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Title: an improved genetic algorithm and its application in neural network adversarial attack.

Abstract: 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.

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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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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.

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• Published: 08 February 2021

A machine learning method based on the genetic and world competitive contests algorithms for selecting genes or features in biological applications

• Yosef Masoudi-Sobhanzadeh 1 ,
• Habib Motieghader 2 , 3 ,
• Yadollah Omidi 4 &
• Ali Masoudi-Nejad 5  

Scientific Reports volume  11 , Article number:  3349 ( 2021 ) Cite this article

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Gene/feature selection is an essential preprocessing step for creating models using machine learning techniques. It also plays a critical role in different biological applications such as the identification of biomarkers. Although many feature/gene selection algorithms and methods have been introduced, they may suffer from problems such as parameter tuning or low level of performance. To tackle such limitations, in this study, a universal wrapper approach is introduced based on our introduced optimization algorithm and the genetic algorithm (GA). In the proposed approach, candidate solutions have variable lengths, and a support vector machine scores them. To show the usefulness of the method, thirteen classification and regression-based datasets with different properties were chosen from various biological scopes, including drug discovery, cancer diagnostics, clinical applications, etc. Our findings confirmed that the proposed method outperforms most of the other currently used approaches and can also free the users from difficulties related to the tuning of various parameters. As a result, users may optimize their biological applications such as obtaining a biomarker diagnostic kit with the minimum number of genes and maximum separability power.

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Introduction.

In computational biology, researchers may be involved with the handling of large omics datasets with many features (e.g., genomics, proteomics, metabolomics, etc.) 1 . For instance, the total number of profiled genes is usually more than 20,000 in human samples, which have been exploited for different purposes such as the detection of biomarkers 2 . Given that the number of features from proteomics and metabolomics data is potentially much larger 3 , it is almost impossible to extract a set of biomarkers kit of a manageable size from such large data sets 4 . For instance, in the field of genomic data, researchers aim to (i) select genes having higher separability power between different states, such as cancerous and noncancerous samples, and (ii), confine them to a reasonable number to be handled 5 . From the machine learning perspective, features or genes can be categorized into three classes as follows:

Negative features 6 , which can mislead a learner and reduce its performance. Thus, they must not be selected in the application.

Neutral features 7 , which do not play any role in the performance of a learner and can only increase the time of predicting. Like the first group, these features should be avoided.

Positive features 8 , which play a determinant role in distinguishing between samples and enhance the performance of a learner. For such features, the feature selection (FS) methods need to be applied since some of the features may have redundant roles as others. Further, a large set of them may be represented by a small set.

Due to the combinatorial nature of FS, it is a nondeterministic polynomial (NP-hard) problem that cannot be solved in a polynomial-time order, in large part because of being accepted by nondeterministic Turing machines 9 . To overcome the time complexity, heuristic and metaheuristic algorithms, which find acceptable answers to these problems, have been developed 10 .

In different studies, it has been shown that the metaheuristic algorithms, which do not confine themselves to a specific range of the search space, are generally more suitable than heuristic algorithms 11 , 12 , 13 . In addition, two-step methods may obtain better results than single methods 14 , 15 . Therefore, in this study, we capitalized on a two-step method, which is based on a genetic algorithm (GA) 16 and our previously developed world competitive contests (WCC) optimization algorithm 17 , the so-called “GA_WCC method”. In the first step of the GA_WCC method, the GA reduces the total number of features to a minimum upper bound. Next, the WCC selects an optimal subset of features for the desired application. Overall, the GA_WCC method is based on a two-step process for FS, which (i) does not require limiting the number of features to a predefined value, and (ii) outperforms other currently used methods.

Related works

In this section, we discuss the limitation of related approaches works that can be divided into six classes as follows:

Filter methods: These techniques look for the relationships among features and investigate how much information exists in a feature. For this purpose, various mathematical formulas have been proposed, including Entropy 18 , mutual information 19 , Fisher score 20 , correlation 21 , Laplacian 22 , etc. Although these approaches are simple and have a low time-complexity, their performance is lower than the other categories 23 . To tackle such a limitation, wrapper-based method has been developed and are built-upon in this paper.

Wrapper methods: Unlike the first class, these approaches score the selected features by a learner such as a support vector machine (SVM) 24 , artificial neural networks (ANN) 25 , decision tree (DT) 26 , or others 27 , 28 , 29 . Usually, optimization algorithms are applied to select an optimal subset of features 30 , 31 . In different studies, it has been shown that these approaches can achieve remarkable outcomes 32 , but most of the FS studies do not employ state-of-the-art algorithms for the FS. Here, we used the WCC algorithm for the FS problem.

Ensemble methods: For the FS, ensemble methods create a learner such as a decision tree 33 and selects features in such a way that the learner chooses them for generating a model 34 , 35 . Due to their greedy nature, ensemble methods may fall into local optima solutions and do not reach the optimal result. To deal with this limitation, we introduce the WCC algorithm, which features a low probability of falling into local optima.

