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Large-scale optimization problems (LSOPs) become increasingly ubiquitous but complicated in real-world scenarios. Confronted with such sophisticated optimization problems, most existing optimizers dramatically lose their effectiveness. To tackle this type of problems effectively, we propose a heterogeneous cognitive learning particle swarm optimizer (HCLPSO). Unlike most existing particle swarm optimizers (PSOs), HCLPSO partitions particles in the current swarm into two categories, namely superior particles (SP) and inferior particles (IP), based on their fitness, and then treats the two categories of particles differently. For inferior particles, this paper devises a random elite cognitive learning (RECL) strategy to update each one with a random superior particle chosen from SP. For superior particles, this paper designs a stochastic dominant cognitive learning (SDCL) strategy to evolve each one by randomly selecting one guiding exemplar from SP and then updating it only when the selected exemplar is better. With the collaboration between these two learning mechanisms, HCLPSO expectedly evolves particles effectively to explore the search space and exploit the found optimal zones appropriately to find optimal solutions to LSOPs. Furthermore, to help HCLPSO traverse the vast search space with promising compromise between intensification and diversification, this paper devises a dynamic swarm partition scheme to dynamically separate particles into the two categories. With this dynamic strategy, HCLPSO gradually switches from exploring the search space to exploiting the found optimal zones intensively. Experiments are executed on the publicly acknowledged CEC2010 and CEC2013 LSOP benchmark suites to compare HCLPSO with several state-of-the-art approaches. Experimental results reveal that HCLPSO is effective to tackle LSOPs, and attains considerably competitive or even far better optimization performance than the compared state-of-the-art large-scale methods. Furthermore, the effectiveness of each component in HCLPSO and the good scalability of HCLPSO are also experimentally verified. [ABSTRACT FROM AUTHOR]

• The finish time and total costs are extracted as the optimization objectives based on problem characteristics. • The dynamic task disassembling mechanism (DTDM) and four technician scheduling modes are novelly proposed. • A flexible time is introduced into DTDM to provide decision-makers with a larger pool of choices to meet specific needs. • A new solution method suitable for both AMTS model and ATMS-DTDM model is designed based on PSO and MOPSO algorithms. This paper focuses on the aviation maintenance technician scheduling (AMTS) problem and formulates AMTS and AMTS-DTDM model with a practical dynamic task disassembly mechanism (DTDM) and arrange maintenance technicians across shifts in short-term maintenance situations (less than 24–48 h). In DTDM, four technician scheduling modes are devised to flexibly disassemble the overtime work or reassigned it to other maintenance technicians according to work efficiency and progress, which could shorten the maintenance time and save the total cost. Moreover, a flexible time interval is designed to adjust the boundary of task disassembly. To further study the effectiveness of DTDM in reducing maintenance time and total costs, this paper divides both the AMTS and AMTS-DTDM models into three sub-models (i.e., two single-objective models and one multi-objective model), respectively. After that, we design solution methods as well as the encoding schemes compatible with both the AMTS model and the AMTS-DTDM model for different problem scales. Finally, to verify the effectiveness of DTDM, four groups of experiments are set up and particle swarm optimization (PSO) and multi-objective particle swarm optimization (MOPSO) are applied to compare AMTS and AMTS-DTDM sub-models. The experimental results show that the AMTS-DTDM model can effectively shorten the maintenance time and reduce the total costs for different scaled problems. Furthermore, the flexible time interval can facilitate more options for airlines to adjust the two above objectives to a small extent. The increase in flexible time may weaken the advantages of the AMTS-DTDM model while improving the rationality of the ultimate technician scheduling scheme. [ABSTRACT FROM AUTHOR]

• Introduced the signal-to-noise ratio distance metric in metric learning to the PSO community. • A new adaptive strategy selection framework is proposed, named ESE-SNR. • Nonlinear acceleration coefficient based on singer mapping is used to better balance diversity and convergence. • A global best perturbation mechanism is employed to help the population escape from the local optimum. • The results show the algorithm outperforms or is comparable to other PSO variants and meta -heuristic evolutionary algorithms. This paper proposes an adaptive multistrategy ensemble particle swarm optimization (PSO) with signal-to-noise ratio (SNR) distance metric called AMSEPSO, which aims to solve the problems of a single learning mode of PSO and easy premature convergence when solving complex problems. In AMSEPSO, an evolutionary state estimation (ESE) strategy selection framework is proposed based on the SNR distance metric, named ESE-SNR. The appropriate learning strategy is adaptively selected through the ESE-SNR framework. To balances diversity and convergence better, nonlinear acceleration coefficient based on Singer mapping is adopted. Finally, a global best perturbation mechanism is employed to help the population escape from the local optimum. On the CEC2017 benchmarks, comparison with other advanced PSO variants and meta -heuristic algorithms show that AMSEPSO achieves remarkable performance in solving functions with different characteristics, ranking first in the results. The results show that the ESE-SNR framework can effectively evaluate the search state of the population and can greatly save the computational time of the evaluation. The ESE-SNR framework proposed in this paper provides an innovative idea for the development of multistrategy ensemble learning, and the introduction of metric learning into the PSO community helps further promote the organic integration of machine learning and swarm intelligence. [ABSTRACT FROM AUTHOR]

Due to the simplicity of the learning strategy, the original particle swarm optimization (PSO) has various deficiencies, such as entrapment in local optima, rapid loss of diversity and a poor balance between exploration and exploitation, especially for many complex optimization problems. To overcome these shortcomings, this paper proposes a hybrid particle swarm optimizer with fitness-distance balance and individual self-exploitation strategies, namely, HPSO-FDB-ISE. First, to reduce the probability of becoming trapped in a local optimum for the population, fitness-distance balance is employed to construct an alternative learning exemplar to the global best position. Second, individual self-exploitation is introduced to achieve intelligent exploitation by learning from individual current information for particles. Finally, a nonlinear time-varying inertia weight is used to efficiently balance the exploitation and exploration in the search process. The proposed HPSO-FDB-ISE is evaluated on the CEC 2017 test suite against six state-of-the-art meta -heuristics and seven state-of-the-art PSO variants. Experimental results and statistical analysis reveal that the proposed HPSO-FDB-ISE algorithm yields excellent performances compared to other algorithms that are considered in this paper in the majority of cases. [ABSTRACT FROM AUTHOR]

Particle Swarm Optimization(PSO) is a well-known and powerful meta-heuristic algorithm in Swarm Intelligence (SI), and it was invented by simulating the foraging behavior of bird flock in 1995. Recently, many different PSO variants were proposed to tackle different optimization applications, however, the overall performance of these variants were not satisfactory. In this paper, a new PSO variant is advanced to tackle single-objective numerical optimization, and there are three contributions mentioned in the paper: First, a sorted particle swarm with hybrid paradigms is proposed to improve the optimization performance; Second, novel adaptation schemes both for the ratio of each paradigm and the constriction coefficients are proposed during the iteration; Third, a fully-informed search scheme based on the global optimum in each generation is proposed which helps the algorithm to jump out the local optimum and improve the overall performance. A large test suite containing benchmarks from CEC2013, CEC2014 and CEC2017 test suites on real-parameter single-objective optimization is employed in the algorithm validation, and the experiment results show the competitiveness of our algorithm with the famous or recently proposed state-of-the-art PSO variants. [ABSTRACT FROM AUTHOR]

