplinary technologies that aim to assist radiologists in faster and more accurate image analysis by detection, segmentation, and classification of normal and pathological patterns found on various imaging modalities. These include X-rays, magnetic resonance imaging (MRI), compute tomography (CT) scan, and ultrasound. 13

In machine vision, an image of scenery (such as organs of the human body in radiology images) is acquired, processed, and interpreted. The boundaries (shape) and sizes of objects within the images need to be determined to assess the objects in more detail. Therefore, the process of edge detection becomes one of the integral parts of automatic image processing techniques. 14 Several researchers have used the GAs for edge detection of images acquired using different imaging modalities including MRI, CT, and ultrasound. 14 - 16

Screening mammography is the gold standard for detection of breast cancer; however, due to its failure rate, 17 , 18 researchers have tried to apply computational tools to improve the sensitivity of the system. In fact, the majority of the applications of GAs in radiology were performed on breast cancer screening primarily using mammography.

Karnan and Thangavel 19 applied the GA to detect microcalcifications in mammograms suggesting of breast cancer. In their method, after enhancement and normalization of the mammograms, the border of breast and the nipple position was detected by the GA. Using the border and the nipple position of the right and left breasts as a reference, the mammogram images were aligned and subtracted from each other to find the asymmetry image suggestive of breast cancer. The Az value, which is the area under the receiver operating characteristic (ROC) curve, has been used as a useful measure for assessing the diagnostic performance of a system. 20 The Az value for their proposed algorithm was about 0.9. 19

In another study, Pereira et al, 21 applied a set of computational tools for mammogram segmentation to improve the detection of breast cancer. An algorithm was first designed to eliminate artifacts followed by denoising and image enhancement. Consecutively, combining wavelet analysis and the GA allowed detection and segmentation of suspicious areas with 95% sensitivity. GAs have also been successfully used for classification and detection of clustered microcalcifications in digital mammograms. 22 - 24

In machine learning, feature selection is the process of selecting a subset of relevant features to construct a model by removing variables with little or no analytical value. Feature selection is important since choosing irrelevant features would increase the time, cost, and complexity of computation and reduce the accuracy of the model. 25 Besides, reducing the number of features would avoid the problem of over-fitting, reduce the chance of failure upon missing data, and allow for a better explanation and generalization of the model. 26

GAs have been applied for feature selection in studies aiming to identify a region of interest in mammograms as normal or containing a mass, 27 and to differentiate benign and malignant breast tumors in ultrasound images. 25

de Carvalho Filho et al, 28 developed a GA for automatic detection and classification of solitary lung nodules. The designed algorithm could detect lung nodules with about 86% sensitivity, 98% specificity, and 98% accuracy.

Image registration or fusion is the process of optimal aligning of two or more images into one coordinate system. Precise integration of images becomes crucial when valuable information is embedded within several images acquired under different conditions (viewpoint, sensor, or time). 29 GAs have successfully been used to align MRI and CT scan images in several studies. 30 , 31 In another study, positron emission tomography (PET) images were fused with MRI images by a GA to generate colored breast cancer images. 32

Precise tumor staging is an important part of designing a treatment plan. Accurate tumor size and volume determination using non-invasive imaging studies becomes essential for tumor staging. Zhou et al, 33 developed a system for extraction of tongue carcinoma from head and neck MRIs. A GA was applied for segmentation of images followed by an artificial neural network (ANN)-based symmetry-detection algorithm to reduce the number of false positive results. This approach was able to extract tongue carcinoma from an MRI with high accuracy and minimal user-dependency.

Screening tests offer a valuable opportunity for early cancer detection, which if followed by proper treatment could improve the survival rate of patients.

