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Order picking, which is collecting a set of products from different locations in a warehouse, has repeatedly been described as one of the most laborious and time-consuming internal logistic processes. Each order is issued to pick some products located at given locations in the warehouse. In this paper, we consider an order picking problem, in which a number of orders with different delivery due dates are going to be retrieved by a limited number of order pickers in multiperiods such that the total tardiness is minimized. The aim is to determine a retrieval plan in terms of order batching and order picker multitrip routing as decision variables. Besides, products are arrived and replenished at the predetermined locations at different periods. Therefore, products sitting in those locations should be delivered soon to provide empty rooms for replenishment. A mixed integer linear programming formulation is proposed for this new problem. The model is optimally solved for small-size problems. For larger instances, grouping metaheuristic algorithms are proposed based on particle swarm optimization and the league championship algorithm that use group-based operators to generate reasonable batches of orders. Improvement heuristics are designed as well. The performance of the MILP formulation and metaheuristic algorithms is analyzed for different problem instances whose designs are based on real data gathered from an auto parts warehouse. Results indicate that our algorithms can stably solve large instances of the problem in a reasonable time. [ABSTRACT FROM AUTHOR]

Intelligent manufacturing capability evaluation is the key for enterprises to scientifically formulate the implementation path and continuously improve the level of intelligent manufacturing. To help manufacturing enterprises diagnose the level of intelligent manufacturing capability, this paper conducts research on intelligent manufacturing capability maturity evaluation based on maturity theory. The evaluation problem is a complex nonlinear problem, and BP neural network is particularly suitable for solving such complex mapping problems. Aiming at the problem that the BP neural network is sensitive to initial weights and thresholds, the sparrow search algorithm (SSA) is used to optimize the initial weights and thresholds of the BP neural network. In order to overcome the shortcoming of SSA that it is easy to fall into the local optimum, the firefly disturbance strategy is introduced to improve it, a new sparrow search algorithm (FASSA) is proposed, and on this basis, an intelligent manufacturing capability maturity evaluation model based on the FASSA-BP algorithm is constructed. Finally, a large battery manufacturing enterprise in China is selected for empirical research, and the comparison experiments are carried out on the FASSA-BP model, BP model, SSA-BP model, and PSO-BP model in terms of accuracy, stability, etc. The results show that the evaluation of intelligent manufacturing capability maturity through this model can effectively help companies diagnose problems in the construction of intelligent manufacturing and provide a reference for companies to accurately improve their intelligent manufacturing capabilities. [ABSTRACT FROM AUTHOR]

Metaheuristic algorithms are often applied to global function optimization problems. To overcome the poor real-time performance and low precision of the basic salp swarm algorithm, this paper introduces a novel hybrid algorithm inspired by the perturbation weight mechanism. The proposed perturbation weight salp swarm algorithm has the advantages of a broad search scope and a strong balance between exploration and exploitation and retains a relatively low computational complexity when dealing with numerous large-scale problems. A new coefficient factor is introduced to the basic salp swarm algorithm, and new update strategies for the leader position and the followers are introduced in the search phase. The new leader position updating strategy has a specific bounded scope and strong search performance, thus accelerating the iteration process. The new follower updating strategy maintains the diversity of feasible solutions while reducing the computational load. This paper describes the application of the proposed algorithm to low-dimension and variable-dimension functions. This paper also presents iteration curves, box-plot charts, and search-path graphics to verify the accuracy of the proposed algorithm. The experimental results demonstrate that the perturbation weight salp swarm algorithm offers a better search speed and search balance than the basic salp swarm algorithm in different environments. [ABSTRACT FROM AUTHOR]

As the Internet of Things (IoT) smart mobile devices explode in complex opportunistic social networks, the amount of data in complex networks is increasing. Large amounts of data cause high latency, high energy consumption, and low-reliability issues when dealing with computationally intensive and latency-sensitive emerging mobile applications. Therefore, we propose a task-sharing strategy that comprehensively considers delay, energy consumption, and terminal reputation value (DERV) for this context. The model consists of a task-sharing decision model that integrates latency and energy consumption, and a reputation value-based model for the allocation of the computational resource game. The two submodels apply an improved particle swarm algorithm and a Lagrange multiplier, respectively. Mobile nodes in the complex social network are given the opportunity to make decisions so that they can choose to share computationally intensive, latency-sensitive computing tasks to base stations with greater computing power in the same network. At the same time, to prevent malicious competition from end nodes, the base station decides the allocation of computing resources based on a database of reputation values provided by a trusted authority. The simulation results show that the proposed strategy can meet the service requirements of low delay, low power consumption, and high reliability for emerging intelligent applications. It effectively realizes the overall optimized allocation of computation sharing resources and promotes the stable transmission of massive data in complex networks. [ABSTRACT FROM AUTHOR]

