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Differential evolution algorithm is a very powerful and recently proposed evolutionary algorithm. Generally, only a mutation operator and predefined parameter values of differential evolution algorithm are utilized to solve various optimization problems, which limits the performance of the algorithm. In this paper, six commonly used mutation operators are divided into three categories according to their own features. A mutation pool is established based on the three categories. A parameter pool with three predefined values is designed. During evolution, three mutation operators are randomly chosen from the three categories, and three parameter values are also randomly selected from the parameter pool. The three groups of mutation operators and parameter values are employed to produce trial vectors. The proposed algorithm makes good use of different mutation operators. Three recently proposed differential evolution variants and three non-differential evolution algorithms are used to make comparisons on the 29 testing functions from CEC. The experimental results have demonstrated that the proposed algorithm is very competitive. The proposed algorithm is utilized to solve three real applications, and the results are superior. [ABSTRACT FROM AUTHOR]

The moth search algorithm (MSA) is a meta-heuristic optimization technique inspired by moth behavior, has shown remarkable efficacy in solving optimization challenges. However, its poor exploration capability results in an imbalance between exploitation and exploration. To address this issue, this research introduces a new mutation operator to enhance exploration by increasing population diversity. The proposed enhanced moth search algorithm (EMSA) aims to expedite convergence and improve overall robustness by exploring new solutions more effectively. Evaluation on ten benchmark functions demonstrates EMSA's superior exploration capabilities, efficiently tackling optimization problems and yielding more optimal solutions within the search space. Compared to conventional MSA and other established algorithms, EMSA delivers well-balanced results, showcasing its effectiveness in optimizing the search space. In the future, the EMSA could potentially find applications in addressing real-world engineering optimization challenges. [ABSTRACT FROM AUTHOR]

Abstract This paper proposes a preventive maintenance decision model for electric vehicle charging stations based on mutation operators and lifecycle optimization to address the impact of potential faults on maintenance effectiveness. By introducing the particle swarm optimization algorithm with mutation operator, a comprehensive analysis of opportunity service age factor and safety failure probability factor was conducted to establish an indicator system for the operation status of charging piles, and a potential fault identification model was constructed. By optimizing the life cycle, the balance problem between optimal maintenance life and optimal opportunity maintenance life has been solved, thus completing preventive maintenance decisions. The experimental results show that the accuracy of this method in preventive maintenance decision‐making for electric vehicle charging piles can reach 98%, with an average preventive maintenance decision‐making time of 1.6 s for load piles. At the same time, the risk probability value and load loss value are effectively controlled. This study has good application prospects in improving the preventive maintenance effect of electric vehicle charging piles.

This paper proposes a preventive maintenance decision model for electric vehicle charging stations based on mutation operators and lifecycle optimization to address the impact of potential faults on maintenance effectiveness. By introducing the particle swarm optimization algorithm with mutation operator, a comprehensive analysis of opportunity service age factor and safety failure probability factor was conducted to establish an indicator system for the operation status of charging piles, and a potential fault identification model was constructed. By optimizing the life cycle, the balance problem between optimal maintenance life and optimal opportunity maintenance life has been solved, thus completing preventive maintenance decisions. The experimental results show that the accuracy of this method in preventive maintenance decision‐making for electric vehicle charging piles can reach 98%, with an average preventive maintenance decision‐making time of 1.6 s for load piles. At the same time, the risk probability value and load loss value are effectively controlled. This study has good application prospects in improving the preventive maintenance effect of electric vehicle charging piles. [ABSTRACT FROM AUTHOR]