To develop a non-invasive technique for cervical cancer detection, Duraipandian et al, 34 acquired Raman spectra from the cervical area via colposcopy. The biomolecular information generated via the Raman spectroscopy was analyzed by a GA-partial least square-discriminant analysis system to differentiate between a normal and dysplastic cervix. Partial least square (PLS) is a statistical method aiming to find a linear regression model between a dependent variable and some predictor variables. 35 This system was able to differentiate dysplasia from a normal cervix with 72% sensitivity and 90% specificity. 34

The advent of DNA microarrays has paved the way for massive gene expression profiling that could revolutionize the field of molecular diagnostics and prognosis. However, generation of large sets of data poses statistical and analytical challenges necessitating the need to find key predictive genes. 36 Due to the inherent capability of GAs to search and find the optimal solution among large and complex possible solutions with multiple simultaneous interactions, they have been applied to analyze microarray data from several cancer cell lines. 36 Dolled-Filhart et al, 37 generated microarray data by staining breast cancer tissues with several antibodies specific for various markers to find a minimum set of biomarkers with maximum classification and prognostication values in breast cancer patients. The data analyzed using GAs showed that three markers with available antibodies could define a population of patients with more than a 95% five-year survival rate.

Tan et al, 38 conducted a study to investigate the relationship between soil trace elements and cervical cancer mortality in China. A combination of GA and PLS was used to choose five out of 25 trace elements. Then a least square support vector machine (LSSVM) model was developed. LSSVM is a method used in machine learning to infer a function from or find a pattern in training data. 39 The results showed that a combination of GA-PLS and LSSVM could predict the mortality of cervical cancer based on trace elements. 38

One of the important and informative factors influencing the choice of an appropriate therapeutic approach for cancer patients is determination of the disease prognosis. In a retrospective study on more than 200 patients, Bozcuk et al, 40 compared the performance of four different data mining methods to determine the outcome of cancer patients not being in terminal stages after hospitalization. In comparison to other methods, GA selected the least number of explanatory variables (lactate dehydrogenase and the reason for admission) to predict the outcome of patients.

GAs have been used in different fields of cardiovascular medicine. Atherosclerotic plaques are hallmarks of most myocardial infarctions and strokes. Determination of plaque mechanical properties such as elasticity would enable physicians to locate better and map vulnerable or unstable plaques. Khalil et al, 41 used a system involving GAs for parameter estimation necessary for accurate elasticity quantification to determine tissue elasticity. This system is superior to gradient-based methods used for parameter estimation of the inefficiency of gradient-based techniques for inhomogeneous solution spaces containing several local minima and requirement for substantial computational time limits their application. 41

The field of biomarker discovery and clinical proteomics is rapidly growing in medical diagnosis, prognosis, and disease follow-up. Advanced technologies such as mass spectrometry can generate readouts of thousands of proteins from patient samples; however, the cost and complexity of such techniques on the one hand and computational and statistical methods for analysis, on the other hand, necessitates the selection of a few, relevant markers for clinical assay development. Zhou et al, 42 employed an improved version of the GA supported by a recursive local floating enhancement technique to predict the risk of a major adverse cardiac event (MACE). This technique was able to select a panel of seven proteins including myeloperoxidase to predict the risk of MACE with 77% accuracy, which outperformed over several current methods.

Logistic regression models have been frequently used in diagnosing diseases. Due to its outstanding performance, a GA has been used to select the best variables for a logistic regression system aiming to model the presence of myocardial infarction in patients with chest pain. The GA-based method was superior in variable selection to other traditional methods. 26

One of the key elements in the automatic interpretation of the electrocardiogram (ECG) is the detection of QRS complexes that would allow assessment of heart rate variability and other relevant diagnostic parameters. Tu et al, 43 introduced a simple and effective GA to detect QRS complexes. Then, p-waves and f-waves, which happen in normal ECG and after atrial fibrillation, respectively, were successfully extracted from patient databases. Such algorithms could allow comprehensive research into ECG details.