In this paper, a new method of reactive power compensation is proposed for reducing power loss of distribution power networks. The new method is the combination of local compensation at each load and distribution line compensation. In the method, local capacitors at each load are determined to increase power factor of load to an expected value first and then a number of capacitors are placed in distribution lines with two factors, location and capacity by using the three applied methods. Particle swarm optimization (PSO), parasitism predation algorithm (PPA), and tunicate swarm algorithm (TSA) are applied for the proposed method on four distribution systems with 15, 33, 69, and 85 buses. The comparisons of results with previous methods indicate that the three applied methods can reach higher loss reduction for all study cases. TSA can reach loss reduction more effectively than others by 19.4%, 0.5%, 7.9%, and 10.76% for the four distribution systems, respectively. The most important emphasis is that PSO, which was considered to be of low effectiveness in previous studies, can reach much better loss than approximately all previous methods thank to the proposed compensation method. PSO also reached better loss reduction than others by 18.97%, 0.4%, 7.73%, and 10.21%, respectively. Consequently, it is recommended that the proposed compensation method is useful for distribution systems in minimizing total power loss and TSA can be selected a new and powerful method for the problem. [ABSTRACT FROM AUTHOR]

Aiming at the shortcomings of standard particle swarm optimization (PSO) algorithms that easily fall into local optimum, this paper proposes an optimization algorithm (LTQPSO) that improves quantum behavioral particle swarms. Aiming at the problem of premature convergence of the particle swarm algorithm, the evolution speed of individual particles and the population dispersion are used to dynamically adjust the inertia weights to make them adaptive and controllable, thereby avoiding premature convergence. At the same time, the natural selection method is introduced into the traditional position update formula to maintain the diversity of the population, strengthen the global search ability of the LTQPSO algorithm, and accelerate the convergence speed of the algorithm. The improved LTQPSO algorithm is applied to landscape trail path planning, and the research results prove the effectiveness and feasibility of the algorithm. [ABSTRACT FROM AUTHOR]

Constrained optimization plays an important role in many decision-making problems and various real-world applications. In the last two decades, various evolutionary algorithms (EAs) were developed and still are developing under the umbrella of evolutionary computation. In general, EAs are mainly categorized into nature-inspired and swarm-intelligence- (SI-) based paradigms. All these developed algorithms have some merits and also demerits. Particle swarm optimization (PSO), firefly algorithm, ant colony optimization (ACO), and bat algorithm (BA) have gained much popularity and they have successfully tackled various test suites of benchmark functions and real-world problems. These SI-based algorithms follow the social and interactive principles to perform their search process while approximating solution for the given problems. In this paper, a multiswarm-intelligence-based algorithm (MSIA) is developed to cope with bound constrained functions. The suggested algorithm integrates the SI-based algorithms to evolve population and handle exploration versus exploitation issues. Thirty bound constrained benchmark functions are used to evaluate the performance of the proposed algorithm. The test suite of benchmark function is recently designed for the special session of EAs competition in IEEE Congress on Evolutionary Computation (IEEE-CEC′13). The suggested algorithm has approximated promising solutions with good convergence and diversity maintenance for most of the used bound constrained single optimization problems. [ABSTRACT FROM AUTHOR]

Constrained optimization plays an important role in many decision-making problems and various real-world applications. In the last two decades, various evolutionary algorithms (EAs) were developed and still are developing under the umbrella of evolutionary computation. In general, EAs are mainly categorized into nature-inspired and swarm-intelligence- (SI-) based paradigms. All these developed algorithms have some merits and also demerits. Particle swarm optimization (PSO), firefly algorithm, ant colony optimization (ACO), and bat algorithm (BA) have gained much popularity and they have successfully tackled various test suites of benchmark functions and real-world problems. These SI-based algorithms follow the social and interactive principles to perform their search process while approximating solution for the given problems. In this paper, a multiswarm-intelligence-based algorithm (MSIA) is developed to cope with bound constrained functions. The suggested algorithm integrates the SI-based algorithms to evolve population and handle exploration versus exploitation issues. Thirty bound constrained benchmark functions are used to evaluate the performance of the proposed algorithm. The test suite of benchmark function is recently designed for the special session of EAs competition in IEEE Congress on Evolutionary Computation (IEEE-CEC′13). The suggested algorithm has approximated promising solutions with good convergence and diversity maintenance for most of the used bound constrained single optimization problems. [ABSTRACT FROM AUTHOR]