Hybrid methods: A combination of the three mentioned methods is applied to the FS problem 36 . For example, the total number of features is reduced by filter methods, and then an optimal subset of features is chosen by wrapper or ensemble methods 37 , 38 . In this class of related works, it is essential to combine the algorithms properly. Therefore, we assumed that a combination of wrapper-wrapper approaches, which merge two wrapper-based algorithms, might be a suitable option for FS.

Hypothesis-based studies: A concept is hypothesized based on prior knowledge and the correctness of which is tested via various experiments on gold-standard datasets 39 . Although these techniques can help in making a proper decision, they do not prevent the mentioned limitations.

Review works: These works survey different methods such as filter 40 , wrapper 41 , ensemble 42 , hybrid 43 , and discuss their advantages and disadvantages. Further, they study the role of FS in diverse areas and often constitute the future directions 44 .

Materials and methods

The datasets.

Several datasets with diverse properties have been selected from various sources such as the machine learning repository developed at the University of California Irvine (UCI) 45 and published seminar literature sources. For every dataset, the total number of samples is almost the same in its different classes. Table 1 shows the properties of the datasets and describes them.

The proposed method

Our proposed GA_WCC method (Fig.  1 ) selects the features using a two-step wrapper approach. To this end, as the first step, the Genetic Algorithm (GA) limits the total number of genes or, generally, features, and then the World Competitive Contests (WCC) selects an optimal subset of them from the reduced set of features. Overall, this study has been established based on the following rationale:

The GA starts with a first population of candidate solutions, which each consists of several variables (a subset of features). Unlike other optimization algorithms such as the particle swarm optimization (PSO) 53 , for the GA, the probability of falling into local optima is minimal, because it produces a high number of candidate sets. However, the convergence speed of GA is usually less than other optimization algorithms (e.g., TLBO 54 and FOA 55 ). Hence, this limitation may be addressed when the GA algorithm is combined with other state-of-the-art optimization algorithms. This issue is considered in the present study, by merging the GA and WCC algorithm.

The WCC begins with a first population of potential answers and applies its all the operators to all the existing candidate solutions (CSs), so it spends more times than other optimization algorithms. Hence, when applying the WCC algorithm to an optimization problem, the total number of CSs is limited. This algorithm has an acceptable convergence speed, but the main limitation of WCC relates to its complex stages, which increase the execution time. Further, for a CS, WCC calls the cost function more than other algorithms due to the nature of its operators. At the last steps of the algorithm, the applied operators make CSs similar to each other, so the convergence speed of the algorithm is reduced (due to the limited number of CSs).

The framework of the proposed method based on the wrapper-wrapper feature selection technique, consisting of two phases. First, the GA confines the total number of features and then passes them towards the WCC. All the CSs are scored by the SVM. At the end of the method, the best CS is introduced as an answer to the problem. CS, candidate solution; GA, genetic algorithm; SVM, support vector machines; WCC, world competitive contests algorithms.

Optimization algorithms differ from each other from a way that they change CSs (the operators of the algorithms). In this study, the WCC algorithm is developed to the FS problem, and its operators are modified to select an optimal subset of features. Given the advantages and disadvantages of the GA and WCC algorithm (the modified version of the WCC algorithm), it is expected that their limitations will be diminished when combined with each other. Inspired by this idea, this study has been designed, and an efficient two step feature selection method based on a wrapper approach has been introduced. As shown in Fig.  1 , the GA_WCC method includes several steps as follows:

Applying the genetic algorithm: In the first step of the proposed method, a version of GA is used for the FS 56 . In different FS studies, CSs are binary, while their length is constant and equal to the total number of features. In this study, for both GA and WCC algorithms, CSs have variable sizes and contain the indices of the selected features. In the optimization scope, the GA is the basis for other optimization algorithms. However, GA generally exhibits a low level of performance in comparison with other algorithms. This notwithstanding, GA produces different CSs, which may help other optimization algorithms to obtain better results 57 . In Fig.  2 , the flowchart of the employed GA is shown, which includes the following main steps:

Creating a first population of CSs: potential answers or CSs are called ‘chromosomes’ in the GA algorithm, and their values of genes are randomly quantified. Every CS incorporates some features, which are chosen from a given feature set (the total number of variables in a CS depends on the size of a dataset). In the proposed method, initially, the CSs have an identical length, but their length may vary from each other because of some repeated values. For instance, in generating initial CSs, it is possible that a CS contains some repeated features. In such a case, only one of the repeated values is remained and the remaining ones are ignored.

Applying GA operators: The GA consists of three main operators named mutation, crossover, and selection. In the employed mutation operator, a variable of a chromosome is randomly selected, and its value is replaced by another randomly selected variable. In the crossover operator, two ranges of the CSs with the same length are randomly chosen, and their contents are exchanged. Finally, in the selection operator, elitism technique has been used, which forms the new population based on the most deserve chromosomes of the current population. In Figs.  3 and 4 , the instances of the mutation and crossover operators are depicted, which describes, how the mentioned operators are applied to generating new CSs.