Endocrinology

Hypoglycemia is the most common complication of insulin therapy in patients with type 1 diabetes mellitus (T1DM). Hypoglycemia can induce alterations in the patterns of electroencephalograms (EEGs). Nguyen et al, 44 combined ANNs, GAs, and Levenberg-Marquardt (LM) training techniques to detect hypoglycemia based on EEG signals. ANN was used to model the relationship between blood glucose and EEG signals. For training ANN, the global search ability of GA and the local search capability of LM were combined. Data from four EEG parameters derived from two EEG channels were used by the analyzing system to detect hypoglycemia with 75% sensitivity and 60% specificity. In another paper, a GA-based multiple regression with fuzzy inference system was developed to detect non-invasive episodes of nocturnal hypoglycemia in children with T1DM. Using heart rate and corrected QT interval, hypoglycemia was detected with a sensitivity of 75% and specificity of over 50%. 45

Obstetrics and gynecology

The differentiation between normal and prolonged delivery allows obstetricians to determine the optimal timing for interventions, if necessary, during childbirth. One of the parameters that can help to forecast the delivery time and segregate normal versus prolonged labor is the time to reach full cervical dilation. Hoh et al, 46 applied a three-parameter logistic model using GA or the Newtone-Raphson (NR) method to predict the time to reach full cervical dilation. The GA-based algorithm outperformed the NR method by more accurately predicting the time to full cervical dilation.

A Pap smear is a cytology test for detection of precancerous and cancerous cervical changes. In this method, 20 features of cells are assessed to describe them as normal or abnormal or, more specifically, categorize them into seven classes. Marinakis et al, 47 generated a hybrid model that took advantage of the feature-selection capability of GAs to reduce the complexity of features necessary for a nearest neighbor algorithm for classification of Pap smear results. The new method outperformed several other previously used approaches by accurately classifying the Pap smear results.

GAs have also been applied in prenatal diagnosis. One of the fetal features that can complicate delivery is fetal macrosomia. In an attempt to differentiate the large-for-gestational-age (LGA) from the appropriate-for-gestational-age (AGA) infants, amniotic fluid from the second trimester was evaluated by capillary electrophoresis. Bayesian statistics was applied for data analysis. A GA was used to select the suitable wavelets (variables) of the electropherogram to minimize the computation time required for the Bayesian computation. This system was able to differentiate LGA from AGA using only two wavelets, one of albumin and the other of a negatively-charged unknown small molecule with 100% sensitivity and 98% specificity. 48

The prediction of fetal weight before delivery can reduce the potential problems associated with low-birth-weight infants. Yu et al, 49 introduced fuzzy logic into the support vector regression (FSVR) to estimate the fetal weight. GAs were used to generate an evolutionary FSVR to select the optimal features for the FSVR system. This outperformed a back-propagation neural network by achieving the lowest mean absolute percent error (6.6%) and the highest correlation coefficient (0.902) between the estimated and the actual fetal birth weight.

Cardiotocography is a cheap and non-invasive technique to assess the fetal heart rate and uterine contractions to determine fetal well-being. Ocak 50 applied a GA to select the optimal features of cardiotocogram recordings for a support vector machine (SVM) classifier. The results showed that the new system classified fetal health status as normal or abnormal with 99.3% and 100% accuracy, which was superior to an ANN algorithm designed for the same purpose.

Autism is a neurodevelopmental disease that appears in early childhood and is characterized by impaired social functioning and verbal and non-verbal communications and repetitive behavior. To recognize autism based on the microarray gene expression data, Latkowski and Osowski 51 used GAs to select the most relevant genes associated with the disease. Frequently selected genes include RMI1, NRIP1, TOP1, ZFHX3, CEP350, NFYA, PSENEN, ANP32A, SEMA4C, and SP1. These genes provided an input for an ensemble of classifiers including SVM and random forest classifiers. The introduced system recognized autism with 96% sensitivity and 83% specificity. 51

Acute lymphoblastic leukemia (ALL) is the most common type of leukemia in children and has many subtypes. Analysis of gene expression data derived from tumor cells can help classifying cancers. Due to the enormous size of information generated from microarray gene expression profiling, Lin et al, 52 used a GA to select the most relevant genes needed for ALL classification. Silhouette statistics was applied as a discriminant function to differentiate between six ALL subtypes. The proposed technique reached a 100% classification accuracy and used fewer discriminating genes compared to other methods.