Comparative view of the cost function when using the GWO, GD, and PSO algorithms. [Display omitted] • A Policy Iteration Reinforcement Learning-based control approach is proposed. • A Grey Wolf Optimizer algorithm trains the policy neural network. • A comparison with classical Gradient Descent and metaheuristic PSO is offered. • The validation is done on real-time nonlinear servo system position control. • The fast convergence of the suggested approach is proved. This paper presents a new Reinforcement Learning (RL)-based control approach that uses the Policy Iteration (PI) and a metaheuristic Grey Wolf Optimizer (GWO) algorithm to train the Neural Networks (NNs). Due to an efficient tradeoff to exploration and exploitation, the GWO algorithm shows good results in NN training and solving complex optimization problems. The proposed approach is compared to the classical PI RL-based control approach using the Gradient Descent (GD) algorithm, and with the RL-based control approach which uses the metaheuristic Particle Swarm Optimization (PSO) algorithm. The experiments are conducted using a nonlinear servo system laboratory equipment. Each approach evaluated on how well it solves the optimal reference tracking control for an experimental servo system position control system. The policy NNs specific to all three approaches are implemented as state feedback with integrator controllers to remove the steady-state control errors and thus ensure the convergence of the objective function. Because of the random nature of metaheuristic algorithms, the experiments for GWO and PSO algorithms are run multiple times and the results are averaged before the conclusions are presented. The experimental results shows that for the control objective considered in this paper, the GWO algorithm represents a better solution compared to GD and PSO algorithms. [ABSTRACT FROM AUTHOR]

Velocity planning serves as an important issue in motion planning for autonomous vehicles. The presented paper proposes a novel velocity planning method with minimum moving time on the basis of path curvature which is accomplished in three steps. First, the assigned path is divided into some elementary parts based on the path curvature. Second, the velocity planning is transformed into an unconstrained optimization problem by assuming the velocity of vehicle to be a specific cubic polynomial on every elementary part to avoid a sudden acceleration in path switching. Finally, we use a modified projection particle swarm optimization (PPSO) algorithm to obtain the time-optimal velocity profile. The proposed method can generate a smooth time-optimal velocity profile while considering all possible relevant constraints. Three examples are provided on different types of path to demonstrate that the final velocity profile is efficient to avoid the sudden acceleration change. Furthermore, the modified PPSO algorithm in this paper is used to solve the optimization problem with high dimensional variables when its upper bound is known, which can not be achieved by the general PPSO algorithm. [ABSTRACT FROM AUTHOR]

• PSO-ELPM makes some modifications over PSO to enhance its search capabilities. • This PSO variant uses elite pbests and the gbest as the exemplars of all particles. • The self-cognition coefficients are defined proportional to the quality of elites. • An exponential mutation operator is proposed to escape from local optimums. • This operator determines the mutation probability and the number of mutated genes. Particle Swarm Optimization (PSO) has been widely used to solve optimization problems. Although a large number of PSO variants have been proposed so far, they suffer from the shortcomings of the original PSO. This paper proposes PSO with Elite Learning, enhanced Parameter updating, and exponential Mutation operator (PSO-ELPM) to balance the exploration and exploitation capabilities of PSO. In this algorithm, the best-performing particles in the population, known as the elites, are used as exemplars to guide the optimization process. The elitism scheme helps to discover valuable knowledge about the solution space. The adopted elites are also used to compute self-cognition coefficients of particles. Additionally, the inverse of the cube root function is applied to ensure a smooth distribution of weight among the elites. The final improvement is to apply an exponential mutation operator, which determines the mutation probability per particle based on the current iteration and its history. The comparisons among PSO-ELPM and 10 state-of-the-art PSO variants on the CEC 2017 benchmark functions reveal that the proposed algorithm yields higher accuracy with acceptable time complexity. According to the Wilcoxon rank sum test, PSO-ELPM at-least outperforms the competitive algorithms on six and seven functions in 30 and 50-dimensional problems, respectively. [ABSTRACT FROM AUTHOR]

[Display omitted] • A framework is proposed for population-based optimization algorithms' convergence. • DIRECT's partition and population evolutions are repeated in this framework. • The global convergence of the framework is proved. • Framework is applied successfully on three population-based optimization algorithms. Population-based optimization algorithms, such as genetic algorithm and particle swarm optimization, have become a class of important algorithms for solving global optimization problems. However, there is an issue that the global convergence is often absent for most of them. This paper proposes a partition-based convergence framework for population-based optimization algorithms to solve this troubling problem. In this framework, regular partitions and evolutions of populations are implemented alternatively. Specifically, the initial population is generated from a regular partition on the search space; after several generations of evolution of the population, the evolution result is returned to join in the regular partition again, and a new population is generated. Repeat such progress until some stop condition is satisfied. Global convergence is guaranteed for the framework. Then this convergence framework is applied to particle swarm optimization, differential evolution, and genetic algorithm. The modified algorithms are globally convergent and perform better than the original version. [ABSTRACT FROM AUTHOR]

In a multi-objective particle swarm optimization (MOPSO), the selection strategies of the personal best solution (pBest) for a single particle and the global best solution (gBest) for the whole swarm are two key challenges to balance the convergence and diversity of an algorithm during its iterative process. Many selection strategies in the existing literatures were emphasized on the individual characteristics of the separate particles rather than the collective features of the whole swarm. In this paper, a novel gBest selection strategy based on a new defined virtual generational distance indicator, which is calculated from a virtual Pareto front fabricated according to the geometry of a given elite archive, is proposed for selecting the most appropriate Pareto optimal solution as the gBest with respect to the comprehensive convergence and diversity contribution to improve the search effectiveness and efficiency of a MOPSO. Besides, an adaptive pBest selection strategy based on the evolutionary state in different iterations is designed for identifying the more suitable pBest from its personal archive for each particle to strengthen the exploitation or exploration ability adaptively. The experimental results show that a MOPSO with the new gBest and pBest selection strategies outperforms ten state-of-the-art competitive algorithms on DTLZ, F, WFG and ZDT series of benchmark problems. In addition, a case study on the site selection for mobile earthquake monitoring stations is also illustrated the effectiveness of the proposed algorithm in the real-world application. [ABSTRACT FROM AUTHOR]

Multiple-swarm approach is a quite successful evolutionary computation framework for multi-objective particle swarm optimization algorithm (MOPSO) to solve multi-objective optimization problems (MOPs). However, the main challenge of using this framework lies in the lack of leader selection, resulting in the optimal solutions being distributed loosely, as well as far away from the true Pareto-optimal front. To overcome this problem, a multi-swarm MOPSO with an adaptive multiple selection strategy (MOPSO-AMS) is investigated in this paper. This proposed MOPSO-AMS is able to guide each swarm with a suitable leader to improve the evolutionary performance. The novelties and advantages of MOPSO-AMS include the following three aspects. First, a hierarchical evolutionary state detection mechanism, based on the distribution and dominance information of non-dominated solutions, is designed to obtain the evolutionary state of current iteration. Then, the requirements of evolutionary process can be detected. Second, an adaptive multiple selection strategy, using the evolutionary state information and spatial features of candidate solutions, is developed to select leaders of sub-swarms in multiple evolutionary states. Then, suitable leaders can be selected to keep the balance between convergence and diversity. Third, an adaptive parameter adjustment mechanism, based on the dominance relationship of each particle, is introduced to further improve the evolutionary performance of MOPSO-AMS. Finally, numerical simulations and a practical application are used to validate the analytical results and demonstrate the significant improvement of MOPSO-AMS. [ABSTRACT FROM AUTHOR]