The optimization of high-dimensional functions is an important problem in both science and engineering. Wolf pack algorithm is a technique often used for computing the global optimum of a multivariable function. In this paper, we develop a new wolf pack algorithm that can accurately compute the optimal value of a high-dimensional function. First, chaotic opposite initialization is designed to improve the quality of initial solution. Second, the disturbance factor is added in the scouting process to enhance the searching ability of wolves, and an adaptive step length is designed to enhance the global searching ability to prevent wolves from falling into the local optimum effectively. A set of standard test functions are selected to test the performance of the proposed algorithm, and the test results are compared with other algorithms. The high-dimensional and ultrahigh-dimensional functions (500 and 1000) are tested. The experimental results show that the proposed algorithm features in good global convergence, high accuracy calculation, strong robustness, and excellent performance in high-dimensional functions. [ABSTRACT FROM AUTHOR]

Contactors are important components in circuits. To solve the multiobjective optimization problems (MOPs) of contactors, a niching multiobjective particle swarm optimization (NMOPSO) with the entropy weight ideal point theory is proposed in this paper. The new algorithm selecting and archiving the nondominated solutions based on the niching theory to ensure the diversity of the nondominated solutions. To avoid missing the extreme solutions of each objective during the multiobjective optimization process, extra particle swarms used to search the independent optimal solution of each objective are supplemented in this algorithm. In order to determine the best compromise solution, a method to select the compromise solution based on entropy weight ideal point theory is also proposed in this paper. Using the algorithm to optimize the characteristics of a typical direct-acting contactor, the results show that the proposed algorithm can obtain the best compromise solution in MOPs. [ABSTRACT FROM AUTHOR]

Sine cosine algorithm (SCA) is a new meta-heuristic approach suggested in recent years, which repeats some random steps by choosing the sine or cosine functions to find the global optimum. SCA has shown strong patterns of randomness in its searching styles. At the later stage of the algorithm, the drop of diversity of the population leads to locally oriented optimization and lazy convergence when dealing with complex problems. Therefore, this paper proposes an enriched SCA (ASCA) based on the adaptive parameters and chaotic exploitative strategy to alleviate these shortcomings. Two mechanisms are introduced into the original SCA. First, an adaptive transformation parameter is proposed to make transformation more flexible between global search and local exploitation. Then, the chaotic local search is added to augment the local searching patterns of the algorithm. The effectiveness of the ASCA is validated on a set of benchmark functions, including unimodal, multimodal, and composition functions by comparing it with several well-known and advanced meta-heuristics. Simulation results have demonstrated the significant superiority of the ASCA over other peers. Moreover, three engineering design cases are employed to study the advantage of ASCA when solving constrained optimization tasks. The experimental results have shown that the improvement of ASCA is beneficial and performs better than other methods in solving these types of problems. [ABSTRACT FROM AUTHOR]

In recent years, swarm-based stochastic optimizers have achieved remarkable results in tackling real-life problems in engineering and data science. When it comes to the particle swarm optimization (PSO), the comprehensive learning PSO (CLPSO) is a well-established evolutionary algorithm that introduces a comprehensive learning strategy (CLS), which effectively boosts the efficacy of the PSO. However, when the single modal function is processed, the convergence speed of the algorithm is too slow to converge quickly to the optimum during optimization. In this paper, the elite-based dominance scheme of another well-established method, grey wolf optimizer (GWO), is introduced into the CLPSO, and the grey wolf local enhanced comprehensive learning PSO algorithm (GCLPSO) is proposed. Thanks to the exploitative trends of the GWO, the algorithm improves the local search capacity of the CLPSO. The new variant is compared with 15 representative and advanced algorithms on IEEE CEC2017 benchmarks. Experimental outcomes have shown that the improved algorithm outperforms other comparison competitors when coping with four different kinds of functions. Moreover, the algorithm is favorably utilized in feature selection and three constrained engineering construction problems. Simulations have shown that the GCLPSO is capable of effectively dealing with constrained problems and solves the problems encountered in actual production. [ABSTRACT FROM AUTHOR]

