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The mutation is one of the most important stages in the genetic algorithm (GA) because of its influence on exploring solution space and overcoming premature convergence. Since there are many types of mutation operators, the problem lies in selecting the appropriate type, and so, researchers usually need more trial and error. This paper investigates a new mutation operator based on teaching–learning-based optimization (TLBO) to enhance the performance of genetic algorithms. This new mutation operator treats intelligently instead of the random type, enhances the quality of solution, and speeds up the convergence of GA simultaneously. Several experiments are conducted on six standard test functions to evaluate the effect of the proposed mutation operator. First, proper comparisons are made between the performance of the proposed mutation to the classic mutation of GA and their combinatorial format. The result indicates the effect of the proposed mutation operator on the significant enhancement of the genetic algorithms' performance particularly. Due to computational analysis with Intel(R) Core(TM) i5-2430 M CPU @ 2.40 GHz processor, this method causes 32–53.3% reduction in essential iteration to present zero amount as the final value for four test functions (i.e., Beale, Himmelblau, Booth, and Rastrigin). For the two other functions that provides a non-zero value (i.e., Ackley and Sphere), the proposed method improves nearly 100% in average of objective. According to the result, the final solutions of the proposed method are equal or better than the classic GA in all six problems. Then, the performance of the proposed algorithm in comparison to five well-known algorithms ensures its superiority. In all comparisons, the proposed method performs equal or better than five other algorithms in CPU time and quality solutions. [ABSTRACT FROM AUTHOR]

Prediction models are used to prevent and prepare for corresponding events according to various types of data generated in production. Aiming at the problems of lower predictive accuracy and slower convergent speed of the existing prediction models, a prediction model based on fireworks algorithm (FWA) and long short-term memory (LSTM) is proposed to predict time-related data. Firstly, we establish the interconnection structure model of the hidden layer nodes in the LSTM. Then, considering the diversity and concurrency of the group, we optimize the hyperparameters combination of LSTM. Finally, we improve FWA by adding three mutation operators (Gaussian mutation operator, Cauchy mutation operator, and discrete mutation operator). Based on the enhanced FWA, we achieve a better optimization effect by increasing the diversity of hyperparameters combination. The experimental results show that the performance of the proposed LSTM-enhanced FWA model has been significantly improved by comparing to the existing LSTM and LSTM-GS models. The mean absolute error (MAE) is reduced by 38.49% and 17.79%, respectively; the root mean squared error (RMSE) is reduced by 29.47% and 19.28%, respectively; and the mean absolute percentage error (MAPE) is reduced by 36.67% and 26.92%, respectively. MAE and MAPE represent the degree of deviation between the predicted value and actual value, and RMSE well reflects the precision. This means that the proposed LSTM-enhanced FWA model is better than existing LSTM and LSTM-GS models because all three types of error are reduced, meanwhile three kinds of error better reflect accuracy and precision of error. [ABSTRACT FROM AUTHOR]

The widely employed mutation operator D E / c u r r e n t - t o - p b e s t / 1 in the differential evolution algorithm (DE) is further developed to a new version D E / c u r r e n t - t o - p b e s t / 1 - X in this paper. To test its performance, it has been embedded in the novel successful history-based adaptive DE (L-SHADE) and compared with other recently proposed mutation operators. In D E / c u r r e n t - t o - p b e s t / 1 - X , the updated parameter memories in each generation are not adopted when the initial value can still maintain an acceptable successful rate of finding better offspring. Also, the generated worse offsprings with acceptable fitness values are partially archived to generate differential vectors. The experimental results show that D E / c u r r e n t - t o - p b e s t / 1 - X has a comparable performance than D E / c u r r e n t - t o - p b e s t / 1 , D E / c u r r e n t - t o - o r d _ p b e s t / 1 and D E / c u r r e n t - t o - o r d _ b e s t / 1 . [ABSTRACT FROM AUTHOR]