Scoring the selected features: The proposed method is a wrapper method in which a learner evaluates the selected features. Due to the nature of the datasets, which are approximately class-balanced, we basically use the accuracy score (Eq.  1 ). Other criteria are also inspected in the experimental section.

where TP, TN, FP, and FN represent true positives, true negatives, false positives, and false negatives, respectively. Because of their performance and reasonable time in generating a model, Support Vector Machines (SVMs) have been used for assessing the CSs. Considering the popularity and performance of SVMs, many libraries and packages have been developed accordingly. In this study, the LibSVM library, which is one of the most popular libraries with different options, was employed 58 .

Investigating the termination condition: when the value of the best CS is remained constant for 10 consequent iterations (generations), the GA is terminated, and all its CSs are passes to the WCC algorithm.

Applying the proposed algorithm (the WCC): As mentioned before, at the end of the first step, GA passes the created CSs to the proposed algorithm (the flowchart of the WCC algorithm is shown in Fig.  5 ) and constitutes its first population of CSs. Next, WCC changes the CSs using its operators, which are explained and formulated as follows:

Attacking operator: For a given CS, this operator selects some variables randomly and assigns them new values by chance from [1, n], where n is the total number of the existing features/genes. Equation 2 formulates the attacking operator:

where CS, n, and k are a given candidate solution, the total number of features, and an integer random value between 1 and n, respectively. In other words, the k parameter determines how many variables of a CS must be changed. Further, the sigma sign denotes a loop, and r is an integer value between 1 and n as is k. Here, is an example of the attacking operator in Fig.  6 .

Transferring operator: Based on the scores (classification accuracy using a given CS), this operator selects several CSs with the highest score ( Selected_CS ), and then, chooses randomly some values (features) from them. Next, for a given CS, this operator imports the selected values. Equation 3 formulates the mentioned steps. Figure  7 describes the transferring operator in detail.

where \(l\) , R, and m are the length of the selected_CS , a random integer value between 1 and the total number of selected CSs, and an index which shows the randomly selected_CS , respectively. Further, other parameters have been described in Eq.  2 .

Passing operator: While the transferring and attacking operators may result in large changes in a CS, this operator guarantees low modifications. For this purpose, the operator only selects a variable by chance and changes its value. Equation  4 , whose parameters are explained in Eq.  2 , formulates the passing operator.

Figure  8 illustrates an example of the passing operator and explains how the operator can be applied to the FS problem.

Each of the changes induced by the operators will be accepted if they increase the accuracy score. Further, repeated features may appear by applying the operators. In these situations, only one of the repeated features is kept and all others are removed. Hence, the length of CSs may vary.

Investigating the termination conditions: For terminating the algorithms, several options (e.g., predefined number of iterations, time, accuracy, etc.) can be used. In the present study, two different strategies are chosen for terminating the algorithm. As mentioned before, when the value of accuracy remains about constant in the last ten iterations, the GA is finished. For the WCC algorithm, a predetermined number of iterations has been considered as the termination condition.

Flowchart of the employed GA. This algorithm begins with several randomly generated potential answers (a subset of the existing features) and applies its operators to produce new CSs, which contain the selected features. To calculate fitness of the CSs, a model is created using SVM, and its accuracy (based on fivefold cross-validation) is reported. Also, to generate new population, elitism method (which generates new population based on the CSs having the higher value of fitness) has been used. CS, candidate solution; GA, genetic algorithm; SVM, support vector machines.

An example of the utilized mutation operator, which choses a variable randomly and changes its value. ( a ) The status of a CS has been shown before applying the operator. ( b ) The status of a CS has been shown after applying the operator. CS, candidate solution.

An instance of the utilized crossover operator. ( a ) A range from two CSs are randomly chosen, which their length is the same. ( b ) The values of the specified ranges are transferred. ( c ) After changing the values, the repeated values are removed, and the others are sorted. CS, candidate solution.

Flowchart of the WCC algorithm (the algorithm developed here). The WCC algorithm receives its first population of CSs from the GA and applies its operators on them. If the changes induced by the operators improve the accuracy, they are accepted. Otherwise, the changes are ignored. CS, candidate solution; GA, genetic algorithm; SVM, support vector machines.

An example of the attacking operator. The array presents a CS which includes a set of the features. ( a ) Some indices of a CS are randomly chosen. The values of the selected indices have been highlighted by the pink colors. ( b ) The values of the determined indices are replaced by other randomly generated values. The blue colors show the replaced values. If repeated values appear, one of them remains and others are eliminated. The size of a CS may be reduced after applying the attacking operator. CS, candidate solution.

