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In multi-objective optimization, the Pareto-optimal solutions must be widely and uniformly distributed on the Pareto-optimal front. When this condition is satisfied, decision makers can choose satisfactory solutions. In this paper, gaps in the evolving nondominated front are filled by a multi-objective evolutionary algorithm using a uniformly evolving scheme (MOEA/UE), thus generating a uniform and wide Pareto-optimal front. The MOEA/UE first calculates the distance between the points on the nondominated front and identifies those with relatively wide gaps. At the widely spaced points, the objective and constraint functions are approximated by linear functions expressed as Taylor series in auxiliary linear programs. Finally, the MOEA/UE solves these auxiliary linear programs and retains the optimal or intermediate solutions as the potentially superior individuals that will be selected in the next generation of the population. Convergence toward potentially superior solutions is accelerated by a mutation operator (a basic differential evolution operator). In constrained multi-objective optimization problems, the MOEA/UE implements a new constraint-handling strategy that pulls infeasible solutions into or nearby the feasible domain. Experimental results illustrate that MOEA/UE obtains wider and more uniform Pareto-optimal fronts and better Pareto-optimal solutions.

Inspired by the learning rules of humans/animals, self-paced learning (SPL) ranks the samples from easy to complex and assigns real-valued weights to the samples. The current SPL regimes adopt an increasing pace parameter to select the training samples. Obviously, it is difficult to tune the pace parameter during iterations. Furthermore, the current SPL regimes cannot go back to the previous stage even when the current model is worse than the previous one. In this article, a novel Pareto SPL (PSPL) approach is proposed to address the above issues. In PSPL, the SPL problem is considered as a multiobjective optimization problem. Then, a Pareto-based differential evolution algorithm is utilized to optimize the self-paced function and the weighted loss function simultaneously. In PSPL, a new representation method is designed to assign nonpositive weights to the unselected samples. Then, a modified mutation operator inspired by the SPL idea is proposed to generate new population based on ranking the individuals and assigning weights. No pace parameters are introduced in the proposed technique and PSPL can obtain entire solution spectrum to automatically adjust the solution path. The effectiveness of the PSPL has been demonstrated through rigorous studies with matrix factorization and multiclass classification problems.

To deal with the radio frequency threat posed by modern complex radar networks to aircraft, we researched the unmanned aerial vehicle (UAV) formations radar countermeasures, aiming at the solution of radar jamming resource allocation under system countermeasures. A jamming resource allocation method based on an improved firefly algorithm (FA) is proposed. Firstly, the comprehensive factors affecting the level of threat and interference efficiency of radiation source are quantified by a fuzzy comprehensive evaluation. Besides, the interference efficiency matrix and the objective function of the allocation model are determined to establish the interference resource allocation model. Finally, A mutation operator and an adaptive heuristic are integtated into the FA algorithm, which searches an interference resource allocation scheme. The simulation results show that the improved FA algorithm can compensate for the deficiencies of the FA algorithm. The improved FA algorithm provides a more scientific and reasonable decision-making plan for aircraft mission allocation and can effectively deal with the battlefield threats of the enemy radar network. Moreover, in terms of convergence accuracy and speed as well as algorithm stability, the improved FA algorithm is superior to the simulated annealing algorithm (SA), the niche genetic algorithm (NGA), the improved discrete cuckoo algorithm (IDCS), the mutant firefly algorithm (MFA), the cuckoo search and fireflies algorithm (CSFA), and the best neighbor firefly algorithm (BNFA).

In recent years, many different differential evolution (DE) variants have been proposed to solve real-world optimization problems. However, the performance of them is largely determined by the selection of the mutation strategy, an approach to choose favorable mutation strategy when solving various optimization problems has attracted increasing attention recently. In this paper, we propose a DE with an adaptive mutation operator based on fitness landscape (FLDE). The application of fitness landscape to DE requires three stages. First, we analyzed the fitness landscape features of each benchmark training function, a total of 45 benchmark functions are taken from CEC2014 and 2015. Then, the relationship between three mutation strategies and fitness landscape features is trained by random forest (RF) offline. Finally, the trained RF is used to predict which mutation strategy should be utilized to perform mutation operator for each problem during the evolutionary process. Besides, a historical memory parameter adaption mechanism and population size linear reduction are applied to the FLDE. The CEC2017 benchmark set is utilized to perform the experiments, and five well-known DE variant algorithms are compared with the FLDE algorithm. The experimental results attest that the proposed FLDE algorithm is highly competitive with the other five DE algorithms.

The idea of hybrid algorithms is formed due to the functional and structural differences in optimization algorithms. The goal is to create hybrid algorithms that can combine the strengths of the optimization algorithms to perform better in solving different problems. The Emperor Penguins Colony (EPC) algorithm is a population-based and nature-inspired optimization algorithm. This algorithm is powerful in finding global optima. In this paper, the standard EPC is improved by combining with genetic operators to finding better global optima. The genetic crossover and mutation operators have been used for modifying the decision vectors. These operators can cause a balance between exploration and exploitation. The balance between exploration and exploitation is effective in achieving a better optimal solution. The proposed algorithm called Hybrid-EPC is compared with GA, PSO, standard EPC, and Hybrid-PSO and tested on 20 various benchmark test functions. Also as an application, the proposed Hybrid-EPC algorithm is used for community detection in complex networks. For this purpose, the algorithm is tested on four social datasets and is compared with other community detection algorithms. The results show that this hybridization improves the standard EPC algorithm and has been successful in community detection.

This paper considers a passive target localization problem based on the noisy time of arrival measurements obtained from multiple receivers and a single transmitter. The maximum likelihood (ML) estimator for this localization problem is formulated as a highly nonlinear and non-convex optimization problem, where conventional optimization methods are not suitable for solving such a problem. Consequently, this paper proposes an improved adaptive hybrid firefly differential evolution (AHFADE) algorithm, based on hybridization of firefly algorithm (FA) and differential evolution (DE) algorithm to estimate the unknown position of the target. The proposed AHFADE algorithm dynamically adjusts the control parameters, thus maintaining high population diversity during the evolution process. This paper aims to improve the accuracy of the global optimal solution by incorporating evolutionary operators of the DE in different searching stages of the FA. In this regard, an adaptive parameter is employed to select an appropriate mutation operator for achieving a proper balance between global exploration and local exploitation. In order to efficiently solve the ML estimation problem, this paper proposes the well-known semidefinite programming (SDP) method to convert the non-convex problem into a convex one. The simulation results obtained from the proposed AHFADE algorithm and well-known algorithms, such as SDP, DE and FA, are compared against Cramer–Rao lower bound (CRLB). The statistical analysis has been performed to compare the performance of the proposed AHFADE algorithm with several well-known algorithms on CEC2014 benchmark problems. The obtained simulation results show that the proposed AHFADE algorithm is more robust in high-noise environments compared to existing algorithms.