• New group theory based PSO learning for optimal parameters of fuzzy inference system. • Concept and an overview of the new algorithm for determining the filter coefficients. • Three-process analytical design for filter coefficient extraction to design person independent wavelet. • The energy compaction ratio is lower than the db4 coefficients. This paper presents a new method for designing matched digital filters with discrete valued coefficients. The fuzzy particle swarm optimization vector quantization (FPSOVQ) has been applied to obtain the optimum codebook in design of matched wavelet function. Abelian group has been used to extract the similarity present in the input voiced signal. Fuzzy particle swarm optimization (FPSO) process is used to find approximate ideal vector quantization (VQ) codebook to be carried out for compression of data. FPSOVQ scheme utilises features of fuzzy inference method (FIM) and expert particle swarm optimization (PSO). The generated codebook consists of set of highly ideal features, which are considered as the filter coefficients. These coefficients are used in the designing of the filter. All of the phonemes in the American English language were included in the 30 sentences that were chosen from the IEEE database. The sentences were originally down-sampled from 25 kHz to 8 kHz. The magnitude responses of each filter have been drawn, which indicates the characteristics of the filter. A comparison has been provided using energy compaction ratio as a parameter to judge the performance of matched designed filter with db4 filter. Experimental results show the advantage of the developed algorithm as the average value of energy compaction ratio for sampled voice signals is 2.8046 times lower for matched designed filter. [ABSTRACT FROM AUTHOR]

• The IGD indicator is employed as selection criteria to face the challenge of the large ratio of non-dominated solutions that exist in MaPs. • A multi-agent system is used to model the intelligent behavior of multi-swarms. • A new strategy of knowledge sharing based on automated negotiation is proposed. • Empirical studies demonstrate the effectiveness of the proposed algorithm in solving MaOPs. Most evolutionary algorithms, including particle swarm optimization (PSO), use Pareto dominance as a major selection criterion and face significant challenges when dealing with many-objective problems. To tackle this issue, this paper proposes a novel algorithm, termed: Many- Objective PSO with Cooperative Agents (MaOPSO-CA). This exploits an Inverted Generational Distance (IGD) indicator in two innovative ways: firstly, as a leader selection method to select the preferable solution in terms of convergence and diversity, and, secondly, as an archiving method to decide which non-dominated solutions are kept in a bounded archive. The proposed strategy significantly promotes selection pressure toward the Pareto front. The results indicate that the IGD-based selection circumvents the issue of a large ratio of non-dominated solutions that exist in MaOPs. Moreover, a multi-swarm is investigated and modeled as a Multi-Agent System (MAS), so that knowledge sharing among different sub-swarms is easily improved through automated negotiation. The effectiveness of our proposed algorithm is validated with numerous experimental studies in solving 110 benchmark testing instances with up to twenty objectives. Experimental results demonstrate the effectiveness of the new algorithm compared to recent state-of-the-art methods. Finally, the application of MaOPSO-CA to a challenging, real-world water resource-management problem is shown to produce very encouraging results, demonstrating its potential as a benchmark resource for the research community. [ABSTRACT FROM AUTHOR]

DNA sequence reconstruction is a challenging research problem in the computational biology field. The evolution of the DNA is too complex to be characterized by a few parameters. Therefore, there is a need for a modeling approach for analyzing DNA patterns. In this paper, we proposed a novel framework for DNA pattern analysis. The proposed framework consists of two main stages. The first stage is for analyzing the DNA sequences evolution, whereas the other stage is for the reconstruction process. We utilized cellular automata (CA) rules for analyzing and predicting the DNA sequence. Then, a modified procedure for the reconstruction process is introduced, which is based on the Probabilistic Cellular Automata (PCA) integrated with Particle Swarm Optimization (PSO) algorithm. This integration makes the proposed framework more efficient and achieves optimum transition rules. Our innovated model leans on the hypothesis that mutations are probabilistic events. As a result, their evolution can be simulated as a PCA model. The main objective of this paper is to analyze various DNA sequences to predict the changes that occur in DNA during evolution (mutations). We used a similarity score as a fitness measure to detect symmetry relations, which is appropriate for numerous extremely long sequences. Results are given for the CpG-methylation-deamination processes, which are regions of DNA where a guanine nucleotide follows a cytosine nucleotide in the linear sequence of bases. The DNA evolution is handled as the evolved colored paradigms. Therefore, incorporating probabilistic components help to produce a tool capable of foretelling the likelihood of specific mutations. Besides, it shows their capabilities in dealing with complex relations. [ABSTRACT FROM AUTHOR]

Many variants with various strategies have been proposed to improve the efficiency of Particle Swarm Optimization (PSO) algorithm. These strategies are a precious resource waiting to be exploited. We conjecture that some new combinations of strategies selected from different PSO variants may better improve the performance of PSO. Inspired by this idea, this paper proposes a strategy learning framework to learn an optimal combination of strategies and thus derive a new PSO variant based on this combination. In this framework, a strategy pool with strategies selected from existing PSO variants is first constructed. Then, a training engine, implemented by an adaptive differential evolutionary algorithm, is employed to evaluate the performance of strategy combinations on training benchmark functions. Furthermore, a new PSO variant, named SLFPSO, is created based on the strategies learned from training results. This framework provides a novel method to design PSO variants by learning from existing algorithms through a learning mechanism. The performance and scalability of SLFPSO are compared with ten state-of-the-art PSO variants on 10/30/50/100-dimensional CEC2013/2014/2017 benchmark functions. The results verify that SLFPSO performs significantly better than the compared algorithms in most test scenarios. [ABSTRACT FROM AUTHOR]

In high dimensional problem spaces, particle swarm optimization (PSO) is prone to unwanted roaming behaviour due to initial velocity explosion. A particle swarm's movement patterns are strongly influenced by the inertia weight and acceleration coefficients. This paper investigates whether the initial velocity explosion can be curbed by appropriate choice of the inertia weight and the acceleration coefficients, which restrict the standard deviation of particle positions. It is shown that roaming behaviour cannot be solved by reducing swarm variance directly, but that the relationship between the parameters must also be considered. Furthermore, the paper investigates different movement patterns that may be exhibited by the swarm. It is shown that optimal parameter configurations differ between low and high dimensional problems. Specifically, parameter configurations which produce very smooth particle trajectories and restrict the swarm's movement range are advantageous in high dimensional spaces. These movement patterns correspond to high inertia weight and low acceleration coefficients (eg. w = 0.9694 , c 1 = c 2 = 0.099381). Swarms with smooth particle trajectories exhibited significantly less unwanted roaming behaviour than swarms with chaotic or oscillating particle trajectories. [ABSTRACT FROM AUTHOR]

This paper presents an investigation into the short-term versus long-term performance of various particle swarm optimization (PSO) control parameter configurations. While evidence suggests that the best PSO parameter values to employ are time-dependent, this paper provides an in-depth examination of a small set of parameter values to provide a more concrete quantification of the performance degradation observed with specific control parameter configurations over time. Given that the short-term performance is not necessarily indicative of long-term performance, this paper proposes that machine learning techniques be used to build predictive models based on two easily-observable landscape characteristics. Finally, using the predictive models as a basis, this paper also proposes a parameter-free PSO algorithm, which performs on par with other top-performing PSO variants, namely the three best performing static PSO configurations, particle swarm optimization with time-varying acceleration coefficients (PSO-TVAC), and particle swarm optimization with improved random constants (PSO-iRC). [ABSTRACT FROM AUTHOR]

This paper presents a framework for adaptive fuzzy control and optimization of nonlinear systems subject to uncertainties and disturbances. The barrier Lyapunov function (BLF) technique was adopted to determine output constraints. To enhance the tracking performance of the system, fuzzy logic systems (FLSs) were introduced to approximate nonlinear terms. Subsequently, a combination of Bayesian optimization and particle swarm optimization (BO-PSO) was employed for gains optimization to further improve the control performance. Furthermore, the multilayer neural networks (MNNs) were applied as surrogate models of nonlinear systems with interval parameters to improve the computational efficiency of the optimization process. Finally, two simulations were conducted to demonstrate the effectiveness of the proposed framework. [ABSTRACT FROM AUTHOR]