Hydraulic turbine control system is a complex system with strong nonlinearity and multiple variables. Therefore, in order to better control the turbine system, it is necessary to obtain the parameters of key components. Aiming at the limitation of the traditional particle swarm optimization algorithm in global search ability, mutation operator and dynamic inertia weight coefficient are introduced to enhance the search ability of the algorithm. In addition, in order to further improve the global search performance of the algorithm, this paper combines the optimized particle swarm optimization algorithm with genetic algorithm to form a hybrid parameter identification algorithm. The hybrid algorithm not only uses the fast convergence of particle swarm optimization (PSO), but also uses the global search advantage of genetic algorithm (GA) to realize efficient and accurate identification of turbine torque and load parameters. Through MATLAB2021a/Simulink simulation experiments, the application effect of the algorithm in the identification of turbine torque and generator load parameters is verified. The simulation results show that the optimized particle swarm optimization algorithm has significant advantages in the accuracy and robustness of parameter identification, and the identified parameters have a high degree of fitting with the actual measured torque and speed. This study not only provides a new optimization strategy for the parameter identification of turbine regulation system, but also provides an effective intelligent algorithm solution for the parameter identification of nonlinear system. [ABSTRACT FROM AUTHOR]

A mutation operator in a real-coded genetic algorithm is developed and applied for efficient bridge-model optimization. A mutation operator that changes uniformly or dynamically with a crossover operator is proposed to address optimization problems. The performance of the combined genetic operators was verified using a variety of available test problems based on the convergence and search speed of the global optimal solution. It is shown that the genetic algorithm proposed in this study yields relatively better results than the available algorithms and is more effective in constrained optimization problems. The performance of the proposed genetic algorithm is also verified through a sample study using a field load test for the model optimization of an existing bridge. [ABSTRACT FROM AUTHOR]

Genetic algorithms (GAs) are very goodmetaheuristic algorithms that are suitable for solving NP-hard combinatorial optimization problems. A simpleGA begins with a set of solutions represented by a population of chromosomes and then uses the idea of survival of the fittest in the selection process to select some fitter chromosomes. It uses a crossover operator to create better offspring chromosomes and thus, converges the population. Also, it uses a mutation operator to explore the unexplored areas by the crossover operator, and thus, diversifies the GA search space. A combination of crossover and mutation operators makes the GA search strong enough to reach the optimal solution. However, appropriate selection and combination of crossover operator and mutation operator can lead to a very good GA for solving an optimization problem. In this present paper, we aim to study the benchmark traveling salesman problem (TSP). We developed several genetic algorithms using seven crossover operators and six mutation operators for the TSP and then compared them to some benchmark TSPLIB instances. The experimental studies show the effectiveness of the combination of a comprehensive sequential constructive crossover operator and insertion mutation operator for the problem. The GA using the comprehensive sequential constructive crossover with insertion mutation could find average solutions whose average percentage of excesses from the best-known solutions are between 0.22 and 14.94 for our experimented problem instances. [ABSTRACT FROM AUTHOR]

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The brain storm optimization (BSO) algorithm has received increased attention in the field of evolutionary computation. While BSO has been applied in numerous industrial scenarios due to its effectiveness and accessibility, there are few theoretical analysis results about its running time. Running-time analysis can be conducted through the estimation of the upper bounds of the expected first hitting time to evaluate the efficiency of BSO. This study estimates the upper bounds of the expected first hitting time on six single individual BSO variants (BSOs with one individual) based on the average gain model. The theoretical analysis indicates the following results. (1) The time complexity of the six BSO variants is O (n) in equal coefficient linear functions regardless of the presence or absence of the disrupting operator, where n is the number of the dimensions. Moreover, the coefficient of the upper bounds on the expected first hitting time shows that the single individual BSOs with the disrupting operator require fewer iterations to obtain the target solution than the single individual BSOs without the disrupting operator. (2) The upper bounds on the expected first hitting time of single individual BSOs with the standard normally distributed mutation operator are lower than those of BSOs with the uniformly distributed mutation operator. (3) The upper bounds on the expected first hitting time of single individual BSOs with the U − 1 2 , 1 2 mutation operator are approximately twice those of BSOs with the U (− 1 , 1) mutation operator. The corresponding numerical results are also consistent with the theoretical analysis results. [ABSTRACT FROM AUTHOR]