The selection of the mutation strategy for differential evolution (DE) algorithm plays an important role in the optimization performance, such as exploration ability, convergence accuracy and convergence speed. To improve these performances, an improved differential evolution algorithm with neighborhood mutation operators and opposition-based learning, namely NBOLDE, is developed in this paper. In the proposed NBOLDE, the new evaluation parameters and weight factors are introduced into the neighborhood model to propose a new neighborhood strategy. On this basis, a new neighborhood mutation strategy based on DE/current-to-best/1, namely DE/neighbor-to-neighbor/1, is designed in order to replace large-scale global mutation by local neighborhood mutation with high search efficiency. Then, a generalized opposition-based learning is employed to optimize the initial population and select the better solution between the current solution and reverse solution in order to approximate global optimal solution, which can amend the convergence direction, accelerate convergence, improve efficiency, enhance the stability and avoid premature convergence. Finally, the proposed NBOLDE is compared with four state-of-the-art DE variants by 12 benchmark functions with low-dimension and high-dimension. The experiment results indicate that the proposed NBOLDE has a faster convergence speed, higher convergence accuracy, and better optimization capabilities in solving high-dimensional complex functions.

The entire world is under the existential health emergency: the spread of a contagious corona virus. Since this pandemic can be classified as moderate, mild and high risk. But the same method is th...

The paper gives an optimization model named multiple bottleneck traveling salesmen problem (MBTSP), which can model the optimization problems where there are multiple salesmen and tasks. In intelligent transport systems and multiple tasks cooperation, some real-world problems can be modeled by MBTSP, the scale of constructed model usually tends to multiple scales, therefore it is significant to study multiple scales MBTSP and its solving algorithms. The relevant literatures have proved that genetic algorithm and its versions can show good performance for the variants of TSP, thus this paper proposes a novel hybrid genetic algorithm (VNSGA) with variable neighborhood search (VNS) for multi-scale MBTSP. For VNSGA, the feasible solutions are constructed by dual-chromosome coding, then they are updated by the crossover operator, mutation operator and variable neighborhood search. During this process, the VNS can be carried out by the deleting and reinserting operator of the cities for optimization. The experiments show that VNSGA can demonstrate better solution quality than the state-of-the-art algorithms for MBTSP problem.

The k-means problem is one of the most popular models of cluster analysis. The problem is NP-hard, and modern literature offers many competing heuristic approaches. Sometimes practical problems require obtaining such a result (albeit notExact), within the framework of the k-means model, which would be difficult to improve by known methods without a significant increase in the computation time or computational resources. In such cases, genetic algorithms with greedy agglomerative heuristic crossover operator might be a good choice. However, their computational complexity makes it difficult to use them for large-scale problems. The crossover operator which includes the k-means procedure, taking the absolute majority of the computation time, is essential for such algorithms, and other genetic operators such as mutation are usually eliminated or simplified. The importance of maintaining the population diversity, in particular, with the use of a mutation operator, is more significant with an increase in the data volume and available computing resources such as graphical processing units (GPUs). In this article, we propose a new greedy heuristic mutation operator for such algorithms and investigate the influence of new and well-known mutation operators on the objective function value achieved by the genetic algorithms for large-scale k-means problems. Our computational experiments demonstrate the ability of the new mutation operator, as well as the mechanism for organizing subpopulations, to improve the result of the algorithm.

In this paper, a heterogeneous comprehensive learning and dynamic multi-swarm particle swarm optimizer with two mutation operators (HCLDMS-PSO) is presented. In addition, a comprehensive learning (CL) strategy with the global optimal experience of the whole population is conducted to generate an exploitation subpopulation exemplar. However, a modified dynamic multi-swarm (DMS) strategy is specially designed to construct the exploration subpopulation exemplar. In the canonical DMS strategy, it is unfavorable for different sub-swarms to use the same linear decreasing inertia weight parameter. We first propose classifying the DMS sub-swarms at the search level and then constructing a novel nonlinear adaptive decreasing inertia weight for different sub-swarms, introducing a non-uniform mutation operator to enhance its exploration capability. Finally, the gbest of the whole population also adopts a Gaussian mutation operator to avoid falling into the local optimum. The particles of the two subpopulations will update their velocity independently without crippling one another to prevent a loss of diversity. The performance of HCLDMS-PSO is compared with those of 8 other PSO variants and 11 evolutionary algorithms on two classical benchmark optimization problems and a real-world engineering problem. Experimental results demonstrate that the HCLDMS-PSO improves the convergence speed, accuracy, and reliability on most optimization problems.

In this paper, a comprehensive empirical study is conducted to evaluate the performance of a new real-coded crossover operator called Fisk crossover (FX) operator. The basic aim of the proposed study is to preserve population diversity as well as to avoid local optima. In this context, a new crossover operator is designed and developed which is linked with Log-logistic probability distribution. For its global performance, a realistic comparison is made between FX versus double Pareto crossover (DPX), Laplace crossover (LX), and simulated binary crossover (SBX) operators. Moreover, these crossover operators are also used in conjunction with three mutation operators called power mutation (PM), Makinen, Periaux, and Toivanen mutation (MPTM), and nonuniform mutation (NUM) for inclusive evaluation. The performance of probabilistic-based algorithms is tested on a set of twenty-one well-known nonlinear optimization benchmark functions with diverse features. The empirical results show a substantial dominance of FX over other crossover operators with authentication of performance index (PI). Moreover, we also examined the significance of the proposed crossover scheme by administrating ANOVA and Gabriel pairwise multiple comparison test. Finally, the statistically significant results of the proposed crossover scheme have a definite edge over the other schemes, and it is also expected that FX has a great potential to solve complex optimization problems.