• A new MPSACO algorithm with CWBPSO and ACO is proposed. • A new pheromone initialization approach by using CWBPSO is proposed. • A pheromone hybrid strategy based on pheromone allocation mechanism and pheromone update strategy is proposed. • A taxiway planning approach based on MPSACO is proposed to plan airport taxiway. • A taxiway conflict adjustment strategy with FCFS principles and speed priority is designed. As the connecting hub of the airport runways and gates, the taxiway plays a very important role in the rational allocation and utilization of the airport resources. In this paper, a multi-strategy particle swarm and ant colony hybrid optimization algorithm, namely MPSACO is proposed to solve the airport runway planning problem and avoid taxiway conflicts and conflict propagation. Firstly, a reasonable mathematical model of airport taxiway planning is constructed. Secondly, the multi-strategy particle swarm optimization algorithm (CWBPSO) is employed to propose a new pheromone initialization approach for ACO. And a new pheromone allocation mechanism is designed and a new pheromone update strategy based on the principle of wolf predation is developed, which are combined to design a new pheromone hybrid strategy to enhance the pheromone influence of the optimal solution, dynamically adjust the search direction, and avoid to decline the best search ability, so as to greatly improve the optimization performance of the algorithm. Finally, an airport taxiway planning approach based on MPSACO is proposed, and a conflict adjustment strategy based on speed priority and the idea of first come and first serve (FCFS) is designed to effectively optimize the airport taxiway path. In order to prove the effectiveness of the proposed algorithm/method, 10 traveling salesman problems (TSP) with different scales and an actual airport taxiway planning problem are selected in here. The experiment results show that the proposed MPSACO can effectively solve TSP and obtain the better optimal solutions, and the proposed airport taxiway planning approach can effectively plan the airport taxiing path, avoid the airport taxiing conflicts, and improve the utilization rate of taxiway resources. [ABSTRACT FROM AUTHOR]

To accelerate the convergence of multi-objective optimization algorithm and achieve an optimization solution set with good diversity, this paper proposes the Pacesetter-Lévy Multi-Objective Particle Swarm Optimization using Arnold Chaotic Map with Opposition-Based Learning algorithm (PLMOPSOCO). Firstly, the Arnold Chaotic Map with Opposition-based Learning is proposed to generate some valuable particles in the stage of initialization while maintaining the diversity of population, which can speed up exploration. Secondly, a competition mechanism with k-means clustering is integrated to categorize particles into losers and winners. The flight direction of the loser particles is adjusted according to the Pacesetter-Lévy kinetic equation, an innovative approach to effectively enhance the population's exploitative ability. Thirdly, a crossover mutation is implemented to assist particles to escape local optima and prevent population stagnation. Comparative studies on benchmark functions demonstrate that this new algorithm is more competitive in terms of both diversity and convergence when compared to several advanced multi-objective algorithms. [ABSTRACT FROM AUTHOR]

Particle swarm optimization (PSO) is a classical evolutionary algorithm and has been widely used to solve continuous optimization problems. However, the performance of the PSO algorithm is highly sensitive to its control parameters and learning strategies. To address this problem, a multi-subswarm cooperative particle swarm optimization algorithm (MSC-PSO) is proposed in this paper. In MSC-PSO, firstly, a population muti-subswarm division method is designed to enhance the global exploration capability. Secondly, a level-based particle adaptive inertia weight strategy is introduced to adjust control parameters. Finally, a level-based update learning mechanism is used for particles adaptive selection learning strategy. The performance of the MSC-PSO is evaluated by the CEC2020 test suite, and five heuristic algorithms are compared with the MSC-PSO in the experiments. The experimental results demonstrate that the proposed MSC-PSO algorithm has significant advantages in terms of convergence speed and solving optimal solutions. Furthermore, the proposed MSC-PSO algorithm is used to solve the plant protection unmanned aerial vehicles (UAV) path planning problem. The experimental results proved that the proposed MSC-PSO algorithm effectively solves the real-world UAV path planning problem, and achieves at most a 34 % reduction in round-trip distance and a 24.1 % reduction in total non-spraying time compared to classical PSO. [ABSTRACT FROM AUTHOR]

While building stochastic configuration networks (SCNs), there is no guarantee that the randomly generated weights will satisfy the supervisory mechanism and that the adopted weights will significantly reduce the training error. This paper extends SCN by applying the particle swarm optimisation (PSO) technique for one-step optimising of the set of random weights generated. These optimised weights provide a higher likelihood of satisfying the supervisory mechanism and improving the learning rate. Simulations are carried out over five regression and three classification datasets. Results demonstrate that an improved training rate and generalisation can be achieved. • Extend Stochastic Configuration Networks by improving the random weight generation. • Use particle swarm optimization to optimize the set of randomly generated weights. • Higher probability of finding weights that satisfy the supervisory mechanism. • Provide a better search, and in turn, a better training rate. • Demonstrate generalisation, and the trained model's efficiency is improved. [ABSTRACT FROM AUTHOR]

Many real-world optimization problems are dynamic by nature, exhibiting temporal variations in objective functions, constraints, and parameters. These problems present significant challenges for algorithm convergence and diversity, as they require the ability to adapt appropriately to new environments. To address these challenges, a Dynamic Multi-objective Particle Swarm Optimization algorithm with an Adaptive Response Strategy (DMOPSO-ARS) is proposed in this paper. The DMOPSO-ARS possesses the capability to detect the degree of change and apply a suitable response strategy accordingly. Specifically, the change response strategy encompasses initialization-based prediction and elite-based learning methods, designed to speed up convergence speed and enhance algorithm diversity in the face of high/low severity environmental changes. To assess the effectiveness of the DMOPSO-ARS, we select the standard CEC 2018 benchmark, noisy test functions, and the recently released OL-DOP 2022 benchmark. Empirical studies indicate the robustness of the DMOPSO-ARS in tracking evolving solutions over time, showcasing its significant superiority compared to state-of-the-art methods. • An adaptive response strategy is proposed to handle environmental changes. • LSTM prediction is used to generate an initial population of high-quality solutions. • For small change degree, solutions are updated using elite learning with knee point. • Multi-swarm with shared information is used to promote solutions' diversity. • Experiments on IEEE CEC 2018 DMOP and OL-DOPs benchmarks validated our DMOPSO-ARS. [ABSTRACT FROM AUTHOR]

As the generalization of fuzzy covering, fuzzy β covering can effectively deal with uncertain information in hybrid data. Swarm intelligence algorithm has unique advantages in feature selection. This paper proposes a novel cooperative swarm intelligence feature selection method for hybrid data based on fuzzy β covering and fuzzy self-information. First, the parameterized fuzzy β neighborhood and fuzzy decision in a fuzzy β covering decision information system are defined, and the lower and upper fuzzy approximations are further studied. Fuzzy rough set model exclusively focuses on the information derived from the lower fuzzy approximation within a decision. In actual circumstances, the uncertainty of fuzzy information is linked to not only the lower fuzzy approximation but also the upper fuzzy approximation. Then, by incorporating the lower and upper fuzzy approximations of a decision, fuzzy self-information and relative fuzzy self-information are introduced as two evaluation indicators of feature selection. Next, a forward feature selection algorithm based on heuristic search strategy is designed by means of these two evaluation indicators. Moreover, in order to effectively explore feature subsets to a greater extent, a cooperative swarm intelligent feature selection algorithm based on random search strategy is also designed by combining particle swarm optimization algorithm and cuckoo search algorithm. Finally, an array of experiments is executed to compare two designed algorithms with five other existing feature selection algorithms. Experimental results show that these two designed algorithms achieve a high feature selection rate while improving the classification accuracy of the raw data. [ABSTRACT FROM AUTHOR]