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]

The major purpose of this article is to enhance the performance of GOA algorithm by integrating a new mutation operator to the standard GOA algorithm. A series of six different variants of enhanced GOA is proposed by integrating GOA with six different variants of the mutation operator. The new enhanced metaheuristic optimization method is called EGOAs. EGOA aims to address the problems of slow convergence and trapping into local optima, by achieving a good balance between exploration and exploitation, using a special mutation operator that enhances the diversity of the standard GOA, to find the best solution for global optimization problems. The implementation process for enhancing the GOA algorithm is presented and the effectiveness of the enhanced algorithm is evaluated against 60 of the optimization benchmark functions, and compared to that of the standard GOA, as well as to other metaheuristic optimization algorithms. The performance of EGOAs was compared with the other improved methods based on GOA. Experimental results show that EGOAs is clearly superior to the standard GOA algorithm, as well as to other well-known algorithms, in terms of achieving the best optimal value, convergence speed, and avoiding local minima, which makes EGOAs a promising addition to the arsenal of metaheuristic algorithms. [ABSTRACT FROM AUTHOR]

Feature selection (FS) is used to solve hard optimization problems in artificial intelligence and data mining. In the FS process, some, rather than all of the features of a dataset are selected in order to both maximize classification accuracy and minimize the time required for computation. In this paper a FS wrapper method that uses K-nearest Neighbor (KSN) classification is subjected to two modifications using a current improvement algorithm, the Monarch Butterfly Optimization (MBO) algorithm. The first modification, named MBOICO, involves the utilization of an enhanced crossover operator to improve FS. The second, named MBOLF, integrates the Lévy flight distribution into the MBO to improve convergence speed. Experiments are carried out on 25 benchmark data sets using the original MBO, MBOICO and MBOLF. The results show that MBOICO is superior, so its performance is also compared against that of four metaheuristic algorithms (PSO, ALO, WOASAT, and GA). The results indicate that it has a high classification accuracy rate of 93% on average for all datasets and significantly reduces the selection size. Hence, the findings demonstrate that the MBOICO outperforms the other algorithms in terms of classification accuracy and number of features chosen (selection size). [ABSTRACT FROM AUTHOR]

The Swarm based algorithms deliver better performance when it can maintain perfect balance of the exploration and exploitation process and converges faster by successfully avoiding local optima entrapment. At recent time, Crow Search Algorithm (CSA) is developed as a nature inspired swarm based algorithm. It can solve continuous, non-linear and complex day to day life optimization problems. Like many other optimization algorithms, CSA suffers with the problem of local stagnation. This paper introduces an improved version of the CSA, which improves the performance of the existing CSA algorithm by using oppositional learning and mutation operator. The proposed algorithm is termed as OBL-CSA-MO. The OBL-CSA-MO enhances the exploration and exploitation capability in the search space and successfully avoids local optima entrapment. The OBL-CSA-MO is evaluated by considering the IEEE CEC 2017 standard benchmark functions set. The efficiency and robustness of the proposed OBL-CSA-MO is measured using performance metrics, convergence analysis and statistical significance. A demonstration is given as an application of the proposed algorithm for designing fractional order PID controller as the real life problem. For this purpose, the first order and higher order plants are considered in the FOPID designing using the proposed OBL-CSA-MO. The experimental results demonstrate that the developed OBL-CSA-MO can be used for solving optimization problems effectively. [ABSTRACT FROM AUTHOR]

Nowadays, most of the communications in IoT enabled devices are done in the form of images. To protect the images from intruders, there is a need for a secure encryption algorithm. Many encryption algorithms have been proposed, some of the algorithms are based on symmetric-key cryptography and others are based on asymmetric key cryptography. This work proposed a fast, secure, and lightweight symmetric image cryptographic algorithm based on the session key. In this work, for every image encryption, a new session key is generated. Here session keys are generated with the help of crossover and mutation operators of genetic algorithm. This proposed algorithm uses a 64-bit plain text and requires an 80-bit key, where 64-bits of a key is generated via symmetric hexadecimal key and the remaining 16-bits of a key are randomly added, to encrypt the image. Here crossover and mutation operators are used to generate random 64-bits of a key. The proposed algorithm will work for both color and grayscale images. The proposed algorithm is simulated on MATLAB 2017 platform and compared with similar types of the existing algorithm on various parameters. [ABSTRACT FROM AUTHOR]

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.