An instance of the transferring operator. The arrays present CSs which include a set of different features. ( a ) Five CSs with the highest scores are selected. The colored indices are the variables (features), which are imported to the given CS. The blue colors are the variables that are randomly selected and are removed from the given CS. ( b ) The status of the given CS is shown after deleting the blue highlighted features and inserting the pink highlighted features. ( c ) The finalized status of the given CS is presented. In this step, the selected features are sorted, and the repeated ones are removed. CS, candidate solution.

An example of the passing operator. The array presents a CS which includes a set of the features ( a ) The status of a CS before applying the passing operator is presented. One of the features has been randomly selected. ( b ) The status of the CS after applying the passing operator. The determined feature has been replaced by another feature. CS, candidate solution.

To obtain results, a computer system with a dual-core 2.2 GH processor and 12 GB of RAM was employed. Further, our designed FeatureSelect software application and MATLAB programming language were used for the implementations. In this section, all the obtained outcomes refer to results from the five-fold cross-validation technique. For comparing the algorithms and methods, the same conditions were considered. For example, GA, WCC algorithm, and GA_WCC method allowed to run for an identical time for getting the results. The size of populations for the GA, WCC algorithm, and GA_WCC method was determined using a “trial and error” method and their time-consuming parameter, in which the best performance of the algorithms is observed. Based on the outcomes, the population sizes were considered 100, 20, and 100 for the GA, WCC algorithm, and GA_WCC method, respectively. The mutation and crossover rates were set to 30%, because the GA shows a suitable behavior based on them. In addition to the population size parameters, the WCC algorithm consists of the match time (the total number of attempts to change a CS) parameter, which has been set to 2. This parameter was initiated 1 to the GA_WCC method. The outcomes (which encompassed the results of five popular filter FS methods, GA, WCC, a two-step filter-wrapper method (EN_WCC), and the proposed wrapper-wrapper method (GA_WCC)), were divided into the following three categories:

The first category of the results: This class consists of the results obtained from applying the mentioned algorithms and methods to the datasets having more than 50 features and relating to the classification type. Tables 2 and 3 represent the attained outcomes. Also, Fig.  9 depicts the results of the SVM without applying the FS algorithms on the investigated datasets.

Wrapper-based FS methods improve the performance of SVM, whereas Filter-based FS approaches may reduce its performance. Overall, among the filter methods, the entropy-based (EN) FS method has led to more appropriate results than others. Moreover, between GA and WCC algorithms, WCC yields better outcomes. Hence, a combination of EN and WCC (the so-called EN_WCC) is also investigated and compared against the others. For the Cancer dataset, GA_WCC, GA, and WCC have yielded the best solutions. However, GA_WCC and GA classify the data with six features, whereas WCC classifies them with ten attributes. For the Arrhythmia dataset, the proposed approach outperforms others in terms of the total number of features (NOF) and other classification criteria. For the Diabetes dataset, EN_WCC yielded a minimum number of features and have yielded better outcomes than the filter methods, as observed for the cancer dataset. Nevertheless, the data of GA_WCC, WCC, and GA surpass EN_WCC. Similar outcomes are observed for the other datasets. Tables 2 and 3 show that wrapper and two-step methods are more efficient than the filter ones, and their performance can be sorted as GA_WCC, WCC, GA, and EN_WCC, respectively.

For further evaluating the methods, receiving operating characteristic (ROC) curves of the methods are shown in Figs.  10 and 11 . The area under the curve (AUC) values of the approaches on the datasets of the first class of the outcomes are shown in Table 4 . The two-step and wrapper approaches have remarkable functionality compared to the others, and the proposed method outperforms all of them (Figs.  10 , 11 , Tables 2 , 3 , and 4 ). In another evaluation of the algorithm’s performance, the p-value (PV) measurement was considered (Table 5 ). To this end, every algorithm was performed in 50 individual executions, and the results of the proposed method (GA_WCC) were considered as a test base. Next, the outcomes of the other algorithms were compared with them. Except for the Cancer dataset, in which the effectiveness of the algorithms is the same, the proposed method has outperformed the others for the remaining datasets. Figure  12 also presents boxplots of the algorithms’ outputs obtained using One-Way ANOVA test. Every execution consists of 100 iterations of the algorithms step. At the end of an iteration, the best acquired accuracy was stored, and the convergence behavior of the algorithms were investigated for the datasets including more than 1000 features (Fig.  13 ). It was observed that the convergence speed of the proposed method is higher than the GA and WCC algorithms (without merging them). As mentioned before, the combined method can efficiently address the limitations of the GA and WCC algorithm (the low convergence of the GA algorithm and the restricted number of CSs in the WCC) and yield better outcomes when combined than when run individually.

In filter FS methods, determining the total number of features is a challenging problem and plays an essential role in the performance of a model. The results of the five filter approaches are shown in Figs. 14 , 15 , 16 , and 17 . These outcomes show the performance of the filter FS methods with a different number of features.