• A novel mean-median velocity updating formula is proposed to guide individuals motion. • A new random differential mutation strategy is devised. • A back-diffusion strategy is proposed to restore the diversity of population. To accelerate the convergence speed and enhance robustness, a back-diffusion median integrated evolutionary algorithm (BMIEA) is proposed combining the advantages of particle swarm optimization (PSO) and differential evolution algorithm (DE) in this paper. The BMIEA includes three mainly optimization strategies. (1) Firstly, a new mean-median velocity updating formula is proposed to control optimal path of individuals. It can accelerate the convergence speed via reducing adverse effects of outliers on the population. (2) Secondly, a random differential mutation (RDM) inspired by the DE is devised to avoid the individuals trapping into local optimum via getting one more chance to explore optimal position while exploiting local region in each evolution. (3) Thirdly, a targeted exploration method i.e., back-diffusion operation, is proposed inspired by the duality principle to further accelerate the convergence rate and enhance robustness of algorithm. A series of simulation experiments have verified that BMIEA algorithm has revealed competitiveness compared with 13 state-of-art GOBL-based optimization algorithms. [ABSTRACT FROM AUTHOR]

In particle swarm optimization (PSO), the canonical learning exemplars and information sharing mechanism are often criticized due to the loss of population diversity. Aiming at preserving population diversity and promoting search ability of PSO , this paper introduces an elite-ordinary synergistic particle swarm optimization (EOPSO). In EOPSO , particles are divided into elite and ordinary members based on their fitness performance. Each elite individual learns from itself to maintain population diversity and achieve high-level global exploration. The ordinary ones fly toward a unified target and carry out some assistant local exploitation. In addition, an information interaction based jump-out strategy is designed to overcome particles stagnation situations. The benchmark functions in CEC 2017 are employed to compare the performance between the proposed EOPSO with 18 optimization methods (8 state-of-the-art PSO variants and 10 recently proposed non - PSO methods). Experimental comparisons demonstrate that, in EOPSO , the particles have the abilities to reasonably adjust population diversity, effectively avoid local optima, and accurately converge to the global optimum. [ABSTRACT FROM AUTHOR]

• In this paper, a novelty-based driving force is introduced to overcome deficiencies of the fitness-based driving force. • During the evolution, two types of exemplars respectively with high fitness and high novelty are saved in two archives. • In each generation, a particle respectively chooses two exemplars from the two archives to update its velocity. • Three time-varying parameters are introduced to adjust a particle's learning weights for the two driving forces aiming to satisfy distinct requirements of different evolution stages. Particle swarm optimization algorithm (PSO) is a popular optimizer, in which each particle selects its learning exemplars relying on their fitness. Thus, the search process of each particle can be seen as driven by a fitness-based force. Intuitively, the driving force is conducive to the optimizing process. However, it may bring a premature convergence of a population. In this work, a novelty-based driving force is put forward to overcome deficiencies of the fitness-based driving force. In the new proposed adjustable driving force based PSO, named as ADFPSO, two types of exemplars respectively with high fitness and high novelty are saved in two archives. In each generation, a particle respectively chooses two exemplars from the two archives to update its velocity. In addition, three time-varying parameters are introduced to adjust the particle's learning weights for the two exemplars aiming to satisfy distinct requirements of different evolution stages. Comprehensive properties of ADFPSO are extensively testified by a set of experiments, in which nine PSO variants are adopted as peer algorithms and two CEC test suites are selected as optimization problems. Moreover, distinct characteristics of the proposed novelty-based driving force are also analyzed based on a few experiments. [ABSTRACT FROM AUTHOR]

• A level-based population structure is adopted to exploration ability. • A reinforcement learning strategy is introduced to improve the search efficiency. • A level competition mechanism is proposed to optimize the convergence performance. • RLLPSO can achieve good performance for large-scale optimization. Large-scale optimization problems (LSOPs) have drawn researchers' increasing attention since their resemblance to real-world problems. However, due to the complex search space and massive local optima, it is challenging to simultaneously guarantee the diversity and convergence of the algorithms. As a widely used evolutionary algorithm with fast convergence, particle swarm optimization (PSO) shows competitive performances on some LSOPs. Nevertheless, it can easily get trapped into local optima. Overcoming the complexity of LSOPs and improving search efficiency have become vital issues. The reinforcement learning method has proven to be an effective technique in self-adaptive adjustment, which can help search for better results in large-scale solution space more effectively. In this paper, we propose a large-scale optimization algorithm called reinforcement learning level-based particle swarm optimization algorithm (RLLPSO). In RLLPSO, a level-based population structure is constructed to improve population diversity. A reinforcement learning strategy for level number control is employed to help improve the search efficiency of RLLPSO. To further enhance the convergence ability of RLLPSO, a level competition mechanism is introduced. The experimental results from two large-scale benchmark test suites demonstrate that, compared with five state-of-the-art large-scale optimization algorithms, RLLPSO shows superiority in most cases. [ABSTRACT FROM AUTHOR]

In this paper, a parallel deep learning-based community detection method in large complex networks (CNs) is proposed. First, a CN partitioning method is employed to divide the CN into multiple chunks to improve the efficiency in terms of space and time complexities. Next, the method is integrated with two optimization algorithms: (1) backpropagation (BP), which optimizes deep learning locally within each local chunk of the CN; (2) particle swarm optimization (PSO), which is used to improve the BP optimization involving all CN chunks. PSO utilizes a multi-objective function to improve the effectiveness of the proposed method. In addition, a distributed environment is set up to conduct parallel optimization of the proposed method so that multi-local optimizations could be performed simultaneously. A set of 16 real-world CNs in a range from small to large size are used to verify the effectiveness and efficiency of the method in a benchmark study. The proposed method is implemented in multi-machines with central processing unit (CPU) and graphics processing unit (GPU) devices. The results reveal the effective role of the proposed deep learning with hybrid BP–PSO optimization in detecting communities in large CNs, which requires minimum execution time on both CPU and GPU devices. [ABSTRACT FROM AUTHOR]

In this paper, the optimal DoS attack on cyber-physical systems is studied in Stackelberg game framework, which is manifested by energy allocation on communication channels. To give a realistic picture of DoS attack on a normal user launched by several hackers, a Stackelberg game between one defender and multiple attackers is considered. Compared with the existing literature, which mainly focus on equilibrium in static games, the dynamic process of the Stackelberg game is also reflected in this paper, which demonstrates the intelligence of attackers switching channels to allocate aggressive energy. In the solution of Stackelberg equilibrium, self-adaptive Particle Swarm Optimization (PSO) algorithm is utilized to cope with the nonlinearity of the reward function. Besides, for the purpose of better performance of both sides in choosing channels to allocate energy, an online computation algorithm is proposed. Finally, numerical examples are equipped to illustrate the theoretical results proved in this work. [ABSTRACT FROM AUTHOR]