Regression tasks aim to determine accurate and simple relationship expressions between variables, which can be regarded as bi-objective optimization problems. As GP (genetic programming) can use expression trees as representation, it is popularly-used for regression. Introducing multi-objective techniques into GP enables it to solve bi-objective tasks, and the success of memetic algorithms show the importance of local search in improving GP. However, existing memetic GP methods are mainly single-objective, in which the local search operators cannot be applied in multi-objective optimization. Moreover, the popularly-used solution evaluation mechanism (Pareto local search) in existing multi-objective memetic methods cannot assure solution dispersion. To handle these problems, a dispersion-keeping Pareto evaluation (DkPE) mechanism is proposed, based on which new crossover and mutation operators adaptive to bi-objective GP are designed. In addition, two base bi-objective GP methods (NSGP (non-dominated sorting GP) and SPGP (strength Pareto GP)) are developed. Applying the new operators in them respectively forms two bi-objective memetic GP methods (MNSGP (memetic NSGP) and MSPGP (memetic SPGP)). Results show that MNSGP and MSPGP outperform NSGP and SPGP respectively, which reflects that DkPE based crossover/mutation increase the performance of NSGP and SPGP. Moreover, solutions evolved by MNSGP outperform reference GP and non-GP based methods.

This paper addresses the job shop scheduling problem including time lag constraints. This is an extension of the job shop scheduling problem with many applications in real production environments, where extra (minimum and maximum) delays can be introduced between successive operations of the same job. It belongs to a category of problems known as NP-hard problem due to large solution space. Biogeography-based optimization is an evolutionary algorithm which is inspired by the migration of species between habitats, recently proposed by Simon in 2008 to optimize hard combinatorial optimization problems. We propose a hybrid biogeography-based optimization (HBBO) algorithm for solving the job shop scheduling problem with additional time lag constraints with minimization of total completion time. In the proposed HBBO, the effective greedy constructive heuristic is adapted to generate the initial population of habitat. Moreover, a local search metaheuristic is investigated in the mutation step in order to ameliorate the solution quality and enhance the diversity of the population. To assess the performance of HBBO, a series of experiments on well-known benchmark instances for job shop scheduling problem with time lag constraints is performed.

Based on the algorithm structure, each metaheuristic algorithm may have its pros and cons, which may result in high performance in some problems and low functionality in some others. The idea is to hybridize two or more algorithms to cover each other’s weaknesses. In this study, particle swarm optimization (PSO), simulated annealing (SA) and differential evolution (DE) are combined to develop a more powerful search algorithm. First, the temperature concept of SA is applied to balance the exploration/exploitation capability of the hybridized algorithm. Then, the DE’s mutation operator is used to improve the exploration capability of the algorithm to escape the local minimums. Next, DE’s mutation operator has been modified so that past experiences can be used for smarter mutations. Finally, the PSO particles’ tendency to their local optimums or the global optimum, which balances the algorithm’s random and greedy search, is affected by the temperature. The temperature influences the algorithm’s behavior so that the random search is more significant at the beginning, and the greedy search becomes more important as the temperature is reduced. The results are compared with the basic PSO, SA, DE, cuckoo search (CS), and hybridized CS-PSO algorithm on 20 benchmark problems. The comparison reveals that, in most cases, the new algorithm outperforms others.

Aviation control software has become the core control decision-making unit of the aviation system. The Boolean conditional expressions are the main parts of the branch and loop control logic of aviation control software. This paper studies the fault classification and repair method of conditional expression of aviation control software. 1) a two-level Boolean conditional expression fault classification method is proposed; 2) based on the design of mutation operator, repair solution and stop condition of mutation repair, an automatic repair method of conditional expression is proposed; 3) a repair assistant tool for conditional expression is designed and implemented, and 155 fault expressions are repaired. The results show that 55.5% of fault expressions can achieve accurate repair, 44.5% of fault expressions can generate multiple correct versions after a repair, and some versions have operation redundancy, so it is necessary to select the optimal version manually.

Constrained multi-objective optimization problems (CMOPs) are common in engineering design fields. To solve such problems effectively, this paper proposes a new differential evolution variant named IMDE with infeasible-guiding mutation operators and a multistrategy technique. In IMDE, an infeasible solution with lower objective values is maintained for each individual in the main population, and this infeasible solution is then incorporated into some common differential evolution’s mutation operators to guide the search toward the region with promising objective values. Moreover, multiple mutation strategies and control parameters are adopted during the trial vector generation procedure to enhance both the convergence and the diversity of differential evolution. The superior performance of IMDE is validated via comparisons with some state-of-the-art constrained multi-objective evolutionary algorithms over 3 sets of artificial benchmarks and 4 widely used engineering design problems. The experiments show that IMDE outperforms other algorithms or obtains similar results. It is an effective approach for solving CMOPs, basically due to the use of infeasible-guiding mutation operators and multiple strategies.

This paper describes a permutational-based Differential Evolution algorithm implemented in a wrapper scheme to find a feature subset to be applied in the construction of a near-optimal classifier. In this approach, the relevance of a feature chosen to build a better classifier is represented through its relative position in an integer-valued vector, and by using a permutational-based mutation operator, it is possible to create new feasible candidate solutions only. Furthermore, to provide a controlled diversity rate in the population, a straightforward repair-based recombination operator is utilized to evolve a population of candidate solutions. Unlike the other approaches in the existing literature using integer-valued vectors and requiring a predefined subset size, in this approach, this size is determined by an additional element included in the encoding scheme, allowing to find an adequate feature subset size to each specific dataset. Experimental results show that this approach is an effective way to create more accurate classifiers as they are compared with those obtained by other similar approaches.

Feature selection is one of the hottest machine learning topics in recent years. The main purposes of it are to simplify the original model, improve the readability of the model, and prevent over-fitting by searching for a suitable subset of features. There are many methods for this problem, including evolutionary algorithms and particle swarm optimization. Among them, the competitive swarm optimizer is a new optimization algorithm proposed in recent years, which is based on particle swarm optimization algorithm, and has achieved good results in high-dimensional feature selection problems, but it also has the problems of high computation time cost and easily being premature. Aiming at these problems, this paper proposes to add the crossover operator and mutation operator in the genetic algorithm to the competitive swarm optimization, so as to improve the generation speed of new individuals in the algorithm and prevent premature population. After testing on UC Irvine Machine Learning Repository, the new algorithm not only improves the computational efficiency, but also avoids the problem that the competitive swarm optimization algorithm is easy to fall into the local optimum, which greatly improves the calculation effect.