The second category of results: This section includes the results of the algorithms on the datasets having less than 50 features/attributes. The main goal of this section is to check the effect of FS methods on datasets, which consist of fewer numbers of features. For the small datasets, single wrapper methods do not face special challenges in the FS. Indeed, the mentioned FS methods may obtain the best solution by improving the run time. Hence, in this section, the functionality of the GA and WCC algorithms are inspected. Like for the first part, criteria such as sensitivity, specificity, accuracy, precision, and AUC were investigated. The acquired data are listed in Table 6 .

Without applying the GA and WCC algorithms, SVM alone yields 0.5263, 0.6645, and 0.5812 value of accuracy using the fivefold cross-validation technique on the CHD, SHD, and PID datasets, respectively. By applying the algorithms, the value of accuracy improved for the CHD and SHD datasets and remains unchanged for the PID dataset. Further, the total number of features is remarkably reduced. Thus, the obtained models obtained by applying the algorithms operate faster than the model, which uses all the existing features. Having compared GA and WCC algorithms, WCC was seen to lead to a model with lower number of features and higher values of criteria. Therefore, it might be concluded that the state-of-the-art optimization algorithm can get more acceptable data than others.

The third category of the results: In this section, the outcomes of the methods and algorithms are evaluated on the regression-based dataset (WDBC and drug datasets). To this end, the criteria such as root mean squared error (RMSE) and the correlation between predicted and real labels were calculated and gathered (Table 7 ). For the filter FS methods, different numbers of features have been tested, and then, their best results were reported. For the wrapper FS approaches, it is not necessary to limit the total number of features and they can regulate it. Even so, they produce variable results in their different executions, so they must be executed at least 30 times and their best-obtained outcomes among from the executions (different accuracy values of the executions) are reported as a solution to the problem. Thus, several criteria were reported for them, based on the acquired results in 50 individual executions, including confidence interval (CI), p-value, standard deviation (STD), etc.

The performance of the SVM without applying FS algorithms on the datasets.

ROC curves of the methods on the first category of datasets. ( a ) The ROC curve of the manners on the Cancer dataset (Adeno dataset). Although all the methods have acceptable performance, the proposed method (GA_WCC) has higher separating power relative to the others. ( b ) The ROC curve of the methods on the Arrhythmia dataset. Like the first section, GA_WCC show better performance in term of classifying power. ( c ) The ROC curve of the manners on the Diabetes dataset. These results also validate that two-step and wrapper methods obtain better results than filter FS methods. ( d ) The ROC curve of the manners on the Lung dataset. In addition to accrediting the results of the three mentioned section, these diagrams state that EN reaches to a better solution than other filter approaches, and its combination with WCC improves the performance of a model. ROC, receiving operating characteristic; WCC, world competitive contests algorithm; GA, genetic algorithm; PC, Pearson correlation; LA, Laplacian score; EN, entropy; MI, mutual information; FI, Fisher score.

ROC curves of the methods on the second category of datasets (high dimensional). ( a ) The ROC curve of the manners on the QSAR dataset. ( b ) The ROC curve of the methods on the Arcene dataset. ( c ) The ROC curve of the methods on the MicroMass dataset. ( d ) The ROC curve of the manners on the RNA-Seq dataset. Like Fig.  10 , these diagrams state that optimization algorithm can acquire better results than other algorithms, and two-step feature selection method may be a suitable technique for choosing the most effective features or genes in the biology field. ROC, receiving operating characteristic; WCC, world competitive contests algorithm; GA, genetic algorithm; PC, Pearson correlation; LA, Laplacian score; EN, entropy; MI, mutual information; FI, Fisher score.

Boxplot of the GA, WCC, GA_WCC algorithms on the ( a ) Cancer, ( b ) Arrythmia, ( c ) Diabetes, ( d ) Lung, ( e ) QSAR, ( f ) Arcene, ( g ) MicroMass, and ( h ) RNA-Seq datasets. For the Cancer dataset, all the algorithms have shown an identical performance. For the remaining ones, although the error value of the GA and WCC algorithms is lower than the GA_WCC method, the proposed method has outperformed the GA and WCC algorithms in terms of accuracy and other classification criteria. WCC, world competitive contests algorithm; GA, genetic algorithm;

Convergence of the GA, WCC, and GA-WCC algorithms on the ( a ) QSAR, ( b ) Arcene, ( c ) MicroMass, and ( d ) RNA-Seq datasets. In the early stages of the iterations, the algorithms present a similar behavior. However, after elapsing more times, the WCC algorithm shows better performance than the GA, and the proposed method exhibits proper convergence behavior than the WCC algorithm.

Outcomes of the filter FS methods on the Cancer dataset with selecting ( a ) 20, ( b ) 40, ( c ) 60, and ( d ) 80 features. When the number of features (NOF) is confined to 80, all the ways acquire the best possible solution. PC, Pearson correlation; LA, Laplacian score; EN, entropy; MI, mutual information; FI, Fisher score.

Outcomes of the filter FS methods on the Arrhythmia dataset with selecting ( a ) 400, ( b ) 800, ( c ) 120, and ( d ) 160 features. The results of the methods differ from each other with a various number of features. PC, Pearson correlation; LA, Laplacian score; EN, entropy; MI, mutual information; FI, Fisher score.