[Display omitted] • A med-point-example learning strategy is proposed to get stronger exploitation. • A random learning strategy is introduced to obtain stronger exploration. • The two learning strategies are hybridized to balance exploitation and exploration. • A worst-best example learning strategy is embedded to maximize the performance. • The proposed algorithm has greater advantages on test sets and engineering problems. Social Learning Particle Swarm Optimization (SL-PSO) greatly improves the optimization performance of PSO. In solving complex optimization problems, however, it still has some deficiencies, such as poor search ability and low search efficiency. Hence, an improved SL-PSO, namely, Three-Learning Strategy PSO (TLS-PSO) is proposed in this paper. Firstly, a med-point-example learning strategy and a random learning strategy are proposed to replace the imitation component and social influence component of SL-PSO to enhance the exploitation and exploration, respectively. Secondly, the two learning strategies are combined cleverly into an updating equation to balance exploration and exploitation. Finally, a worst-best example learning strategy is merged skillfully to construct TLS-PSO with hybrid learning mechanism and further enhance the search ability. The experimental results on the complex functions from CEC2013 and CEC2017 test sets indicate that TLS-PSO has better performance compared with state-of-the-art PSO variants and other algorithms. For example, TLS-PSO has an advantage over SL-PSO on 50 of the 56 functions from CEC2013, its running time is less than SL-PSO's and it has higher search efficiency. Simulation results on the 10 engineering problems also show that TLS-PSO outperforms 7 excellent algorithms, such as IUDE and iLSHADE ∊ . It is expected to solve practical problems better. [ABSTRACT FROM AUTHOR]

• Four types of forces acting on particles are extracted from the inherent kinematic analogy of PSO's nature. • The stochastic composite dynamic model for PSO is proposed. • The stochastic stability of PSO is analyzed via constructing the corresponding Lyapunov functions. • The different influences from optimization functions to PSO's stability are discussed. • The convergence time is defined to measure the computing efficiency of PSO. The stochastic stability analysis for particle swarm optimization (PSO) has met formidable challenges due to the intricate influences on particles' motion from collaboration capability, cognitive competence, selective randomness and environmental complexity. This paper firstly regards the above-mentioned factors as forces acting on particles of PSO: interaction, damping, randomness and external forces. Based on this mechanical analogy, a novel stochastic composite dynamic model (SCDM) for PSO is proposed which can be classified into two parts: diffusion process and drift process. The diffusion process can not be easily obtained by analytical analysis, but its approximate distribution can be experimentally justified to obey Gaussian model, and the drift process is partly determined by its optimization function.To analyze the influence on PSO from the external environment, linear and quadratic optimization functions are chose to simplify the analysis. And the SCMD's stability is discussed via constructing the responding Lyapunov functions. We conclude that the gradient of linear function only decides the uniform ultimate bound while the gradient of quadratic function affects the stable conditions besides the uniform ultimate bound. Furthermore, the stable point of PSO is proved to be the optimum of quadratic function. The convergence time is also discussed to measure PSO's performance. [ABSTRACT FROM AUTHOR]

A high-dimensional and incomplete (HDI) matrix is a common form of big data in most industrial applications. Stochastic gradient descent (SGD) algorithm optimized latent factor analysis (LFA) model is often adopted in learning the abundant knowledge in HDI matrix. Despite its computational tractability and scalability, when solving a bilinear problem such as LFA, the regular SGD algorithm tends to be stuck in a local optimum. To address this issue, the paper innovatively proposes an Adjusted Stochastic Gradient Descent (ASGD) for Latent Factor Analysis, where the adjustment mechanism is implemented by considering the bi-polar gradient directions during optimization, such mechanism is theoretically proved for its efficiency in overstepping local saddle points and avoiding premature convergence. Also, the hyper-parameters of the model are implemented in a self-adaptive manner using the particle swarm optimization (PSO) algorithm, for higher practicality. Experimental results show that the proposed model outperforms other state-of-the-art approaches on six different HDI matrices from industrial applications, especially in prediction accuracy for missing data. [ABSTRACT FROM AUTHOR]

Thousands of real function evaluations are not burdensome when a surrogate-assisted evolutionary algorithm (SAEA) is used to solve expensive multi-objective optimization problems (MOPs). To reduce the computational overhead, this paper studies a surrogate-assisted multi-objective particle swarm optimization algorithm, named SaMOPSO_NS, in which an external archive-based neighborhood search, as a local search, and a pbest -dominance-based infill criterion are newly developed. The local search works hard to refine exploitation around the current non-dominated individuals once the trigger mechanism is activated, while the pbest -dominance-based infill criterion chooses non-dominated individuals predicted by an ensemble surrogate for actual evaluations. With the collaborative efforts between the local search strategy and the infill criterion, computing resources are more efficiently allocated. Three types of benchmark test instances with different dimensions as well as an engineering expensive MOP are used to examine the proposed algorithm. Experimental results demonstrate that the proposed algorithm significantly outperforms its rivals with fewer real evaluations on most medium-dimensional MOPs. Moreover, the optimized electromagnetic acoustic transducers achieved an amplitude and amplitude ratio of 9.666E-07 mm and 0.1328 respectively, markedly outpacing previously reported results. [ABSTRACT FROM AUTHOR]

This paper develops a particle swarm optimisation (PSO) based framework for multi-objective optimisation (MOO). As a part of development, a new PSO method, named self-adaptive PSO (SAPSO), is first proposed. Since the convergence of SAPSO determines the quality of the obtained Pareto front, this paper analytically investigates the convergence of SAPSO and provides a parameter selection principle that guarantees the convergence. Leveraging the proposed SAPSO, this paper then designs a SAPSO-based MOO framework, named SAMOPSO. To gain a well-distributed Pareto front, we also design an external repository that keeps the non-dominated solutions. Next, a circular sorting method, which is integrated with the elitist-preserving approach, is designed to update the external repository in the developed MOO framework. The performance of the SAMOPSO framework is validated through 12 benchmark test functions and a real-word MOO problem. For rigorous validation, the performance of the proposed framework is compared with those of four well-known MOO algorithms. The simulation results confirm that the proposed SAMOPSO outperforms its contenders with respect to the quality of the Pareto front over the majority of the studied cases. The non-parametric comparison results reveal that the proposed method is significantly better than the four algorithms compared at the confidence level of 90% over the 12 test functions. [ABSTRACT FROM AUTHOR]

Particle swarm optimizations (PSOs) are drawing extensive attention from both research and engineering fields due to their simplicity and powerful global search ability. However, there are two issues needing to be improved: one is that the classical PSO converges slowly; the other is that classical PSO tends to result in premature convergence, especially for multi-modal problems. This paper attempts to address these two issues. Firstly, to improve the convergent efficiency, this paper proposes an asymptotic predicting model of the globally-optimal solution, which is used to predict the global optimum based on extracting the features reflecting the evolutionary trend. The predicted global optimum is then taken as the third exemplar, in a way similar to the individual historical best solution and the swarm historical best solution in guiding the evolutionary process of other particles. To reduce the probability that the population is trapped into a local optimum due to the premature phenomenon, this paper proposes an adaptive mutation strategy, which is used to help the trapped particles to escape away from the local optimum by using the extended non-uniform mutation operator. Finally, we combine the two entities to develop a globally-optimal prediction-based adaptive mutation particle swarm optimization (GPAM-PSO). In numerical experimental parts, we compare the proposed GPAM-PSO with 11 existing PSO variants by using 22 benchmark problems of 30-dimensions and 100-dimensions, respectively. Numerical experiments demonstrate that the proposed GPAM-PSO could improve the accuracy and efficiency remarkably, which means that the combination of the globally-optimal prediction-based search and the adaptive mutation strategy could accelerate the convergence and reduce premature phenomenon effectively. Generally speaking, GPAM-PSO performs most efficiently and robustly. Moreover, the performance on an engineering problem demonstrates the practical application of the proposed GPAM-PSO algorithm. [ABSTRACT FROM AUTHOR]