Aneuploidy is a condition where one or a few chromosomes in the nucleus of a cell are above or below the normal chromosomal number of a species. Conventional chromosomal studies on amniocentesis samples are performed for definite diagnosis of fetal aneuploidy yet the rather long required time for these techniques necessitates the development of faster diagnostic tests. To this end, the proteomic profile of the amniotic fluid specimens was identified via mass spectrometry and the generated data was assessed by a GA. The proposed method could detect aneuploidy with 100% sensitivity, 72%–96% specificity, 11%–50% positive predictive value and 100% negative predictive value. 53

ANNs are powerful mathematical algorithms capable of predicting the behavior of systems. Due to the predictive value of ANNs, a GA-based ANN (GANN) was developed to predict the outcomes after surgery for patients with non-small cell lung cancer (NSCLC). The GA was applied to help optimization not to fall into local minima. The GANN model could predict the outcome of NSCLC patients more accurately and significantly better than logistic regression. Besides, the inclusion of tumor size in calculations significantly improved prediction outcomes. 54

As populations age, the number of geriatric patients needing cardiac surgeries increases. Due to the high prevalence of comorbid conditions in elderly, proper prognostication of postoperative morbidity and mortality would be informative, precluding overestimation of risk and denial of surgery for patients deserving it, which could happen with some prediction models. Applying a GA, Lee et al, 55 showed that a short length of stay after cardiac surgery was correlated with younger age, no preoperative use of beta blockers, shorter cross-clamp time, and absence of congestive heart failure.

Pulmonology

In pulmonology, auscultation is the most common diagnostic method that can differentiate lung diseases and guide the diagnostic approach toward more specific techniques. To automate lung sound diagnosis, a hybrid GANN was designed. The GA was applied to optimize the ANN training parameters and reduce the computation time. The new system could classify the lung sounds into normal, wheeze, and crackle. 56

Assessment of the partial pressure of carbon dioxide in the arterial blood (PaCO 2 ) is important in the management of critically ill patients. To avoid difficulties associated with arterial blood sampling, non-invasive methods for predicting PaCO 2 such as assessment of exhaled carbon dioxide at end-expiration (PetCO 2 ) could be applied in normal individuals; however, their use in sicker persons might be biased and less helpful. Engoren et al, 57 designed a GA to predict the PaCO 2 using 11 variables from capnography of non-intubated patients in the emergency department. The proposed system could improve the precision and bias of PaCO 2 prediction.

Infectious diseases

Tuberculosis is a possible lethal infectious disease not only in developing countries but also in developed nations after the emergence of human immunodeficiency virus (HIV). To predict the diagnosis (tuberculosis vs. non-tuberculosis patients), 38 parameters composed of examination parameters and laboratory data were used to design an ANN trained by a GA. The classification accuracy of the system was about 95%, which was higher than the results obtained by other algorithms. 58

Highly active antiretroviral therapy (HAART), an integral part of the treatment modalities against HIV, is composed of a combination of several antiretroviral medications aiming to decrease the replication of the virus. Since long-term HAART treatment needs patient compliance and might be associated with some side effects, structured treatment interruption has been proposed to reduce not only side effects, but also the selection pressure on the virus that could lead to the emergence of resistant particles. Therefore, Castiglione et al, 59 devised a GA-based system to choose the best HAART treatment schedule to control HIV and help the immune system to reconstitute. A virtual model of the immune system was used to assess the effects of anti-HIV drugs on virtual patients. 59 , 60 The new structured interruption schedule could achieve therapeutic results and protection against an opportunistic infection comparable to a full-length treatment. 61