The selection method of individuals is a crucial step in the mutation operator of differential evolution (DE). Typically, methods that select individuals with better fitness values are used to increase the exploitation ability of the algorithm. However, some researches have shown that incorporating distribution information of target space to measure diversity can improve the exploration ability of the algorithm. With this concept in mind, this paper presents an innovative approach called the adaptive stochastically ranking-based tournament selection method (ASR-TS). ASR-TS initially uses tournament selection and subsequently stochastically ranks selected individuals based on fitness and diversity measurements, leading to the determination of the tournament's winner. Furthermore, the stochastic ranking parameter is adaptively set based on the success rate of the previous generation to strike a balance between the exploitation and exploration abilities of the algorithm. The proposed ASR-TS method was tested on CEC 2013 benchmark functions in several original and improved DEs. To further validate the effectiveness of this method, the ASR-TS method was also tested on CEC 2022 benchmark functions as well as real-world problems. The experimental results demonstrate that the proposed ASR-TS method outperformed various other methods by a significant margin, which proves its efficiency and effectiveness in balancing exploration and exploitation. [ABSTRACT FROM AUTHOR]

While the theoretical analysis of evolutionary algorithms (EAs) has made significant progress for pseudo-Boolean optimization problems in the last 25 years, only sporadic theoretical results exist on how EAs solve permutation-based problems. To overcome the lack of permutation-based benchmark problems, we propose a general way to transfer the classic pseudo-Boolean benchmarks into benchmarks defined on sets of permutations. We then conduct a rigorous runtime analysis of the permutation-based (1 + 1) EA proposed by Scharnow et al. (J Math Model Algorithm 3:349–366, 2004) on the analogues of the LeadingOnes and Jump benchmarks. The latter shows that, different from bit-strings, it is not only the Hamming distance that determines how difficult it is to mutate a permutation σ into another one τ , but also the precise cycle structure of σ τ - 1 . For this reason, we also regard the more symmetric scramble mutation operator. We observe that it not only leads to simpler proofs, but also reduces the runtime on jump functions with odd jump size by a factor of Θ (n) . Finally, we show that a heavy-tailed version of the scramble operator, as in the bit-string case, leads to a speed-up of order m Θ (m) on jump functions with jump size m. A short empirical analysis confirms these findings, but also reveals that small implementation details like the rate of void mutations can make an important difference. [ABSTRACT FROM AUTHOR]

Differential evolution algorithm is a very powerful and recently proposed evolutionary algorithm. Generally, only a mutation operator and predefined parameter values of differential evolution algorithm are utilized to solve various optimization problems, which limits the performance of the algorithm. In this paper, six commonly used mutation operators are divided into three categories according to their own features. A mutation pool is established based on the three categories. A parameter pool with three predefined values is designed. During evolution, three mutation operators are randomly chosen from the three categories, and three parameter values are also randomly selected from the parameter pool. The three groups of mutation operators and parameter values are employed to produce trial vectors. The proposed algorithm makes good use of different mutation operators. Three recently proposed differential evolution variants and three non-differential evolution algorithms are used to make comparisons on the 29 testing functions from CEC. The experimental results have demonstrated that the proposed algorithm is very competitive. The proposed algorithm is utilized to solve three real applications, and the results are superior.

The brain storm optimization (BSO) algorithm has received increased attention in the field of evolutionary computation. While BSO has been applied in numerous industrial scenarios due to its effectiveness and accessibility, there are few theoretical analysis results about its running time. Running-time analysis can be conducted through the estimation of the upper bounds of the expected first hitting time to evaluate the efficiency of BSO. This study estimates the upper bounds of the expected first hitting time on six single individual BSO variants (BSOs with one individual) based on the average gain model. The theoretical analysis indicates the following results. (1) The time complexity of the six BSO variants is O(n) in equal coefficient linear functions regardless of the presence or absence of the disrupting operator, where n is the number of the dimensions. Moreover, the coefficient of the upper bounds on the expected first hitting time shows that the single individual BSOs with the disrupting operator require fewer iterations to obtain the target solution than the single individual BSOs without the disrupting operator. (2) The upper bounds on the expected first hitting time of single individual BSOs with the standard normally distributed mutation operator are lower than those of BSOs with the uniformly distributed mutation operator. (3) The upper bounds on the expected first hitting time of single individual BSOs with the U−12,12 mutation operator are approximately twice those of BSOs with the U(−1,1) mutation operator. The corresponding numerical results are also consistent with the theoretical analysis results.