Arising from the need of all time for optimization of irrigation systems, distribution network and cable network, Clustered Shortest-Path Tree Problem (CluSPT) has been attracting a lot of attention and interest from the research community. On the other hand, the Multifactorial Evolutionary Algorithm (MFEA) is one of the most recently exploited realms of Evolutionary Algorithms (EAs) and its performance in solving optimization problems has been very promising. Considering these characteristics, this paper describes a new approach using the MFEA for solving the CluSPT. The MFEA has two tasks: the goal of the first task is to determine the best tree (w.r.t. cost minimization) which envelops all vertices of the CluSPT while the goal of the second task is to find the fittest solution possible for the problem. The purpose of the second task is to find good materials for implicit genetic transfer process in MFEA to improve the quality of CluSPT. To apply this new algorithm, a decoding scheme for deriving individual solutions from the unified representation in the MFEA is also introduced in this paper. Furthermore, evolutionary operators such as population initialization, crossover and mutation operators are also proposed. These operators are applicable for constructing valid solution from both sparse and complete graph. Although the proposed algorithm is slightly complicated for implementation, it can enhance ability to explore and exploit the Unified Search Space (USS). To prove this increment in performance i.e, to assess the effectiveness of the proposed algorithm and methods, the authors implemented them on both Euclidean and Non-Euclidean instances. Experiment results show that the proposed MFEA outperformed existing heuristic algorithms in most of the test cases. The impact of the proposed MFEA was analyzed and a possible influential factor that may be useful for further study was also pointed out.

Feature selection is an important data preprocessing method. This paper studies a new multi-objective feature selection approach, called the Binary Differential Evolution with self-learning (MOFS-BDE). Three new operators are proposed and embedded into the MOFS-BDE to improve its performance. The novel binary mutation operator based on probability difference can guide individuals to rapidly locate potentially optimal areas, the developed One-bit Purifying Search operator (OPS) can improve the self-learning capability of the elite individuals located in the optimal areas, and the efficient non-dominated sorting operator with crowding distance can reduce the computational complexity of the selection operator in the differential evolution. Experimental results on a series of public datasets show that the effective combination of the binary mutation and OPS makes our MOFS-BDE achieve a trade-off between local exploitation and global exploration. The proposed method is competitive in comparison with some representative genetic algorithm-, particle swarm-, differential evolution-, and artificial bee colony-based feature selection algorithms.

This paper introduces an analysis by suggesting three types of modification to an existing well known algorithm for optimization i.e. Cat swarm optimization. The motivation behind the proposed modification is to provide a superior convergence along with the production of finer results in diverse real world applications. The first modification introduces a modified weight factor by the replacement of traditional weight factor in the original algorithm. In the second proposed modification, a versatile mutation process i.e. sobol mutation operator is embedded in the execution process of cat swarm optimization for further enhancement in the performance of the optimization technique. The third proposed modification uses the sobol mutation operator with the modified version weighted cat swarm optimization algorithm. This paper provides a detailed analysis of the three proposed techniques for establishing the superiority over the traditional algorithm. Standard benchmark functions are used in this paper for analysing the effectiveness of the modification proposals. The third proposed modification combines the best feature of both the first and second modifications and compensates the disadvantages to some extent. This third modified version provides the best results in almost all categories of functions along with higher precision. Moreover, all the modifications are providing superior results in comparison to the standard cat swarm algorithm, but the weighted cat swarm optimization algorithm with sobol mutation is dominating in all the cases.

Recently, the ear biometric has received much attention for human recognition due to its unique shape and rich local features. However, extracting discriminative features from ear images is a crucial task in presence of illumination changes, low contrast, noise, and pose variations. With the aim of neutralizing the effect of these factors, this paper proposes an automatic enhancement technique using meta-heuristic optimization to enhance the ear images. Here, we modified a recent and simple yet meta-heuristic optimization technique known as Jaya algorithm by introducing a mutation operator to enhance the ear images in few iterations and the proposed approach is named as enhanced Jaya algorithm. Then, we employed a pose-invariant local feature extractor, SURF to extract local features. Finally, the k-NN classifier has used to evaluate the rate of correct identification. Extensive experiments are conducted on four standard datasets and the performance evaluation is carried out by qualitative and quantitative measures. Experimental results clearly indicate the proposed enhancement approach is competitive as compared to two classical methods HE, CLAHE, and two meta-heuristic algorithms PSO and DE-based image enhancement techniques.

In conventional differential evolutionary (DE) algorithm, mutation operator has significant influence on generating new vectors by mixing existing target vectors randomly selected from the current population. Recently, many mutation operators, which usually employ the best individual or some high-quality individuals randomly chosen, have been proposed to improve searching capability. However, such designs may easily suffer from premature convergence trapped by local optima. To make a trade-off between exploration and exploitation capability, this paper proposes a novel collective intelligence (CI)-based mutation operator, which is named as “current-to-sa-ci-best.” In the presented mutation operator, the evolutionary information of m best target vectors is linearly combined to generate new mutant vectors. Besides, m is designed as an exponential-distributed random number which could be self-adapted based on successful records of m values alongside evolution. Moreover, this mutation operator could be applied to any DE algorithm without destroying existing search capability by adding a greedy selection operator. To verify its effectiveness, the proposed CI-based mutation strategy, which is named as SaCI, was embedded into some state-of-the-art DE variants on 28 CEC2013 benchmark functions. Numerical results have confirmed that the SaCI operator may be beneficial to DEs to some extent.

Differential search (DSA) is a recently proposed evolutionary algorithm mimicking the Brownian motion-like random movement existing in living beings. Though it has displayed promise for global optimization, the original DSA suffers from relatively poor search capability, especially for exploitation. In this study, an augmented DSA (ADSA) is proposed by integrating memetic framework with multiple strategies. In ADSA, a sub-gradient strategy is combined to improve local exploitation, and the dynamic Levy flight technique is developed to strengthen the global exploration. Moreover, a mutation operator based on differential search is used to increase swarm diversity. An intelligent selection method is implemented to adaptively adjust the strategies based on historical performance. To fully benchmark the proposed algorithm, 35 test functions of various properties in 30-D and 100-D are adopted in numerical experiments. Seven canonical optimization algorithms are involved for experimental comparison. In addition, two real-world problems are also tested to verify ADSA’s practical applicability. Numerical results reveal the efficiency and effectiveness of ADSA.