In this paper, optimization of a linear objective function subject to a generalized fuzzy relational inequalities is investigated in which an arbitrary continuous t-norm is considered as fuzzy composition, and fuzzy inequality replaces ordinary inequality in the constraints. Unlike most optimization algorithms, in fuzzy relational inequalities with fuzzy constraints (FRI-FC) we find a near-feasible solution having a better objective value than those resulting from the resolution of the similar problems with crisp (ordinary) inequality constraints. Such solutions are called super-optima in this paper. Subsequently, an algorithm is proposed to find a super-optimum with pre-specified desirable infeasibility. For this purpose, we firstly study some structural properties of the FRI-FC problem and present a new formulization that is independent of t-norms used in the constraints of the problem. This new formulation converts the primary problem into an equivalent problem with simple constraints without considering any penalty parameters. However, it is proved that the transformed equivalent problem enables our algorithm to distinguish unfavorable points and generate a sequence of solutions converging to a super-optimum under a certain sufficient condition. Finally, a modified PSO is presented in which the ability of PSO to solve unconstrained problems with continuous domain, the structure of the transformed problem and some fuzzy structural modifications are combined and form an efficient algorithm to solve the generalized FRI-FC problems. The modified PSO algorithm has been applied to the generalized FRI-FC problem defined with ten well-known continuous t-norms. Additionally, an idea of the FRI-FC problems as outer approximators for FRI problems with ordinary inequalities is also investigated. [ABSTRACT FROM AUTHOR]

The traditional redundancy allocation problem (RAP) aims to determine a system structure that strikes an appropriate balance between series and parallel components and that maximizes reliability by using redundant components in parallel, thus satisfying resource consumption constraints. The RAP is a well-known NP-hard problem and has been an active area of research for the past four decades. By extending the series–parallel structure to a more general network structure, this paper proposes a novel RAP called the generalized RAP (GRAP). To reduce the computational burden in solving this intractable GRAP, a new algorithm, called the hybrid swarm optimization (HSO), is proposed. The HSO combines concepts from simplified swarm optimization (SSO), particle swarm optimization (PSO), simulated annealing, and network reliability methods. The paper presents designed experiments and computational studies that demonstrate the potential of using the proposed HSO for the GRAP instead of using the genetic algorithm, PSO, or SSO. [ABSTRACT FROM AUTHOR]

• A combination of Deep Q-Learning algorithm and metaheuristic GSA is offered. • GSA initializes the weights and the biases of the neural networks. • A comparison with classical random, metaheuristic PSO and GWO is carried out. • The validation is done on real-time nonlinear servo system position control. • The drawbacks of randomly initialized neural networks are mitigated. This paper presents a novel Reinforcement Learning (RL)-based control approach that uses a combination of a Deep Q-Learning (DQL) algorithm and a metaheuristic Gravitational Search Algorithm (GSA). The GSA is employed to initialize the weights and the biases of the Neural Network (NN) involved in DQL in order to avoid the instability, which is the main drawback of the traditional randomly initialized NNs. The quality of a particular set of weights and biases is measured at each iteration of the GSA-based initialization using a fitness function aiming to achieve the predefined optimal control or learning objective. The data generated during the RL process is used in training a NN-based controller that will be able to autonomously achieve the optimal reference tracking control objective. The proposed approach is compared with other similar techniques which use different algorithms in the initialization step, namely the traditional random algorithm, the Grey Wolf Optimizer algorithm, and the Particle Swarm Optimization algorithm. The NN-based controllers based on each of these techniques are compared using performance indices specific to optimal control as settling time, rise time, peak time, overshoot, and minimum cost function value. Real-time experiments are conducted in order to validate and test the proposed new approach in the framework of the optimal reference tracking control of a nonlinear position servo system. The experimental results show the superiority of this approach versus the other three competing approaches. [ABSTRACT FROM AUTHOR]

This paper proposes a particle swarm optimization with strategy dynamics (SDPSO) to solve single-objective optimization problems. SDPSO consists of four PSO search strategies. Evolutionary game theory is introduced to control the population state. In evolutionary game theory, through the interaction between players, better strategies will eventually dominate among the players. By extending this idea to PSO, a selection mechanism and a mutation mechanism are proposed. By using the selection mechanism, the adoption probability of the high payoff strategies will increase. The mutation mechanism can examine the stability of the incumbent strategy to evolutionary pressures. The performance of SDPSO is compared with 14 algorithms on the CEC 2014 test suite. The results show that SDPSO has the highest rank. SDPSO is applied to solve a real-world problem. SDPSO can find the best mean results comparing with 4 algorithms. The findings show that the proposed evolutionary game theory-based framework can adaptively control the population state. This study proposes a new application of evolutionary game theory to the design of swarm intelligence and contributes to a better understanding of the usefulness of the evolutionary game theory in the optimization method. The source codes of SDPSO are available at https://github.com/zi-ang-liu/SDPSO. [ABSTRACT FROM AUTHOR]

Particle swarm optimization (PSO) is a population-based random-search optimization technique that has become an increasingly important branch of swarm intelligence studies. Population diversity is an effective measurement that shows the distribution of particles in a search space. In this paper, we propose a diversity-based PSO algorithm that is combined with multiple techniques, and population diversity is used as a search-strategy selection criterion for particles. When diversity is high, we suggest implementing a search strategy that has a strong exploration ability. When diversity is low, we suggest implementing a search strategy that has a strong exploitation ability. In addition to our diversity-based method, we introduce a gradient-based local-search technique, multi-crossover operation, and disturbance strategy to help improve the performance of the proposed algorithm. In the experiments, we compare the proposed algorithm with 10 advanced PSO variants based on 40 widely used benchmark functions, including the CEC2017 benchmark. The results indicate that the proposed algorithm yields a better solution accuracy and convergence speed than those of other PSO variants. [ABSTRACT FROM AUTHOR]

Multimodal multi-objective optimization problems (MMOPs) involve locating equivalent Pareto optimal solutions in decision space with the same objective values. The key to handling MMOPs is finding all equivalent Pareto optimal solutions and maintaining a promising balance between the convergence and diversity of solutions in both decision space and objective space. To tackle this issue, a self-organizing quantum-inspired particle swarm optimization algorithm (MMO_SO_QPSO) is proposed in this paper for handling MMOPs. In the proposed MMO_SO_QPSO, a self-organizing map is used to find the best neighbor leader of particles. With the aid of neighbor leader particles, a special zone searching method is adopted to update the position of particles and locate equivalent Pareto optimal solutions in decision space. To maintain diversity and convergence of Pareto optimal solutions, a special archive mechanism that relies on the maximum-minimum distance among solutions is introduced into MMO_SO_QPSO. And some outstanding Pareto optimal solutions are maintained in the special archive. In addition, a new performance indicator is developed to estimate properly the similarity between obtained Pareto optimal solutions and true Pareto optimal solutions. The performance of the proposed MMO_SO_QPSO is compared with six state-of-the-art multimodal multi-objective evolutionary algorithms on two well-known benchmark problems. Experimental results demonstrate the superior performance of MMO_SO_QPSO for solving MMOPs. The effectiveness of several strategies is also discussed. [ABSTRACT FROM AUTHOR]

• The concept and verification method of affine invariance are presented. • Six algorithms are employed to analyze their affine invariances. • PSO, OFA and DE are affine invariant, GWO, SCA and BOA are not affine invariant. • Multiple experimental comparisons are executed to verify algorithms' affine invariance. An algorithm whose performance depends on the objective function being aligned with a privileged coordinate system is a poor choice in general because it is unlikely that the optimal orientation will be known in advance. In this paper, a property of meta -heuristic algorithms, named affine invariance, is introduced to verify whether the algorithm is depended on the privileged coordinate system or not. The concept of affine invariance is described in detail, and some classical algorithms, efficient in most test and actual problems, are proved to be affine invariant. While some recent algorithms in the literature are proved to be not affine invariant. As a conclusion, particle swarm optimization (PSO), differential evolution (DE) and optimal foraging algorithm (OFA) are affine invariant, while grey wolf optimizer (GWO), sine cosine algorithm (SCA) and butterfly optimization algorithm (BOA) are not affine invariant. Furthermore, comparison tests are designed to support the theoretical analysis results. In these tests, same random numbers and initial population are used to avoid the influence of randomness, thus, the conclusion is reliable. [ABSTRACT FROM AUTHOR]