Outcomes of the filter FS methods on the Diabetes dataset with selecting ( a ) 20, ( b ) 30, ( c ) 40, and ( d ) 50 features. The confining total number of features may lead to different results. PC, Pearson correlation; LA, Laplacian score; EN, entropy; MI, mutual information; FI, Fisher score.

Outcomes of the filter FS methods on the Lung dataset with selecting ( a ) 15, ( b ) 20, ( c ) 25, and ( d ) 30 features. The EN method with an average of 81% accuracy is better than other approaches. PC, Pearson correlation; LA, Laplacian score; EN, entropy; MI, mutual information; FI, Fisher score.

From the run-time perspective, filter FS methods require less time than wrapper approaches, but do not result in improved outcomes. For instance, for the WDBC dataset, the entropy FS approach yields the minimum value of error and the maximum value of correlation between the predicted and real labels, when the total number of features is limited to 13. The value of correlation can be calculated not only for the entropy method but also for others. As the first class of results, the second one also shows the remarkable performance of the proposed approach (GA_WCC) in terms of error, correlation, the total number of selected features, run-time, etc. Besides, WCC and GA present that wrapper FS method may acquire better results than the filter FS approaches. In Fig.  18 , the scatter plots of the proposed method on the regression-based datasets are shown.

Scatter plot of the proposed method on the Drug and WDBC datasets. Blue and red points indicate real and predicted values, respectively. The value of RMSE for the drug and WDBC datasets are 0.14 and 0.01, respectively.

Many methods and algorithms have been proposed for selecting an optimal subset of features, which is indeed an NP-hard problem, particularly in machine learning with a biological context. Besides enhancing the separability power of a model, optimal features improve the speed of a model and may lead to valuable results such as acquiring an optimal kit of biomarkers to be used in applications. In this area, it has been shown that two-step FS approaches lead to better outcomes than single methods 59 , and wrapper-based FS methods usually outperform filter and embedded FS techniques 60 . The results of this study also confirm the mentioned observations and allow for the following important key conclusions:

First, wrapper FS methods may obtain an optimal subset of features, which do not require confining the total number of features to a predefined number. Nevertheless, there are some restrictions in determining the total number of selected features. For example, wrapper methods may obtain a subset of attributes with the highest score, while the total number of the selected features may be greater than the required number of features (problem limitations). In this line, we believe that wrapper FS methods are still better than the filter and embedded FS approaches, in large part because they can be formulated in a way to resolve the problem constraints.

Second, limiting the filter methods to a predefined number is a challenging problem and affects the performance of filter FS approaches. The results of this work show that the performance of filter FS approaches vary with the different number of selected features. Thus, this parameter remains a challenge for researchers. However, wrapper methods, which consider a set of features instead of examining each of them separately, do not face this restriction.

Third, the FS is also essential for datasets having a low number of features. In the second part of the results, the performance of wrapper FS methods was investigated on some gold-standard datasets, for which their total number of features is less than 50. Based on other conducted studies 61 , it seems that the FS has been ignored in these works even though it may improve the performance. For this class of datasets, considering the total number of features, single wrapper methods might be a proper method.

Forth, wrapper-wrapper FS methods may be the best option for selecting an optimal subset of features. In the last decade, different types of hybrid methods have been introduced for the FS problem due to their amazing results. However, most of them combine filter-filter or filter-wrapper approaches and a suitable configuration of wrapper-wrapper methods have been ignored. In the present investigation, a wrapper-wrapper approach based on GA and the proposed WCC-algorithm was introduced, which resulted in superior outcomes compared to the other approaches. The WCC algorithm starts with a first population of CSs and, then, applies its operators to them in order to obtain a better solution to the FS problem. The main difference between the WCC algorithm and other optimization algorithms relates to the steps of the algorithm and its operators. The two-step approaches differ from hybrid methods that merge the optimization algorithms such as the whale optimization algorithm and simulated annealing 62 . In this study, to obtain an efficient combination of the algorithms, the advantages and limitations of the GA and WCC algorithm were considered. Since the GA produces various CSs, the WCC algorithm confines them to a limited number. Unlike the WCC algorithm, the GA may suffer from low convergence speed and not show a suitable performance relative to other optimization algorithms. Given the mentioned reasons, GA and WCC algorithm were combined, and the results showed that their combination yields better outcomes.

Fifth, the performance of algorithms and methods varies on different datasets. Every algorithm or method has its own attitude relative to the FS problem, so their functionality may differ on various data. Generally, it is impossible to predict a priori, which of the methods or algorithms is suitable for a given problem. Nonetheless, wrapper-wrapper FS approaches appear promising to produce desired results. As a future work, the proposed method can be applied to other algorithms such as the Salp Swarm Algorithm 63 and DE 64 with considering limitations and disadvantages. Also, the proposed method scores a set of features and does not rank the features of the obtained set. To address this limitation, the proposed approach can be combined with state-of-the-art ranking techniques such as SVM-RFE 65 , 66 .