Aiming at the problem of ease of falling into local optimum and low solution quality when solving optimization problems, this paper proposes an adaptive hybrid cuckoo search (AHCS) algorithm. AHCS improves the Lévy flight method and population evolution strategy of the cuckoo search (CS) algorithm, and introduces a mutation operation operator. Inspired by the idea of position update of particle swarm optimization (PSO) algorithm, this paper introduces the inertia weight w in the Lévy flight method of CS algorithm, and gives the new dynamic adjustment methods of parameters α and β respectively. In order to enhance the local search ability and optimization speed of the algorithm, this paper introduces the mutation operation operator, and presents a new evolution strategy of the hybrid cuckoo search algorithm. In addition, in order to verify the performance of AHCS, 30 benchmark functions and CEC 2017 optimization problems were selected. The calculation results of the 30 benchmark functions and CEC 2017 optimization problems show that compared with other algorithms, the number of winning cases of t-test values and the Friedman average ranking for AHCS are significantly better than other algorithms. Finally, AHCS and various intelligent optimization methods in the literature are used to optimize the structural parameters of the reducer and the cantilever beam. The optimization results show that the quality of AHCS solution is significantly better than other algorithms.

This paper proposes to resolve the limitation of differential evolution (DE) that the difference between the individuals in search behavior has not yet been utilized effectively for guiding the evolution of the population. An adaptive guiding mechanism (AGM) based on the heuristic rules is thus suggested to make possible, individual-dependent guidance. The AGM mainly comprises three stages: construction, separation, and guidance. In the construction stage, the elite leadership team (ELT) is established with an adaptive control scheme by using good information of the population. In the separation stage, the ELT is divided into distinct elite groups that are allocated to different individuals based on their search behaviors. In the guidance stage, the leader that is chosen from the respective elite group, as well as the promising directions extracted from the population, are used together to guide the search of each individual. By incorporating AGM into DE, a novel algorithm framework, named DE with AGM (DE-AGM), is proposed to enhance the performance of DE. As a general framework, DE-AGM can be easily and seamlessly applied to most DE variants. The experimental results on 58 benchmark functions have demonstrated the competitive performance of DE-AGM.

The problem of structures learning in Bayesian networks is to discover a directed acyclic graph that in some sense is the best representation of the given database. Score-based learning algorithm is one of the important structure learning methods used to construct the Bayesian networks. These algorithms are implemented by using some heuristic search strategies to maximize the score of each candidate Bayesian network. In this paper, a bi-velocity discrete particle swarm optimization with mutation operator algorithm is proposed to learn Bayesian networks. The mutation strategy in proposed algorithm can efficiently prevent premature convergence and enhance the exploration capability of the population. We test the proposed algorithm on databases sampled from three well-known benchmark networks, and compare with other algorithms. The experimental results demonstrate the superiority of the proposed algorithm in learning Bayesian networks.

Abstract Reasonable scheduling of flexible job shop is key to improve production efficiency and economic benefits; in order to solve the problem in flexible job shop scheduling problem, a novel flexible job shop scheduling method based on improved artificial immune algorithm is proposed. Firstly, a mathematical model of the flexible job shop scheduling is established, and the total shortest processing time is taken as the objective function. Secondly, artificial immune algorithm is used to solve the problem, and particle swarm optimization algorithm is taken as the operator to embed into manual immune algorithm for maintaining the diversity of population and prevent obtaining local optimal solution. Finally, the performance of the algorithm is tested by simulation experiments on standard set. The results show that the proposed algorithm can obtain better flexible job shop scheduling scheme and especially has more significant advantages in solving large-scale problems in comparison with other algorithms.