In this paper, we present a new approach which is based on using numerical solutions and swarm algorithms (SAs) to solve the interval quadratic programming problem (IQPP). We use numerical solutions for SA to improve its performance. Our approach replaced all intervals in IQPP by additional variables. This new form is called the modified quadratic programming problem (MQPP). The Karush–Kuhn–Tucker (KKT) conditions for MQPP are obtained and solved by the numerical method to get solutions. These solutions are functions in the additional variables. Also, they provide the boundaries of the basic variables which are used as a start point for SAs. Chaotic particle swarm optimization (CPSO) and chaotic firefly algorithm (CFA) are presented. In addition, we use the solution of dual MQPP to improve the behavior and as a stopping criterion for SAs. Finally, the comparison and relations between numerical solutions and SAs are shown in some well-known examples. [ABSTRACT FROM AUTHOR]

The bike-sharing system (BSS), as a sustainable way to deal with the "last mile" problem of mass transit systems, is increasingly popular in recent years. Despite its success, the BSS tends to suffer from the mismatch of bike supply and user demand. BSS operators have to transfer bikes from surplus stations to deficit stations to redistribute them among stations by means of trucks. In this paper, we deal with the bike-sharing rebalancing problem with balance intervals (BRP-BIs), which is a variant of the static bike-sharing rebalancing problem. In this problem, the equilibrium of station is characterized by a balance interval instead of a balance point in the literature. We formulate the BRP-BI as a biobjective mixed-integer programming model with the aim of determining both the minimum cost route for a single capacitated vehicle and the maximum average rebalance utility, an index for the balanced degree of station. Then, a multistart multiobjective particle swarm optimization (MS-MOPSO) algorithm is proposed to solve the model such that the Pareto optimal solutions can be derived. The proposed algorithm is extended with crossover operator and variable neighbourhood search to enhance its exploratory capability. Compared with Hybrid NSGA-II and MOPSO, the computational experimental results demonstrate that our MS-MOPSO can obtain Pareto optimal solutions with higher quality. [ABSTRACT FROM AUTHOR]

Conventional optimization methods are not efficient enough to solve many of the naturally complicated optimization problems. Thus, inspired by nature, metaheuristic algorithms can be utilized as a new kind of problem solvers in solution to these types of optimization problems. In this paper, an optimization algorithm is proposed which is capable of finding the expected quality of different locations and also tuning its exploration-exploitation dilemma to the location of an individual. A novel particle swarm optimization algorithm is presented which implements the conditioning learning behavior so that the particles are led to perform a natural conditioning behavior on an unconditioned motive. In the problem space, particles are classified into several categories so that if a particle lies within a low diversity category, it would have a tendency to move towards its best personal experience. But, if the particle's category is with high diversity, it would have the tendency to move towards the global optimum of that category. The idea of the birds' sensitivity to its flying space is also utilized to increase the particles' speed in undesired spaces in order to leave those spaces as soon as possible. However, in desirable spaces, the particles' velocity is reduced to provide a situation in which the particles have more time to explore their environment. In the proposed algorithm, the birds' instinctive behavior is implemented to construct an initial population randomly or chaotically. Experiments provided to compare the proposed algorithm with the state-of-the-art methods show that our optimization algorithm is one of the most efficient and appropriate ones to solve the static optimization problems. [ABSTRACT FROM AUTHOR]

The accurate and rapid prediction of ticket prices for a public-private partnership (PPP) subway system, which is an important research topic in the field of civil engineering management, is of critical importance to ensure its smooth operation. To effectively cope with the effects of multiple influencing factors and strong nonlinearity among them, the mean impact value (MIV) method and the back-propagation (BP) feed-forward neural network improved by the sparrow search algorithm (SSA) are used in this study to develop an intelligent prediction model. First, we considered the relationship of the supply and the subway system service, which is a typical quasi-public product, and analyzed the relevant factors affecting its price adjustment. Then, we developed an intelligent method for the prediction of ticket prices based on the SSA-BP. This model not only makes full use of the powerful nonlinear modeling ability of the BP algorithm, but also takes advantage of the strong optimization ability and fast convergence speed of the SSA. Finally, this study screened out the key input factors by adopting the MIV method to simplify the structure of the BP algorithm and achieve a high prediction accuracy. In this study, Beijing Subway Line 4, Wuhan Metro Line 2, and Chengdu Metro Line 1 were selected as case study sites. The results showed that the linear correlations between influencing factors and ticket price for the PPP subway system service were weak, which indicated the need for using nonlinear analysis methods such as the BP algorithm. Compared with other prediction methods (the price adjustment method based on PPP contract, the traditional BP algorithm, the BP neural network improved by the genetic algorithm, the BP algorithm improved by the particle swarm optimization, and the support vector machine), the model proposed in this paper showed better prediction accuracy and calculation stability. [ABSTRACT FROM AUTHOR]