For selecting an optimal subset of features, a two-step wrapper-wrapper FS method based on GA and our proposed algorithm (WCC) was introduced and applied to the thirteen biological datasets with different properties. In comparison with other approaches, it can be concluded that two-step techniques may lead to better results than single-step methods. Furthermore, among the two-step approaches, wrapper-wrapper FS methods may be more appropriate than others. For biological applications, it seems that wrapper approaches are the most convenient and reliable method, in large part because they do not need to be restricted to a predefined number of features. Taken together, based on our findings, wrapper-wrapper FS methods can be used to optimize the FS problems and result in robust and desired outcomes.

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The authors would like to appreciate Iranian National Science Founding (INSF) for their supports.

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• Yosef Masoudi-Sobhanzadeh

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Habib Motieghader

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Y.M.-S.: Conceptualization, implementation, formal analysis, investigation, writing, editing, and revising the manuscript. H.M. Validation, data analysis, Editing-manuscript. Y.O.: Results analysis, validation, Conceptualization, writing, editing, and revising the manuscript. A.M.-N.: Conceptualization, Supervision, Project administration, writing, editing, and revising the manuscript. All authors have read and approved the manuscript.

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Masoudi-Sobhanzadeh, Y., Motieghader, H., Omidi, Y. et al. A machine learning method based on the genetic and world competitive contests algorithms for selecting genes or features in biological applications. Sci Rep 11 , 3349 (2021). https://doi.org/10.1038/s41598-021-82796-y

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A survey on biomimetic and intelligent algorithms with applications.

1. Introduction

2. related work, 3. bio-inspired neural network models, 3.1. origin, 3.2. convergence and stability, 3.3. accelerated convergence, 3.3.1. finite-time neural network, 3.3.2. predefined-time neural network, 3.4. noise tolerance neural network, 3.5. convergence accuracy, 3.6. time-varying linear system solving, 3.7. time-varying nonlinear system solving, 3.8. robot control, 3.9. discussion and challenges, 4. intelligence algorithms with applications, 4.1. bio-inspired intelligence algorithm, 4.1.1. genetic algorithm, 4.1.2. particle swarm optimization algorithm, 4.2. ant colony optimization algorithm, 4.3. artificial fish swarm, 4.4. harris hawks optimizer, 4.5. the rest of the swarm intelligence algorithms, 4.6. gene feature extraction, 4.7. intelligence communication, 4.8. image processing, 4.9. other applications, 4.10. discussion and future direction, 5. conclusions, author contributions, data availability statement, conflicts of interest.

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Li, H.; Liao, B.; Li, J.; Li, S. A Survey on Biomimetic and Intelligent Algorithms with Applications. Biomimetics 2024 , 9 , 453. https://doi.org/10.3390/biomimetics9080453

Li H, Liao B, Li J, Li S. A Survey on Biomimetic and Intelligent Algorithms with Applications. Biomimetics . 2024; 9(8):453. https://doi.org/10.3390/biomimetics9080453

Li, Hao, Bolin Liao, Jianfeng Li, and Shuai Li. 2024. "A Survey on Biomimetic and Intelligent Algorithms with Applications" Biomimetics 9, no. 8: 453. https://doi.org/10.3390/biomimetics9080453

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Bibliometrics & citations, view options, recommendations, stabilisation analysis for switched neutral systems based on sampled-data control.

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Robust sampled-data stabilization of uncertain fuzzy systems via input delay approach

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A Review of Production Scheduling Research Based on Genetic Algorithm

• Conference paper
• First Online: 08 April 2023
• Cite this conference paper

• Pengfei Xin 6 ,
• Tianxing Sun 6 ,
• Jiaqi Wang 6 ,
• Ningbo Zhang 6 &
• Yawei Li 6  

Part of the book series: Lecture Notes on Data Engineering and Communications Technologies ((LNDECT,volume 170))

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• International Conference on Applications and Techniques in Cyber Intelligence

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Production scheduling is one of the most important links in Intelligent manufacturing system, which has a significant impact on improving the production efficiency of enterprises. In the past decades, genetic algorithm (GA) has been extensively used in different production scheduling problems and has become the main method to solve scheduling problems. This paper makes a comprehensive literature review on the use of genetic algorithm to solve the production scheduling problem, comprehensively and systematically summarizes the workshop production scheduling such as JSP, FJSP, DFJSP, GSSP and FFJSP, and summarizes the research direction of GA in the future.