To improve the disassembly efficiency, cooperative disassembly is essential for complex products. Operator task allocation is a significant challenge for cooperative disassembly sequence planning; however, it has not been studied previously to the best of our knowledge. To deal with this problem, a novel cooperative disassembly sequence and task planning (CDS&TP) method was proposed based on the genetic algorithm. A mathematical model of the CDS&TP problem was constructed based on the product’s disassembly hybrid graph model (DHGM). Focusing on the characteristics of the CDS&TP, a multi-layer chromosome coding method was proposed to describe the node layer and operator constraint layer. Thus, the initial population could be deduced through the node layer and operator constraints relationship rule model, which was proposed to construct the operator constraint and node layers. To obtain the task sequence of each operator and the disassembly time of each sequence, a chromosome fitness calculation formula was presented based on the disassembly set, which is the collection of all of the detachable nodes with a disassembly priority higher than the node. The chromosome evolution rules, such as the selection, crossover, and mutation operators, were redesigned to obtain the (approximate) optimal multiplayer cooperative disassembly sequences and task planning. Finally, a case study was proposed to validate the method.

Synthetic biology is currently involved in improving the expression levels of proteins. A preeminent strategy herein is to encode multiple copies of the same amino acid sequence (protein) and integrate these copies into the genome of an organism. However, this is a challenging task. First, the different protein-coding sequences (CDSs) should be as different as possible to avoid homologous recombination. The second challenge lies in the fact that some synonymous codons are better adapted than others. Therefore, the best adapted synonymous codons should be employed if possible. These two challenges are conflicting and multi-objective optimization has to be consequently used. For this purpose, we design and implement a Multi-Objective Variable Neighborhood Search (MOVNS) algorithm with new problem-aware mutation operators. Following the related work, we initially define the multi-objective problem based on three optimization objectives. However, after the first experiments, we realize that one of the objectives can be discarded, simplifying the problem without degrading the solutions’ quality. The obtained results confirm the attainment of statistically significant improvements in comparison to related works.

Deep Learning (DL) solutions are increasingly adopted, but how to test them remains a major open research problem. Existing and new testing techniques have been proposed for and adapted to DL systems, including mutation testing. However, no approach has investigated the possibility to simulate the effects of realDL faults by means of mutation operators. We have defined 35 DL mutation operators relying on 3 empirical studies about real faults in DL systems.We followed a systematic process to extract the mutation operators from the existing fault taxonomies, with a formal phase of conflict resolution in case of disagreement.We have implemented 24 of these DL mutation operators into DeepCrime, the first source-level pre-training mutation tool based on real DL faults. We have assessed our mutation operators to understand their characteristics: whether they produce interesting, i.e., killable but not trivial, mutations.Then, we have compared the sensitivity of our tool to the changes in the quality of test data with that of DeepMutation++, an existing post-training DL mutation tool.&nbsp

Knapsack problem with a single continuous variable (KPC) is a natural extension of the standard 0-1 knapsack problem. In the KPC, the capacity of the knapsack is not fixed, so it becomes more difficult to solve. Although several metaheuristics have been proposed to solve the KPC, their performances are not stable enough. This paper proposes a hybrid ant colony optimization (HACO) algorithm to solve the KPC. In the HACO algorithm, a simplified ACO algorithm is designed to search the optimal subset of items, and the mutation operator of differential evolution algorithm is used to search the optimal value of continuous variable. The parameter of the mutation operator is adaptively configured via an ACO algorithm. In the simplified ACO algorithm, an independent selection strategy and a pheromone-based selection strategy are designed to speed up the algorithm and simplify the tuning of parameters respectively. Personal best solutions constructed by each ant are used to deposit pheromone. Furthermore, a value-based greedy optimization strategy is introduced to enhance the solutions. The HACO algorithm is experimentally analyzed on 40 KPC instances. The experimental results show that the HACO algorithm is better than other competitors in terms of obtaining the best solution and the mean solution.

Most evolutionary algorithms have parameters, which allow a great flexibility in controlling their behavior and adapting them to new problems. To achieve the best performance, it is often needed to control some of the parameters during optimization, which gave rise to various parameter control methods. In recent works, however, similar advantages have been shown, and even proven, for sampling parameter values from certain, often heavy-tailed, fixed distributions. This produced a family of algorithms currently known as "fast evolution strategies" and "fast genetic algorithms". However, only little is known so far about the influence of these distributions on the performance of evolutionary algorithms, and about the relationships between (dynamic) parameter control and (static) parameter sampling. We contribute to the body of knowledge by presenting, for the first time, an algorithm that computes the optimal static distributions, which describe the mutation operator used in the well-known simple $(1+\lambda)$ evolutionary algorithm on a classic benchmark problem OneMax. We show that, for large enough population sizes, such optimal distributions may be surprisingly complicated and counter-intuitive. We investigate certain properties of these distributions, and also evaluate the performance regrets of the $(1+\lambda)$ evolutionary algorithm using commonly used mutation distributions., Comment: Submitted for review to GECCO'21

In silico evolutionary optimization of cancer treatment based on multiple nano-particle (NP) assisted drug delivery systems was investigated in this study. The use of multiple types of NPs is expected to increase the robustness of the treatment, due to imposing higher complexity on the solution tackling a problem of high complexity, namely the physiology of a tumor. Thus, the utilization of metameric representations in the evolutionary optimization method was examined, along with suitable crossover and mutation operators. An open-source physics-based simulator was utilized, namely PhysiCell, after appropriate modifications, to test the fitness of possible treatments with multiple types of NPs. The possible treatments could be comprised of up to ten types of NPs, simultaneously injected in an area close to the cancerous tumour. Initial results seem to suffer from bloat, namely the best solutions discovered are converging towards the maximum amount of different types of NPs, however, without providing a significant return in fitness when compared with solutions of fewer types of NPs. As the large diversity of NPs will most probably prove to be quite toxic in lab experiments, we opted for methods to reduce the bloat, thus, resolve to therapies with fewer types of NPs. Namely, the bloat control methods studied here were removing types of NPs from the optimization genome as part of the mutation operator and applying parsimony pressure in the replacement operator. By utilizing these techniques, the treatments discovered are composed of fewer types of NPs, while their fitness is not significantly smaller.