This paper introduces an improved differential evolution algorithm based on cooperative multi-population (CMp-DE for short), which combines diverse population collaboration mechanisms and catalytic factors into an improved differential evolution framework. By harnessing various population collaboration mechanisms, the algorithm enhances the diversity of individuals within populations during initial iterations and reduces it during later iterations, thereby harmonizing the algorithm's exploratory and exploitative capabilities. Furthermore, a novel mutation operator is proposed that divides the iterative process into exploration and exploitation phases, thereby augmenting the algorithm's global exploration prowess. Lastly, a catalytic operator is introduced to generate new individuals near post-crossover individuals based on a specified rule, which enhances the algorithm's ability to escape local optima and increasing stability. The proposed CMp-DE is benchmarked against the CEC2017 benchmark test functions and compared against 13 algorithms, including five differential evolution algorithms and their variants, as well as eight state-of-the-art metaheuristic optimization algorithms. This evaluation assesses the CMp-DE's solution accuracy, convergence, stability, and scalability. Finally, the applicability of CMp-DE is validated by addressing six practical optimization problems. The experimental results show that CMp-DE surpasses other algorithms in terms of both convergence accuracy and robustness. Moreover, integrating a catalytic operator with other optimization algorithms notably boosts performance in convergence accuracy and stability. The inclusion of the catalytic operator has significantly enhanced the performance of algorithms compared to their performance before its addition. This underscores the potential of the catalytic operator in improving the performance of various algorithms, particularly in terms of convergence accuracy and robustness. [ABSTRACT FROM AUTHOR]

The fixed-charge transportation (FCT) problem, an extension of the classical transportation problem, holds significance in practical logistics scenarios where fixed charges play a crucial role. Fixed charges categorize it as an NP-hard problem, posing challenges for conventional methods due to their inefficiency, high computational costs, and susceptibility to local optima. This paper introduces an enhanced evolutionary algorithm, offline learning-based competitive swarm optimization (OLCSO), tailored to address the FCT problems efficiently. OLCSO draws inspiration from offline learning, where particles benefit from the experiences of high performers. The algorithm incorporates (i) a ranking-based mechanism where losers learn from peer-to-peer winners based on their ranks, (ii) a two-phase cooperative evolutionary mechanism enhancing searchability and convergence of the algorithm. In the first phase, losers learn from personal best experiences and the shifted center of the population, boosting diversity. In the second phase, losers learn from winners and the center of the population, improving exploitation, (iii) a mutation strategy is embedded to update winner locations in each evolutionary procedure, and (iv) to ensure a feasible solution to FCT problems, the paper also introduces negative and fractional repair mechanisms. OLCSO is applied to solve two sets of FCT problems, linear and non-linear. Experimental results are compared with various heuristic and metaheuristic techniques, commonly used for these problems, using diverse metrics. A comparative analysis of OLCSO's design elements is also conducted. The results demonstrate OLCSO's superiority over existing algorithms. [ABSTRACT FROM AUTHOR]

In recent years, there have been notable advancements in the theoretical research of existing meta-heuristic algorithms and in the development of novel algorithms. However, the research on the definition and construction methods of the so-called "mutation" operator, a concept widely used in existing meta-heuristic algorithms, remains notably insufficient. In addition, how to directly construct a meta-heuristic algorithm under the guidance of stability and invariance analysis continues to pose a challenge that has yet to resolve. This paper carefully investigates and rigorously defines the concepts of "mutation operator" and "mutation-driven meta-heuristic algorithm" as found in the literature. According to these definitions, a novel meta-heuristic algorithm, called Multi-direction guided Mutation-driven Stable swarm Intelligence algorithm with Translation and Rotation invariance (M2SITRI) is proposed, and the corresponding mutation operator is carefully designed based on the analysis of translation invariance, rotation invariance, order-1 stability, and order-2 stability. The stability and invariance properties of the M2SITRI algorithm are validated through numerical simulations, and its superior solving performance is demonstrated by benchmarking it against several other well-known existing meta-heuristic algorithms across a variety of test problems. • Mutation operator and mutation-driven meta-heuristic algorithm concepts are defined. • A novel translation and rotationally invariant meta-heuristic algorithm termed M2SITRI is proposed. • The invariance and stability properties and the excellent solving performance of M2SITRI algorithm are verified. [ABSTRACT FROM AUTHOR]