Radiotherapy

Intensity modulated radiotherapy (IMRT) was developed to transfer an accurate dose of radiation to a target such as the brain, prostate, or head and neck. Planning IMRT involves selection of 5–10 angles for wavelet projection and determining the radiation dose. The application of GA could improve the selection of gantry angles in a reasonable time frame. 62 Similar GA-based irradiation planning has been applied for patients with other types of cancer including pancreatic, 63 rhabdomyosarcoma, and brain tumors. 64 GAs have also been successfully used to optimize the design of stereotactic radiosurgery, and radiotherapy treatment plans. 65

Rehabilitation medicine

As the need for physical rehabilitation increases, novel treatment equipment and techniques have to be developed and tested. Refinement of these new methods needs changing various parameters and testing of the resultant techniques on individuals, which is time-consuming and costly. Development of musculoskeletal models enables computer simulation of movements to assess the effect of new modifications on the efficiency of training. Pei et al, 66 developed a robotic technique for physiotherapy of the lower limb. A GA was applied to generate custom-made treatment plans for each patient.

In another paper, a therapeutic robot was designed for lower limb exercise. The system that consisted of an ANN and a GA was capable of learning the actions of a physiotherapist for each patient and mimicked its behavior in the absence of a therapist. 67

Orthopedics

Biomedical engineering has offered great solutions to the field of orthopedic surgery. Total hip arthroplasty (THA) has improved the management of various disabling hip joint diseases. Yet, failure of the femoral stem of a THA can compromise the success of treatment. Ishida et al, 68 reported the use of a GA in designing an optimized geometry of the femoral stem component. GAs have also been exploited to select the best design of tibial locking screws to reduce the probability of screw breakage or loosening. 69 In another report, a combination of ANNs and GAs was applied to design spinal pedicle screws used for fixation of spinal fractures. The hybrid algorithm was able to design screws with a higher fatigue life and ideal pullout and bending characteristics. 70

Scoliosis is a three-dimensional deformity of spinal axis curves. The progression of the disease, which only happens in a small percentage of patients, is monitored by serial X-rays over time. Since frequent exposure to X-rays might increase the chance of cancer, it is desirable to assess the disease development using harmless methods. Jaremko et al, 71 developed a GA-based ANN algorithm to estimate the angle of spinal axis deformity from indices of trunk surface deformity. The hybrid system was able to determine the angle deformity within 5% accuracy in more than two third of patients.

Multiple sclerosis (MS) is a debilitating inflammatory disease of the neural system characterized by the formation of white matter scars otherwise known as plaques. Computer-assisted diagnosis has been applied for detection of pathologic features in these patients. In one study, a GA was developed to detect the MS lesions of brain MRIs. The similarity index of lesions determined by the GA and by a radiologist was 87%. 72

The EEG is a useful diagnostic method to detect the abnormal brain electrical discharges occurring during a seizure. To design an automated system for detection of abnormal EEG signals, several learning algorithms (LM, Quickprop, Delta-bar delta, and Momentum and Conjugate gradient) were used to train an ANN for EEG-based classification of epileptic versus healthy individuals. A GA was used to find the optimal parameters for and architecture of the ANN. The results demonstrated that the LM method combined with the GA was the best algorithm for training the ANN, which reached a general success of 96.5% in its performance. 73

Several reports have suggested that mitochondrial dysfunction plays an important role in Parkinson’s disease. Since mitochondrial genetics has its idiosyncrasies, a simple comparison of mitochondrial mutations between healthy and disease conditions might not be so informative. Therefore, Smigrodzki et al, 74 devised a GA to detect biologically important patterns of mitochondrial mutations in Parkinson’s patients. The proposed system was able to diagnose Parkinson’s disease with 100% accuracy based on mutational patterns in mitochondrial DNA.