With recent advancements in data collection tools and the widespread use of intelligent information systems, a huge amount of data streams with lots of redundant, irrelevant, and noisy features are collected and a large number of features (attributes) should be processed. Therefore, there is a growing demand for developing efficient Feature Selection (FS) techniques. Gravitational Search algorithm (GSA) is a successful population-based metaheuristic inspired by Newton’s law of gravity. In this research, a novel GSA-based algorithm with evolutionary crossover and mutation operators is proposed to deal with feature selection (FS) tasks. As an NP-hard problem, FS finds an optimal subset of features from a given set. For the proposed wrapper FS method, both K-Nearest Neighbors (KNN) and Decision Tree (DT) classifiers are used as evaluators. Eighteen well-known UCI datasets are utilized to assess the performance of the proposed approaches. In order to verify the efficiency of proposed algorithms, the results are compared with some popular nature-inspired algorithms (i.e. Genetic Algorithm (GA), Particle Swarm Optimizer (PSO), and Grey Wolf Optimizer (GWO)). The extensive results and comparisons demonstrate the superiority of the proposed algorithm in solving FS problems.

Many-objective optimization problems abbreviated as MaOPs with more than three objectives have attracted increasing interests due to their widely existing in a variety of real-world applications. This paper presents a novel many-objective population extremal optimization called MaOPEO-HM algorithm for MaOPs by introducing a reference set based many-objective optimization mechanism into a recently developed population extremal optimization framework and designing an adaptive hybrid mutation operation for updating the population. Despite of the successful applications of extremal optimization in different kinds of numerical and engineering optimization problems, it has never been explored to the many-objective optimization domain so far. Because most of the existing many-objective evolutionary algorithms are usually guided by a single mutation operation, which has insufficient ability to exploit the search space of MaOPs and will get stuck at any local efficient front, it is the first attempt to design a novel hybrid mutation scheme in MaOPEO-HM algorithm by combining the advantages of polynomial mutation operator and multi-non-uniform mutation operator effectively. The experiment results for DTLZ test problems with 3, 5, 8, 10, and 15 objectives and WFG test problems with 3, 5, and 8 objectives have demonstrated the superiority of the proposed MaOPEO-HM to five state-of-the-art decomposition-based many-objective evolutionary algorithms including NSGA-III, RVEA, EFR-RR, θ-DEA, and MOEA/DD and two non-decomposition-based algorithms including GrEA and Two_Arch2. Furthermore, the great ability of the designed adaptive hybrid mutation operation incorporated into many-objective population extremal optimization (MaOPEO) has also been illustrated by comparing MaOPEO-HM and two MaOPEO algorithms only based on traditional multi-non-uniform mutation or polynomial mutation for DTLZ problems.

Biogeography-Based Optimization (BBO), a good meta-heuristic optimization algorithm, has drawn much attention and been applied widely to many areas. However, BBO can not do well in solving some complex and diversified optimization problems. In order to obtain an algorithm with better optimization performance, this paper presents a hybrid BBO with Shuffled Frog Leaping Algorithm (SFLA), named HBBOS. Firstly, we improve BBO. BBO's mutation operator is got rid of and its migration operator is improved. Two novel updating mechanisms, i.e. a hybrid cross mechanism and a hybrid disturbance mechanism, are introduced instead of the original migration mechanism to update the immigration habitats' Suitability Index Variables (SIVs) and non-immigration habitats' SIVs, respectively. A differential mechanism is also introduced to prevent the algorithm from falling into local optima to some degree. These improvements can enhance exploration and exploitation and balance them. Secondly, we merge the improved migration operator into SFLA's group structure framework. This can balance exploration and exploitation further. So HBBOS is obtained. HBBOS can effectively maximize the two algorithms' advantages and minimize the defects so that it can obtain better optimization performance. A large number of experiments are made on benchmark functions with various types and complexities, such as a set of classic functions and CEC2014 test set. HBBOS is also applied to minimum spanning tree problems. The experimental results show that HBBOS outperforms quite a few state-of-the-art algorithms.

Outbound container storage location assignment problem (OCSLAP) could be defined as how a series of outbound containers should be stacked in the yard according to certain assignment rules so that the outbound process could be facilitated. Considering the NP-hard nature of OCSLAP, a novel particle swarm optimization (PSO) method is proposed. The contributions of this paper could be outlined as follows: First, a neighborhood-based mutation operator is introduced to enrich the diversity of the population to strengthen the exploitation ability of the proposed algorithm. Second, a mechanism to transform the infeasible solutions into feasible ones through the lowest stack principle is proposed. Then, in the case of trapping into the local solution in the search process, an intermediate disturbance strategy is implemented to quickly jump out of the local solution, thereby enhancing the global search capability. Finally, numerical experiments have been done and the results indicate that the proposed algorithm achieves a better performance in solving OCSLAP.

The paper gives an applicable model called colored balanced traveling salesman problem (CBTSP), it is utilized to model optimization problems with partially overlapped workspace such as the scheduling and deploying of the resources and goods. CBTSP is NP-hard problem, the traditional nature-inspired algorithms, such as genetic algorithm (GA), hill-climbing GA and simulated annealing GA, are easy to fall into local optimum. In order to improve it, the paper proposes a novel genetic algorithm (NGA) based on ITO process to solve CBTSP. First of all, NGA utilizes the dual-chromosome coding to represent solution of this problem, and then updates the solution by the crossover and mutation operator. During the process of crossover operator, the length of crossover can be affected by activity intensity, which is directly proportional to environmental temperature and inversely proportional to particle radius. The experiments verify that NGA can demonstrate better solution quality than the compared algorithms for large scale CBTSP.