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College of Mechanical and Electrical Engineering, Zhengzhou University of Light Industry, Zhengzhou, 450002, Henan, China

Pengfei Xin, Tianxing Sun, Jiaqi Wang, Ningbo Zhang & Yawei Li

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Faculty of Science, Engineering and Built Environment, Deakin University, Geelong, VIC, Australia

Jemal H. Abawajy

School of Computer Engineering and Sciences, Shanghai Polytechnic University, Shanghai, China

School of Computer Science, University of Oklahoma, Norman, OK, USA

Mohammed Atiquzzaman

Department of Information Systems and Cyber Security, The University of Texas at San Antonio, San Antonio, TX, USA

Xiaolu Zhang

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Xin, P., Sun, T., Wang, J., Zhang, N., Li, Y. (2023). A Review of Production Scheduling Research Based on Genetic Algorithm. In: Abawajy, J.H., Xu, Z., Atiquzzaman, M., Zhang, X. (eds) Tenth International Conference on Applications and Techniques in Cyber Intelligence (ICATCI 2022). ICATCI 2022. Lecture Notes on Data Engineering and Communications Technologies, vol 170. Springer, Cham. https://doi.org/10.1007/978-3-031-29097-8_52

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DOI : https://doi.org/10.1007/978-3-031-29097-8_52

Published : 08 April 2023

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Evaluation of Regional-Scale Optimization of Autumn Irrigation Patterns Based on Coupled Genetic Algorithm and Distributed Swap-Wofost Model

60 Pages Posted: 25 Jul 2024

Taiyuan University of Technology

Junfeng Chen

AbstractAutumn irrigation is an important measure for leaching soil salt and ensuring adequate soil water content for crop cultivation in the following year within the Hetao Irrigation District (HID). Exploring relatively suitable autumn irrigation patterns on a regional scale is conducive to ensuring normal crop growth and saving the irrigation water diverted from the Yellow River. However, there are relatively few studies on a regional scale to optimize and evaluate the autumn irrigation patterns based on coupled genetic algorithm (GA) and distributed SWAP-WOFOST model. In this study, a distributed SWAP-WOFOST model that couples crop growth with soil water, heat and salt transport was constructed, calibrated and validated on a regional scale. The calibrated and validated model was then used to analyze the effects of various autumn irrigation patterns on sunflower yield and Water Productivity (WP) in the HID from 2000 to 2017 under different precipitation year types. In order to improve WP of sunflower, the regional-scale autumn irrigation patterns were optimized and evaluated based on the coupled GA and the distributed SWAP-WOFOST model. The findings indicated that the distributed SWAP-WOFOST model, which has been constructed, calibrated, and validated,can better simulate the dynamics of crop growth and soil water, salinity and temperature transport in HID. The average annual yield of sunflower was 3423~4012 kg/ha, the average annual WP was 1.1~1.2 kg/m3 under different autumn irrigation patterns from 2000 to 2017 in HID. After optimization based on the genetic algorithm, in wet years, the recommended autumn irrigation time for HID was maintained from October 10th to October 16th, and the recommended autumn irrigation quota was basically maintained at 140 mm. In normal years, Wulateqianqi (WQQ) was recommended to irrigate around 134 mm on September 30th, and the rest of the counties were recommended to irrigate between October 12th and October 22nd, and the autumn irrigation quota was maintained at about 190 mm. In dry years, all counties in HID were recommended to irrigate on October 30th, with the autumn irrigation quota of 200 mm. Under the recommended autumn irrigation patterns, the yield of sunflower in HID was stable and the average WP increased by 1.1%~2.1%. In addition, during wet and normal years, adopting the recommended autumn irrigation patterns could save about 410 million m3 and 158 million m3 of water per year, respectively, diverted from the Yellow River for autumn irrigation.

Keywords: Hetao Irrigation District, sunflower, distributed SWAP-WOFOST model, autumn irrigation pattern, genetic algorithm optimization

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Taiyuan University of Technology ( email )

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• DOI: 10.1021/acsomega.4c01568
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Prediction of Coal Ash Flow Temperature Based on Gray Relational Analysis, Support Vector Regression and Genetic Algorithm

• Kaidi Sun , Zhen Liu , +2 authors Lingmei Zhou
• Published in ACS Omega 25 July 2024
• Engineering, Environmental Science, Materials Science

19 References

A deep insight into the dynamic crystallization of coal slags and the correlation with melt microstructure, the influence of mineral addition on the optimised advanced ash fusion test (oaaft) and its thermochemical modelling and prediction, a structural viscosity model for silicate slag melts based on md simulation, evaluation of tar from the microwave co-pyrolysis of low-rank coal and corncob using orthogonal-test-based grey relational analysis (gra), the fusion mechanism of complex minerals mixture and prediction model for flow temperature of coal ash for gasification, modeling and optimization of a light-duty diesel engine at high altitude with a support vector machine and a genetic algorithm, neural network prediction of parameters of biomass ashes, reused within the circular economy frame, hybrid algorithm for the classification of prostate cancer patients of the mcc-spain study based on support vector machines and genetic algorithms, prediction of ash flow temperature based on liquid phase mass fraction by factsage, flow properties of ash and slag under co-gasification of coal and extract residue of direct coal liquefaction residue, related papers.

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