In this paper, we present a novel adaptive differential evolution algorithm for global optimization problems by introducing an enhanced mutation operator and a new mixed control parameter setting based on dual performance evaluation metrics. To further strengthen the search efficiency of algorithm and availably balance its exploration and exploitation, a dual performance metrics-based mutation operator is first proposed to implement the search of population by organically integrating the fitness value and history update of individual to find the potential promising areas and allocate the suitable search resources for them. Meanwhile, a dual performance metrics-based mixed parameter setting is developed to yield appropriate associated parameters for each individual by comprehensively measuring its search characteristic and requirement based on both its fitness value and history update. In addition, a new restart strategy is further put forward to boost the search performance of algorithm by reasonably replacing the meaningless individuals measured by both their fitness values and history updates with the randomly generated individuals based on Gaussian walk. In contrast to the existing DE versions, the new algorithm organically takes advantage of the fitness value and history update of individual to assign the proper computational resources for each potential promising region, create the suitable parameters for different individuals, and eliminate the valueless individuals from population. Thereby, it is capable of heightening the search efficiency of algorithm and maintaining a good balance between exploration and exploitation effectively. At last, the performance of the proposed algorithm is evaluated by comparing with 19 typical or up-to-date algorithms on 42 benchmark functions from both IEEE CEC2017 and CEC2022 test suites. Compared to these opponents, the proposed algorithm achieves significantly better performance on 60 out of 77 cases based on the multiproblem Wilcoxon signed-rank test at a significant level of 0.05, and thus is a more promising optimizer. [ABSTRACT FROM AUTHOR]

In this article, a series of learning strategies are proposed to enhance the optimization ability of the artificial electric field algorithm. Orthogonal learning is an important mathematical tool that can greatly influence the adaptability of population-based optimization algorithms. This article proposes, (i) an orthogonal array-based learning strategy to generate a better initial population for the artificial electric field algorithm. Along with the changes in the initialization mechanism, this article also proposes, (ii) an archive-based self-adaptive learning strategy for an artificial electric field algorithm. The proposed learning strategy divides the population into ordinary and extraordinary sub-populations, each with distinct learning mechanisms. The ordinary sub-population utilizes six learning strategies based on three archives, which contain individuals of different quality levels. We incorporate, (iii) a mutation strategy also to update the extraordinary sub-population. Finally, (iv) a self-adaptive strategy is implemented to dynamically adjust the parameters of the proposed algorithm. The effectiveness of these mechanisms is assessed through an extensive analysis of exploration–exploitation dynamics and diversity. Furthermore, an independent structural study is conducted to examine the impact of implemented mechanisms on the algorithm's behavior and efficiency. The proposed algorithm is evaluated on real parameter CEC 2017 problems across different dimensional search spaces. It is compared to eleven state-of-the-art algorithms, and the results demonstrate superior performance in terms of solution accuracy, convergence rate, search capability, and stability. The overall ranking highlights its exceptional potential for solving challenging optimization problems. Additionally, it outperforms other state-of-the-art algorithms across various dimensions, achieving accuracy rates of 64.48%, 70.05%, 78.73%, and 79.25% for dimensions 10, 30, 50, and 100, respectively. Furthermore, it demonstrates superior performance, outperforming others in 73.13% and 60.61% of the problems concerning average accuracy and statistical significance across all dimensions, respectively. [Display omitted] • Introducing an archive-based self-adaptive artificial electric field algorithm (AEFA) with orthogonal initialization for real-parameter optimization problems. • Proposal of an orthogonal array into the AEFA to initialize the population along with a self-adaptive parameter mechanism. • A novel strategy is proposed to divide the population into two homogeneous sub-populations. • Introduction of six learning strategies based on three elite archives and utilizing mutation mechanism. • A rigorous analysis of the proposed algorithm in terms of diversity, exploration–exploitation, convergence, and statistical validation. [ABSTRACT FROM AUTHOR]