Shape memory alloy- (SMA-) based actuators are widely applied in the compliant actuating systems. However, the measured data of the SMA-based compliant actuating system reveal the input-output hysteresis behavior, and the actuating precision of the compliant actuating system could be degraded by such hysteresis nonlinearities. To characterize such nonlinearities in the SMA-based compliant actuator precisely, a Jiles-Atherton model is adopted in this paper, and a modified particle swarm optimization (MPSO) algorithm is proposed to identify the parameters in the Jiles-Atherton model, which is a combination of several differential nonlinear equations. Compared with the basic PSO identification algorithm, the designed MPSO algorithm can reduce the local optimum problem so that the Jiles-Atherton model with the identified parameters can show good agreements with the measured experimental data. The good capture ability of the proposed identification algorithm is also examined through the comparisons with Jiles-Atherton model using the basic PSO identification algorithm. [ABSTRACT FROM AUTHOR]

It is urgent to combine knowledge resources with manufacturing business processes to form a knowledge service in the cloud mode, so as to provide intelligent support for business activities in product development process. The main challenge of knowledge resource service, however, is how to rapidly construct the complex resource service system and respond promptly to the changeable service requirements in the business process, which is similar to the software system modeling using a component in software engineering. This paper is concerned with an optimal composition framework (OCF) of knowledge resource service, including service decomposition, component encapsulation, and optimal composition. Firstly, the typical business processes are decomposed into the dynamic knowledge element (DKE), and all kinds of knowledge resources and service behaviors are encapsulated into the reusable resource service components (RSC). Then, a multicomponent optimal composition mathematical model is presented, which transforms the problem of component composition into a multiobjective optimization problem. On this basis, a heuristic algorithm with the adaptive mutation probability is introduced to composite the multigranularity service component dynamically and robustly. Finally, the case of component composition for maintenance resource service is studied and the simulation results are provided to verify the efficacy of the proposed model and algorithms. [ABSTRACT FROM AUTHOR]

The aim of this article is to present a chaotic fruit fly algorithm (CFFA) as an optimization approach for solving engineering design problems (EDPs). In CFFA, the fruit fly algorithm (FFA), which is recognized for its durability and efficiency in addressing optimization problems, was paired with the chaotic local search (CLS) method, which allows for local exploitation. CFFA will be set up to work in two phases: in the first, FFA will be used to discover an approximate solution, and in the second, chaotic local search (CLS) will be used to locate the optimal solution. As a result, CFFA can address difficulties associated with the basic FFA such as falling into local optima, an imbalance between exploitation and exploration, and a lack of optimum solution acquisition (i.e., overcoming the drawback of premature convergence and increasing the local exploitation capability). The chaotic logistic map is employed in the CLS because it has been demonstrated to be effective in improving the quality of solutions and giving the best performance by many studies. The proposed algorithm is tested by the set of CEC'2005 special sessions on real parameter optimization and many EDPs from the most recent test suite CEC'2020. The results have demonstrated the superiority of the proposed approach to finding the global optimal solution. Finally, CFFA′s results were compared to those of earlier research, and statistical analysis using Friedman and Wilcoxon's tests revealed its superiority and capacity to tackle this type of problem. [ABSTRACT FROM AUTHOR]