• This paper focuses on the tourist trip design problem in a fuzzy environment. • A rough approximation based model is proposed to deal with the fuzzy variables. • A hybrid genetic algorithm is designed to search the optimal route. • Our approach performs significantly better than current methods. • The evolution strategies based on the improved PSO can achieves better efficiency. Trip planning significantly improves tourists' experiences and enhances the competitive advantage of tourist attractions. We focus on the tourist trip design problem (TTDP) under a fuzzy environment, which is an extension of TTDP that considers the spatiotemporal route structure and variable sightseeing value at points of interest. A rough approximation-based model is proposed to deal with fuzzy variables, and a hybrid genetic algorithm is designed to identify the optimal route. We conduct a numerical experiment to assess the performance of the presented approach. The results of the Wilcoxon rank sum tests indicate that our approach performs significantly better than currently available methods. The evolution strategies based on improved particle swarm optimization also demonstrate better efficiency than existing approaches. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new multiattribute decision making (MADM) method based on the interval-valued intuitionistic fuzzy weighted geometric average (IIFWGA) operator, the accuracy function of interval-valued intuitionistic fuzzy values (IVIFVs) and particle swarm optimization (PSO) techniques, where the weights of attributes and the evaluating values of alternatives with respect to attributes are represented by IVIFVs. First, the proposed method uses an accuracy function to transform the decision matrix given by the decision maker and represented by IVIFVs into a transformed decision matrix represented by real values in [ − 1 , 1 ] . Then, it produces the optimal weights of the attributes based on the obtained transformed decision matrix and PSO techniques. It determines the weighted evaluating IVIFV of each alternative based on the IIFWGA operator, the obtained optimal weights of the attributes and the decision matrix given by the decision maker represented by IVIFVs. Finally, it calculates the transformed value of the weighted evaluating IVIFV of each alternative based on the accuracy function to get the preference order of the alternatives. The main contribution of this paper is that we propose a new MADM method based on the IIFWGA operator of IVIFVs, the accuracy function of IVIFVs and PSO techniques, which can overcome the drawbacks of the existing MADM methods for MADM in interval-valued intuitionistic fuzzy (IVIF) environments. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new fuzzy forecasting method based on two-factors second-order fuzzy-trend logical relationship groups (TSFTLRGs), particle swarm optimization (PSO) techniques and similarity measures between the subscripts of fuzzy sets (FSs) for forecasting the Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX) and the New Taiwan Dollar/US Dollar (NTD/USD) exchange rates. First, we propose a PSO-based optimal-intervals partition algorithm to get the optimal partition of the intervals in the universe of discourse (UOD) of the main factor TAIEX and to get the optimal partition of the intervals in the UOD of the secondary factor SF , where SF ∈ {Dow Jones, NASDAQ, M1B}. Based on the proposed PSO-based optimal-intervals partition algorithm, the constructed TSFTLRGs, and similarity measures between the subscripts of FSs, we propose a new method for forecasting the TAIEX and the NTD/USD exchange rates. The main contribution of this paper is that we propose a new fuzzy forecasting method based on TSFTLRGs, PSO techniques and similarity measures between the subscripts of FSs for forecasting the TAIEX and the NTD/USD exchange rates to get higher forecasting accuracy rates than the ones of the existing fuzzy forecasting methods. [ABSTRACT FROM AUTHOR]

Many-objective problems refer to the optimization problems containing more than three conflicting objectives. To obtain a representative set of well-distributed non-dominated solutions close to Pareto front in the objective space remains a challenging problem. Many papers have proposed different Multi-Objective Evolutionary Algorithms to solve the lack of the convergence and diversity in many-objective problems. One of the more promising approaches uses a set of reference points to discriminate the solutions and guide the search process. However, this approach was incorporated mainly in Multi-Objective Evolutionary Algorithms, and there are just some few promising adaptations of Particle Swarm Optimization approaches for effectively tackling many-objective problems regarding convergence and diversity. Thus, this paper proposes a practical and efficient Many-Objective Particle Swarm Optimization algorithm for solving many-objective problems. Our proposal uses a set of reference points dynamically determined according to the search process, allowing the algorithm to converge to the Pareto front, but maintaining the diversity of the Pareto front. Our experimental results demonstrate superior or similar performance when compared to other state-of-art algorithms. [ABSTRACT FROM AUTHOR]

Over the last two decades numerous metaheuristics have been proposed and it seems today that nobody is able to understand, evaluate, or compare them all. In principle, optimization methods, including the recently popular Evolutionary Computation or Swarm Intelligence-based ones, should be developed in order to solve real-world problems. Yet the vast majority of metaheuristics are tested in the source papers on artificial benchmarks only, so their usefulness for various practical applications remains unverified. As a result, choosing the proper method for a particular real-world problem is a difficult task. This paper shows that such a choice is even more complicated if one wishes, with good reason, to use metaheuristics twice, once to find the best and then to find the worst solutions for the specific numerical real-world problem. It often occurs that for either case different optimizers are to be recommended. The above finding is based on testing 30 metaheuristics on numerical real-world problems from CEC2011. First we solve 22 minimization problems as defined for CEC2011. Then we reverse the objective function for each problem and search for its maximizing solution. We also observe that algorithms that are highly ranked on average may not perform best for any given specific problem. Rather, the highest average ranking may be achieved by methods that are never among the poorest ones. In other words, occasional winners may get less attention than rare losers. [ABSTRACT FROM AUTHOR]

In the field of network security, it is of great significance to accurately detect various types of Internet of Things (IoT) network intrusion attacks which launched by the attacker-controlled zombie hosts. In this paper, we propose a novel IoT network intrusion detection approach based on Adaptive Particle Swarm Optimization Convolutional Neural Network (APSO-CNN). In particular, the PSO algorithm with change of inertia weight is used to adaptively optimize the structure parameters of one-dimensional CNN. The cross-entropy loss function value of the validation set, which is obtained from the first training of CNN, is taken as the fitness value of PSO. Especially, we define a new evaluation method that considers both the prediction probability assigned to each category and prediction label to compare the proposed APSO-CNN algorithm with CNN set parameters manually (R-CNN). Meanwhile, the comprehensive performance of proposed APSO-CNN and other three well known algorithms are compared in the five traditional evaluation indicators and the accuracy statistical characteristics of 10 times independent experiments. The simulation results show that the multi-type IoT network intrusion attack detection task based on APSO-CNN algorithm is effective and reliable. [ABSTRACT FROM AUTHOR]

This paper investigates the parameter estimation of multivariable Wiener nonlinear systems. To solve the inconsistency problem of the parameter vector and the parameter matrix, the coupling identification concept is applied. Combined with particle swarm optimization (PSO) and an auxiliary model, the partially coupled improved particle swarm optimization (PC-IPSO) method is proposed. In this algorithm, the adaptive feedback inertia weight is improved to accelerate the convergence speed, and the retirement update mechanism is introduced to improve the optimization ability of the basic PSO algorithm. To verify the performance of PC-IPSO, we also derive a multivariable improved PSO (M-IPSO) method for comparison. The computational complexity analysis shows that the PC-IPSO algorithm requires less computational resources than the M-IPSO algorithm. Then, the convergence of the improved PSO method is analyzed. The simulation results indicate that the PC-IPSO method has a faster convergence speed and higher identification accuracy than the M-IPSO and several existing state-of-the-art methods for multivariable Wiener system identification. [ABSTRACT FROM AUTHOR]