There is an ongoing evolution involving a new approach to large-scale optimisations based on co-evolutionary searches using interacting heterogeneous agent-processes via the implementation of synchronised genetic algorithms with local populations. The individualisation of heuristic operators at the level of agent-processes that implement independent evolutionary searches facilitate the improved likelihood of obtaining the best solutions in the fastest time. Based on this property, a parallel multi-agent single-objective real-coded genetic algorithm for large-scale constrained black-box single-objective optimisations ( L S O P s ) is proposed. This facilitates the effective frequency exchange of the best potential decisions between interacting agent-processes with individual parameters, such as types of crossover and mutation operators with their own characteristics. We have improved the quality of both solutions and the time-efficiency of a multi-agent real-coded genetic algorithm ( M A − R C G A ). A novel framework was developed that represents the aggregation of M A − R C G A with simulation models by implementing a set of objective functions for real-world large-scale optimisation problems such as the simulation model of the ecological-economics system implemented in the AnyLogic tool.

The quantum particle swarm optimization algorithm is a global convergence guarantee algorithm. Its searching performance is better than the original particle swarm optimization algorithm (PSO), but the control parameters are less and easy to fall into local optimum. The paper proposed teamwork evolutionary strategy for balance global search and local search. This algorithm is based on a novel learning strategy consisting of cross-sequential quadratic programming and Gaussian chaotic mutation operators. The former performs the local search on the sample and the interlaced operation on the parent individual while the descendants of the latter generated by Gaussian chaotic mutation may produce new regions in the search space. Experiments performed on multimodal test and composite functions with or without coordinate rotation demonstrated that the population information could be utilized by the TEQPSO algorithm more effectively compared with the eight QSOs and PSOs variants. This improves the algorithm performance, significantly.

WOS:000464822300001 Recent trend of research is to hybridize two and more metaheuristics algorithms to obtain superior solution in the field of optimization problems. This paper proposes a newly developed wrapper-based feature selection method based on the hybridization of Biogeography Based Optimization (BBO) and Sine Cosine Algorithm (SCA) for handling feature selection problems. The position update mechanism of SCA algorithm is introduced into the BBO algorithm to enhance the diversity among the habitats. In BBO, the mutation operator is got rid of and instead of it, a position update mechanism of SCA algorithm is applied after the migration operator, to enhance the global search ability of Basic BBO. This mechanism tends to produce the highly fit solutions in the upcoming iterations, which results in the improved diversity of habitats. The performance of this Improved BBO (IBBO) algorithm is investigated using fourteen benchmark datasets. Experimental results of IBBO are compared with eight other search algorithms. The results show that IBBO is able to outperform the other algorithms in majority of the datasets. Furthermore, the strength of IBBO is proved through various numerical experiments like statistical analysis, convergence curves, ranking methods, and test functions. The results of the simulation have revealed that IBBO has produced very competitive and promising results, compared to the other search algorithms.

This paper presents a novel differential evolution algorithm for numerical optimization by designing the neighborhood-based mutation strategy and adaptive evolution mechanism. In the proposed strategy, two novel neighborhood-based mutation operators and an individual-based selection probability are developed to adjust the search performance of each individual suitably. Meanwhile, the evolutionary dilemmas of the neighborhood are identified by tracking its performance and diversity, and alleviated by designing a dynamic neighborhood model and two exchanging operations in the proposed mechanism. Furthermore, the population size is adaptively adjusted by a simple reduction method. Differing from differential evolution variants based on neighborhood and evolutionary state, the proposed algorithm makes full use of the characteristics of individuals, identifies and alleviates the neighborhood evolutionary dilemmas of each individual. Compared with 21 typical algorithms, the numerical results on 30 benchmark functions from CEC2014 show that the proposed algorithm is reliable and has better performance.

Differential evolution (DE) is a simple yet powerful evolutionary algorithm for numerical optimization. However, the performance of DE significantly relies on its mutation operator and control parameters (scaling factor and crossover rate). In this paper, we propose a novel DE variant by introducing a series of combined strategies into DE, called CSDE. Specifically, in CSDE, to obtain a proper balance between global exploration ability and local exploitation ability, we adopt two mutation operators with different characteristics to produce the mutant vector, and provide a mechanism based on their own historical success rate to coordinate the two adopted mutation operators. Moreover, we combine a periodic function based on one modulo operation, an individual-independence macro-control function and an individual-dependence function based on individual’s fitness value information to adaptively produce scaling factor and crossover rate. To verify the effectiveness of the proposed CSDE, comparison experiments contained seven other state-of-the-art DE variants are tested on a suite of 30 benchmark functions and four real-world problems. The simulation results demonstrate that CSDE achieves the best overall performance among the eight DE variants.

The problem of bi-level optimization has always been a hot topic due to its extensive application. Increasing size and complexity have prompted theoretical and practical interest in the design of effective algorithm. This paper adopts particle swarm algorithm (PSO) at both level. First, given the nested nature of bi-level problem, we introduce a hyper-sphere search into PSO as mutation operator to maintain the swarms diversity. Second, for complex constraints processing, the proposed algorithm adopts a dynamic constraint handling strategy, which makes the solution located on the constraint boundary easier to be obtained. Third, a quadratic approximation mutation is introduced into PSO, which guides particles to a better search area. Finally, the convergence is proved and the simulation results show that the proposed algorithm is effective.

A decomposition-based multi-objective evolutionary algorithm with a differential evolution variation operator (MOEA/D-DE) shows high performance on challenging multi-objective problems (MOPs). The DE mutation consists of three key components: a mutation strategy, an index selection method for parent individuals, and a bound-handling method. However, the configuration of the DE mutation operator that should be used for MOEA/D-DE has not been thoroughly investigated in the literature. This configuration choice confuses researchers and users of MOEA/D-DE. To address this issue, we present a review of the existing configurations of the DE mutation operator in MOEA/D-DE and systematically examine the influence of each component on the performance of MOEA/D-DE. Our review reveals that the configuration of the DE mutation operator differs depending on the source code of MOEA/D-DE. In our analysis, a total of 30 configurations (three index selection methods, two mutation strategies, and five bound handling methods) are investigated on 16 MOPs with up to five objectives. Results show that each component significantly affects the performance of MOEA/D-DE. We also present the most suitable configuration of the DE mutation operator, which maximizes the effectiveness of MOEA/D-DE., This is an accepted version of a paper published in Soft Computing

Due to the lack of global search capacity, most evolutionary or swarm intelligence based algorithms show their inefficiency when optimizing multi-modal problems. In this paper, we propose a grouping particle swarm optimizer (GPSO) to solve this kind of problem. In the proposed algorithm, the swarm consists of several groups. For every several iterations, an elite group is constructed and used to replace the worst one. The thought of grouping is helpful for improving the diversity of the solutions, and then enhancing the global search ability of the algorithm. In addition, we apply a simple mutation operator to the best solution so as to help it escape from local optima. The GPSO is compared with several variants of particle swarm optimizer (PSO) and some state-of-the-art evolutionary algorithms on CEC15 benchmark functions and three practical engineering problems. As demonstrated by the experimental results, the proposed GPSO outperforms its competitors in most cases.