For obtaining optimal cross-sectional dimensions of rods for a 3-RRR planar parallel manipulator (PPM) to minimize energy consumption, the inverse dynamics of the manipulator is modeled based on the Newton–Euler method, after which the coefficient matrix of the inverse dynamics equation is decomposed based on matrix theory. Hence, the objective function, that is, the logical relationship between the energy consumption of the manipulator and the cross-sectional dimension of each rod, is established. However, in solving the multidimensional constrained single-object optimization problem, there are difficulties such as the penalty function's sensitivity to the penalty factors if the problem is transformed into the one of unconstrained multiobjective optimization. Therefore, to properly handle the constraints, an improved butterfly optimization algorithm (IBOA) is presented to ensure that the new iterated point always falls into the feasible region according to the butterfly optimization algorithm (BOA). Finally, the comparisons among the IBOA, particle swarm optimization (PSO), and BOA and further experiments of the physical prototype are implemented to validate the effectiveness of the proposed theoretical model and numerical algorithm. Results indicate that the proposed IBOA is more suitable for solving the constrained single-object optimization problem with better convergence speed and accuracy. [ABSTRACT FROM AUTHOR]

The optimal resource allocation in the large-scale intelligent device-to-device (D2D) communication system is of great importance for improving system spectrum efficiency and ensuring communication quality. In this study, the D2D resource allocation is modelled as an ultrahigh-dimensional optimization (UHDO) problem with thousands of binary dimensionalities. Then, for efficiently optimizing this UHDO problem, the coupling relationships among those dimensionalities are comprehensively analysed, and several efficient variable-grouping strategies are developed, i.e., cellular user grouping (CU-grouping), D2D pair grouping (DP-grouping), and random grouping (R-grouping). In addition, a novel evolutionary algorithm called the cooperatively coevolving particle swarm optimization with variable-grouping (VGCC-PSO) is developed, in which a novel mutation operation is introduced for ensuring fast satisfaction of constraints. Finally, the proposed UHDO-based allocation model and VGCC-PSO algorithm as well as the grouping and mutation strategies are verified by a comprehensive set of case studies. Simulation results show that the developed VGCC-PSO algorithm performs the best in optimizing the UHDO model with up to 6000 dimensionalities. According to our study, the proposed methodology can effectively overcome the "curse of dimensionality" and optimally allocate the resources with high accuracy and robustness. [ABSTRACT FROM AUTHOR]

Efficient community detection in a complex network is considered an interesting issue due to its vast applications in many prevailing areas such as biology, chemistry, linguistics, social sciences, and others. There are several algorithms available for network community detection. This study proposed the Sigmoid Fish Swarm Optimization (SiFSO) algorithm to discover efficient network communities. Our proposed algorithm uses the sigmoid function for various fish moves in a swarm, including Prey, Follow, Swarm, and Free Move, for better movement and community detection. The proposed SiFSO algorithm's performance is tested against state-of-the-art particle swarm optimization (PSO) algorithms in Q-modularity and normalized mutual information (NMI). The results showed that the proposed SiFSO algorithm is 0.0014% better in terms of Q-modularity and 0.1187% better in terms of NMI than the other selected algorithms. [ABSTRACT FROM AUTHOR]

Efficient community detection in a complex network is considered an interesting issue due to its vast applications in many prevailing areas such as biology, chemistry, linguistics, social sciences, and others. There are several algorithms available for network community detection. This study proposed the Sigmoid Fish Swarm Optimization (SiFSO) algorithm to discover efficient network communities. Our proposed algorithm uses the sigmoid function for various fish moves in a swarm, including Prey, Follow, Swarm, and Free Move, for better movement and community detection. The proposed SiFSO algorithm's performance is tested against state-of-the-art particle swarm optimization (PSO) algorithms in Q-modularity and normalized mutual information (NMI). The results showed that the proposed SiFSO algorithm is 0.0014% better in terms of Q-modularity and 0.1187% better in terms of NMI than the other selected algorithms. [ABSTRACT FROM AUTHOR]

In order to solve the shortcomings of particle swarm optimization (PSO) in solving multiobjective optimization problems, an improved multiobjective particle swarm optimization (IMOPSO) algorithm is proposed. In this study, the competitive strategy was introduced into the construction process of Pareto external archives to speed up the search process of nondominated solutions, thereby increasing the speed of the establishment of Pareto external archives. In addition, the descending order of crowding distance method is used to limit the size of external archives and dynamically adjust particle parameters; in order to solve the problem of insufficient population diversity in the later stage of algorithm iteration, time-varying Gaussian mutation strategy is used to mutate the particles in external archives to improve diversity. The simulation experiment results show that the improved algorithm has better convergence and stability than the other compared algorithms. [ABSTRACT FROM AUTHOR]