Accurate intrusion detection is necessary to preserve network security. However, developing efficient intrusion detection system is a complex problem due to the nonlinear nature of the intrusion attempts, the unpredictable behaviour of network traffic, and the large number features in the problem space. Hence, selecting the most effective and discriminating feature is highly important. Additionally, eliminating irrelevant features can improve the detection accuracy as well as reduce the learning time of machine learning algorithms. However, feature reduction is an NP-hard problem. Therefore, several metaheuristics have been employed to determine the most effective feature subset within reasonable time. In this paper, two intrusion detection models are built based on a modified version of the firefly algorithm to achieve the feature selection task. The first and, the second models have been used for binary and multiclass classification, respectively. The modified firefly algorithm employed a mutation operation to avoid trapping into local optima through enhancing the exploration capabilities of the original firefly. The significance of the selected features is evaluated using a Naïve Bayes classifier over a benchmark standard dataset, which contains different types of attacks. The obtained results revealed the superiority of the modified firefly algorithm against the original firefly algorithm in terms of the classification accuracy and the number of selected features under different scenarios. Additionally, the results assured the superiority of the proposed intrusion detection system against other recently proposed systems in both binary classification and multi-classification scenarios. The proposed system has 96.51% and 96.942% detection accuracy in binary classification and multi-classification, respectively. Moreover, the proposed system reduced the number of attributes from 41 to 9 for binary classification and to 10 for multi-classification. [ABSTRACT FROM AUTHOR]

The biogeography-based optimization （BBO） algorithm is applied to the optimization of the firepower strike target allocation，and combined with a three-dimensional mutation operation to optimize the convergence accuracy of the algorithm. The improved three-dimensional variation biogeography-based optimization（Tdv-BBO）algorithm is used to solve the problem of target allocation in fire strike，and the target-fire quantity combination optimization is performed on the enemy scenario. The verification results of numerical examples show that the improved BBO algorithm enhances the global search capability，and can provide an effective method for the target assignment of joint maritime strikes. [ABSTRACT FROM AUTHOR]

Moth-Flame Optimization (MFO) algorithm is a new population-based meta-heuristic algorithm for solving global optimization problems. Flames generation and spiral search are two key components that affect the performance of MFO. To improve the diversity of flames and the searching ability of moths, an improved Moth-Flame Optimization (IMFO) algorithm is proposed. The main features of the IMFO are: the flames are generated by orthogonal opposition-based learning (OOBL); the modified position updating mechanism of moths with linear search and mutation operator. To evaluate the performance of IMFO, the IMFO algorithm is compared with other 20 algorithms on 23 benchmark functions and IEEE (Institute of Electrical and Electronics Engineers) CEC (Congress on Evolutionary Computation) 2014 benchmark test set. The comparative results show that the IMFO is effective and has good performance in terms of jumping out of local optimum, balancing exploitation ability and exploration ability. Moreover, the IMFO is also used to solve three engineering optimization problems, and it is compared with other well-known algorithms. The comparison results show that the IMFO algorithm can improve the global search ability of MFO and effectively solve the practical engineering optimization problems. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

By controlling the cost of power outage caused by distribution network maintenance, optimize the maintenance planning model of distribution network, and consider that the maintenance plan will cause the improvement of power network operation risk, this paper puts forward the maintenance optimization strategy of CTSS distribution network considering variation operator, which maximizes the economy of maintenance plan without reducing the reliability of power network operation. When dealing with the multi-objective and multi-constraint nonlinear model, a mutation operator is introduced in the iterative process of the Algorithm to speed up the detection of the desired region, under the combined action of reliable global optimization and accurate local optimization, the optimal strategy of distribution network maintenance planning is obtained by using nelder-mead Simplex Algorithm In order to verify the effectiveness of the algorithm in optimizing the maintenance period of power grid, the numerical simulation experiment on IEEE-RBTS Bus2 system show that the algorithm can jump out of local extremum point effectively and get the optimal solution of maintenance plan quickly． [ABSTRACT FROM AUTHOR]