A put wall is a hardware composed of containers that is usually used as a sorting station. In this study, the order picking operations, including order batching and picker routing, in a put wall based picking system is studied. Put walls usually have limited capacity and can accommodate only a part of received orders at a time. Hence, scheduling of the orders on the put wall should be considered along with the order batching and picker routing. For this, a mathematical formulation for order batching and picker routing in a put wall based picking system is proposed. To solve the problem, two genetic algorithms (GAs) with random shuffling and inverse–insert–swap mutation operators, a list-based simulated annealing (LBSA) and a hybrid GA–LBSA are proposed. To show the effectiveness of the proposed methods, their results are compared against the best solutions found by Gurobi 7.0. It is found that while for smaller size problems LBSA is a better choice in terms of solution quality, when CPU time is considered, depending on the problem size, GA and GA–LBSA might be the better options.

Birogul, Serdar/0000-0003-4966-5970 WOS: 000510021700004 Harri's Hawk Optimization (HHO) algorithm manifests as a new meta-heuristic algorithm in literature. When we look at studies that have used with this algorithm, we can see that its results in test functions and in the solutions of some test functions in IEEE Congress on Evolutionary Computation (CEC) are much better compared to other heuristic and meta heuristic algorithm results. In this study, an algorithm has been developed which has been hybridized with the mutation operators of Differential Evolution (DE) to further improve the HHO algorithm. This algorithm is named as Hybrid Harris Hawk Optimization based on Differential Evolution (HHODE). Performance of the proposed HHODE algorithm has been first compared with HHO and then compared with the results of other algorithms which have been most commonly used in the literature. In this comparison process, the most commonly used test functions in the literature and some of the other test functions in CEC2005 and CEC2017 as a new application field, have been solved. When the results of the comparison of HHODE with other algorithms are analyzed, it is observed that the balance between the exploratory tendency and exploitative tendency of the algorithm is well consistent. Formula 1 ranking method is used in the order of HHODE according to HHO and other algorithms. When a general evaluation of HHODE was performed, it was found to be an even more powerful algorithm as a result of the combination of strong features of both HHO and DE. The optimal power flow (OPF) problem is one of the most important problems of the modern power system. The HHODE algorithm is proposed to solve the OPF problem, which is considered without valve-point effect and prohibited zones (1) and with prohibited zones (2) in this paper. The effectiveness of the HHODE hybrid algorithm is tested on modified IEEE 30-bus test system. The result of HHODE algorithms are compared with other optimization algorithms in the literature.

Recently, multi-objective evolutionary algorithms (MOEAs) have been extensively used to solve multi-objective optimization problems (MOPs) since they have the ability to approximate a set of non-dominated solutions in reasonable CPU times. In this paper, we consider the bi-objective quadratic assignment problem (bQAP), which is a variant of the classical QAP, which has been extensively investigated to solve several real-life problems. The bQAP can be defined as having many input flows with the same distances between the facilities, causing multiple cost functions that must be optimized simultaneously. In this study, we propose a memetic algorithm with effective local search and mutation operators to solve the bQAP. Local search is based on swap neighborhood structure whereas the mutation operator is based on ruin and recreate procedure. The experimental results show that our bi-objective memetic algorithm (BOMA) substantially outperforms all the island-based variants of the PASMOQAP algorithm proposed very recently in the literature.

The differential evolution (DE) optimization algorithm predominantly relies on elite individuals and random difference to direct evolution. Although the strategy is clear and easy to implement, identifying a suitable direction for the DE mutation strongly depends on the direction information provided beforehand. To address this, we present a neighbor-induced mutation operator that simulates the neighbor-induced movement of Antarctic krill to guide the evolution direction in a natural manner. Additionally, center dispersion is proposed to disperse the population and redistribute individual positions to escape search stagnation, inspired by the spreading out of krill around newly discovered food. Comprising the new operator and the center dispersion pattern, this paper proposes a neighbor-induced DE algorithm with dispersion pattern (NDEd). The results of the comparative experiments verify the effectiveness of the neighbor-induced mutation operator and the dispersion pattern. Further, experimental results from 28 test functions of CEC2013 demonstrate that NDEd performs better compared to the other classic DE algorithms.

In recent years, there have been increasing reports of missing tourists around the world. The use of unmanned aerial vehicles (UAVs) can significantly improve the performance of search and rescue operations. However, planning the search paths of UAVs can be a highly complex optimization problem, and one of the most challenging tasks in the problem formulation is the estimation of target location probability distribution over time. This paper presents a problem of scheduling multiple UAVs to search for missing tourists and proposes a method for estimating tourist location probabilities which change with topographic features, weather conditions, and time. To solve the problem efficiently, we propose a hybrid evolutionary algorithm which consists of the main algorithm and a sub-algorithm. The main algorithm uses specific migration and mutation operators to evolve a population of main solutions, and the sub-algorithm combines a problem-specific heuristic and tabu search method to optimize each UAV path. The experimental results on a wide variety of test instances (including five real-world instances) demonstrate the performance advantages of the proposed method.

Logic minimization has recently attracted significant attention because in many applications it is important to have a compact representation as possible. In this paper, we propose a fast minimization algorithm (FMA) of fixed polarity Reed–Muller expressions (FPRMs). The main idea behind the FMA is to search the minimum FPRM with the fewest products by using the proposed binary differential evolution algorithm (BDE). The BDE can efficiently maintain population diversity and achieve a better tradeoff between the exploration and exploitation capabilities by use of proposed binary random mutation operator and improved selection operator. The experimental results on 24 MCNC benchmark circuits demonstrate that the FMA outperforms the genetic algorithm-based and simulated annealing genetic algorithm-based FPRMs minimization algorithms in terms of accuracy of solutions and solving efficiency. To the best of our knowledge, we are the first to use differential evolution algorithm to minimize FPRMs. The FMA can be extended to derive a minimum mixed polarity Reed–Muller expression.