Pharmacotherapy

Pharmacovigilance, the study of safety and adverse effects of drugs, is not only an integral part of currently-used drug assessment; it is also a crucial element in the evaluation of novel investigational medicines. The clinical judgment of a pharmacotherapist to attribute an observed adverse effect to a drug is valuable yet implicit while algorithms can make a less arbitrary and more objective evaluation. Koh et al, 75 developed a GA-based quantitative system for the evaluation of adverse drug reactions. The new scoring system was able to determine a probability of the causality of an adverse drug reaction to a suspected drug with about 84% sensitivity and 71% specificity.

Tacrolimus is an immunosuppressive agent used to prevent rejection after organ transplantation. The drug has highly variable pharmacokinetics and a narrow therapeutic window making its blood level control an essential and difficult task. In an attempt to predict the blood concentration of tacrolimus in liver-transplanted patients, an ANN algorithm was developed. A GA was used to choose the best set of clinically significant candidate variables. For validation, predicted results were compared to observed figures. The ANN was able to predict the blood level of tacrolimus, with 84% of data sets being within a clinically acceptable range of 3 ng/ml of the observed data. 76

Studies have shown that poor pharmacokinetics and lack of efficiency account for more than 50% of failures in the process of drug development. The traditional assessment of the efficacy and pharmacokinetics of novel investigational agents in animal models is a costly and time-consuming process. Therefore, computational methods have evolved to generate quantitative structure-pharmacokinetic relationship (QSPKR) models for rapid in silico screening of novel potential drugs.

Zandkarimi et al, 77 applied a GA to select the most suitable characteristics out of more than 1480 descriptors of alkaloid drugs. These sets of characteristics were then extracted from known drugs for training an ANN to generate QSPKR prediction models. The new system was able to predict the volume of distribution, clearance, and plasma protein binding of alkaloid drugs with an acceptable efficiency.

Health care management

Proper management of monetary resources and personnel is an integral part of health systems all over the world. One of the important elements of hospital management which can improve patient servicing, satisfaction, and cost-effectiveness ratios is efficient scheduling of patients admission. A mathematical model was developed and optimized using a GA to improve the patient scheduling in an ophthalmology hospital. The new algorithm was superior to the traditional "first come, first serve" model in that it shortened the waiting list, lowered the vacancy rate of hospital beds, reduceed the preoperative waiting time for patients, and increased the number of patients discharged from the hospital. 78 Another report showed that a combination of GA and particle swarm optimization, another powerful metaheuristic algorithm, was able to improve patient scheduling, reduce time wastage, and increase patient satisfaction. 79

In clinical laboratories, regular rotation of staff based on their skills through different facilities is fundamental for maintaining job skills and competence. GAs have been applied to improve staff rotation scheduling in a clinical laboratory. In one report, the GA-based software was capable of planning the rotation of staff effectively, ensuring maintenance of techniques and skills, saving time and the cost necessary for the scheduling process, and it was associated with the satisfaction of responsible supervisory personnel. 80

In this paper, we introduced GAs and some of their applications in various fields of medicine. Although GAs and some other metaheuristics are inspired by biology, the experts of other fields of science are more aware of them and these methods are frequently used to solve complex problems. Due to the inherent complexity of medicine, optimization methods could be of great value for physicians and medical researchers. The lack of an efficient interaction between computer scientists and physicians on the one hand and the unfamiliarity of complex mathematical formulas among the medical professions on the other is responsible for this situation. Therefore, improving the interaction and understanding between physicians, computer scientists, and engineers, which could happen via joint journal clubs or attendance of physicians ground rounds and case report presentations, could solve the problem. Besides, improvement of interdisciplinary courses and efficient involvement of engineering researchers in health care environments and hospitals could offer new solutions for medical problems and new ideas for non-medical researchers.

The authors declared no conflicts of interest. No funding was received for this study.