In this paper, a new particle swarm optimization particle filter (NPSO-PF) algorithm is proposed, which is called particle cluster optimization particle filter algorithm with mutation operator, and is used for real-time filtering and noise reduction of nonlinear vibration signals. Because of its introduction of mutation operator, this algorithm overcomes the problem where by particle swarm optimization (PSO) algorithm easily falls into local optimal value, with a low calculation accuracy. At the same time, the distribution and diversity of particles in the sampling process are improved through the mutation operation. The defect of particle filter (PF) algorithm where the particles are poor and the utilization rate is not high is also solved. The mutation control function makes the particle set optimization process happen in the early and late stages, and improves the convergence speed of the particle set, which greatly reduces the running time of the whole algorithm. Simulation experiments show that compared with PF and PSO-PF algorithms, the proposed NPSO-PF algorithm has lower root mean square error, shorter running time, higher signal-to-noise ratio and more stable filtering performance. It is proved that the algorithm is suitable for real-time filtering and noise reduction processing of nonlinear signals. [ABSTRACT FROM AUTHOR]

The most pressing issue in network security is the establishment of an approach that is capable of detecting violations in computer systems and networks. There have been several efforts for improving it from various points of view. One example is the improvement of the classification of packets on the network, which is imperative in detecting abnormal traffic and hence any potential intrusion. Thus, this study proposes a new approach for intrusion detection that is implemented using an enhanced Bat algorithm (EBat) for training an artificial neural network. The goal of the current study is to increase the accuracy of the classification for malicious and un-malicious network traffic. The proposed study herein includes a comparison with nine other metaheuristic algorithms (conventional and new algorithms) that are used to evaluate the new approach alongside the related works. Firstly, the EBat algorithm was developed and used to select suitable weights and biases. Next, the neural network was employed using the found optimal weights and biases to realize the intrusion detection approach. Four types of intrusion detection evaluation datasets were used to compare the proposed approach against the other algorithms. The findings revealed that the proposed method outperformed the other nine classification algorithms and it is unparalleled for the network intrusion detection. [ABSTRACT FROM AUTHOR]

Success behind nature inspired evolutionary metaheuristic algorithms lies in its seemly combination of operator's castoff for smooth balance between exploration and exploitation. The deficit in such combination leads to untimely convergence of an algorithm, simultaneously failed to attain global optimum by stocking in local optimum. This work represents atypical algorithm termed as OBL-MO-SHO to improve the performance of existing SHO. To deal with more intricate realistic problems and to enhance the explorative and exploitative strength of SHO, we have integrated the oppositional learning concept with mutation operator. The proposed algorithm OBL-MO-SHO (oppositional spotted hyena optimizer with mutation operator) reveals promising performance in terms of achieving global optimum and superior convergence rate which confirms its improved exploration and exploitation capability within searching region. To establish competency of proposed OBL-MO-SHO algorithm the same is appraised by means of standard functions set belongs to IEEE CEC 2017. The efficacy of said method has been proven by means of various performance metrics and the outcomes also compared with state-of-the-art algorithms. To scrutinize its uniqueness statistically, Friedman and Holms test has been performed as one non-parametric test. Additionally as an application to unravel real world intricate difficulties the said OBL-MO-SHO algorithm has been castoff to train wavelet neural network by considering datasets selected from UCI depository. The reported results unveils that the evolved OBL-MO-SHO might be one potential algorithm for enlightening different optimization difficulties effectively. [ABSTRACT FROM AUTHOR]