An expanded particle swarm optimization based on multi-exemplar and forgetting ability

Defense against adversarial attacks: robust and efficient compressed optimized neural networks

In the ongoing battle against adversarial attacks, adopting a suitable strategy to enhance model efficiency, bolster resistance to adversarial threats, and ensure practical deployment is crucial. To achieve this goal, a novel four-component methodology is introduced. First, introducing a pioneering batch-cumulative approach, the exponential particle swarm optimization (ExPSO) algorithm was developed for meticulous parameter fine-tuning within each batch. A cumulative updating loss function was employed for overall optimization, demonstrating remarkable superiority over traditional optimization techniques. Second, weight compression is applied to streamline the deep neural network (DNN) parameters, boosting the storage efficiency and accelerating inference. It also introduces complexity to deter potential attackers, enhancing model accuracy in adversarial settings. This study compresses the generative pre-trained transformer (GPT) by 65%, saving time and memory without causing performance loss. Compared to state-of-the-art methods, the proposed method achieves the lowest perplexity (14.28), the highest accuracy (93.72%), and an 8 × speedup in the central processing unit. The integration of the preceding two components involves the simultaneous training of multiple versions of the compressed GPT. This training occurs across various compression rates and different segments of a dataset and is ultimately associated with a novel multi-expert architecture. This enhancement significantly fortifies the model's resistance to adversarial attacks by introducing complexity into attackers' attempts to anticipate the model's prediction integration process. Consequently, this leads to a remarkable average performance improvement of 25% across 14 different attack scenarios and various datasets, surpassing the capabilities of current state-of-the-art methods.

Effective PID controller design using a novel hybrid algorithm for high order systems

This paper discusses the merging of two optimization algorithms, atom search optimization and particle swarm optimization, to create a hybrid algorithm called hybrid atom search particle swarm optimization (h-ASPSO). Atom search optimization is an algorithm inspired by the movement of atoms in nature, which employs interaction forces and neighbor interaction to guide each atom in the population. On the other hand, particle swarm optimization is a swarm intelligence algorithm that uses a population of particles to search for the optimal solution through a social learning process. The proposed algorithm aims to reach exploration-exploitation balance to improve search efficiency. The efficacy of h-ASPSO has been demonstrated in improving the time-domain performance of two high-order real-world engineering problems: the design of a proportional-integral-derivative controller for an automatic voltage regulator and a doubly fed induction generator-based wind turbine systems. The results show that h-ASPSO outperformed the original atom search optimization in terms of convergence speed and quality of solution and can provide more promising results for different high-order engineering systems without significantly increasing the computational cost. The promise of the proposed method is further demonstrated using other available competitive methods that are utilized for the automatic voltage regulator and a doubly fed induction generator-based wind turbine systems.

A novel particle swarm optimization based on hybrid-learning model

The convergence speed and the diversity of the population plays a critical role in the performance of particle swarm optimization (PSO). In order to balance the trade-off between exploration and exploitation, a novel particle swarm optimization based on the hybrid learning model (PSO-HLM) is proposed. In the early iteration stage, PSO-HLM updates the velocity of the particle based on the hybrid learning model, which can improve the convergence speed. At the end of the iteration, PSO-HLM employs a multi-pools fusion strategy to mutate the newly generated particles, which can expand the population diversity, thus avoid PSO-HLM falling into a local optima. In order to understand the strengths and weaknesses of PSO-HLM, several experiments are carried out on 30 benchmark functions. Experimental results show that the performance of PSO-HLM is better than other the-state-of-the-art algorithms.

Gaussian bare-bone slime mould algorithm: performance optimization and case studies on truss structures

The slime mould algorithm (SMA) is a new meta-heuristic algorithm recently proposed. The algorithm is inspired by the foraging behavior of polycephalus slime moulds. It simulates the behavior and morphological changes of slime moulds during foraging through adaptive weights. Although the original SMA's performance is better than most swarm intelligence algorithms, it still has shortcomings, such as quickly falling into local optimal values and insufficient exploitation. This paper proposes a Gaussian barebone mutation enhanced SMA (GBSMA) to alleviate the original SMA's shortcomings. First of all, the Gaussian function in the Gaussian barebone accelerates the convergence while also expanding the search space, which improves the algorithm exploration and exploitation capabilities. Secondly, the differential evolution (DE) update strategy in the Gaussian barebone, using rand as the guiding vector. It also enhances the algorithm's global search performance to a certain extent. Also, the greedy selection is introduced on this basis, which prevents individuals from performing invalid position updates. In the IEEE CEC2017 test function, the proposed GBSMA is compared with a variety of meta-heuristic algorithms to verify the performance of GBSMA. Besides, GBSMA is applied to solve truss structure optimization problems. Experimental results show that the convergence speed and solution accuracy of the proposed GBSMA are significantly better than the original SMA and other similar products.

Supplementary Information

The online version contains supplementary material available at 10.1007/s10462-022-10370-7.

Velocity pausing particle swarm optimization: a novel variant for global optimization

Particle swarm optimization (PSO) is one of the most well-regard metaheuristics with remarkable performance when solving diverse optimization problems. However, PSO faces two main problems that degrade its performance: slow convergence and local optima entrapment. In addition, the performance of this algorithm substantially degrades on high-dimensional problems. In the classical PSO, particles can move in each iteration with either slower or faster speed. This work proposes a novel idea called velocity pausing where particles in the proposed velocity pausing PSO (VPPSO) variant are supported by a third movement option that allows them to move with the same velocity as they did in the previous iteration. As a result, VPPSO has a higher potential to balance exploration and exploitation. To avoid the PSO premature convergence, VPPSO modifies the first term of the PSO velocity equation. In addition, the population of VPPSO is divided into two swarms to maintain diversity. The performance of VPPSO is validated on forty three benchmark functions and four real-world engineering problems. According to the Wilcoxon rank-sum and Friedman tests, VPPSO can significantly outperform seven prominent algorithms on most of the tested functions on both low- and high-dimensional cases. Due to its superior performance in solving complex high-dimensional problems, VPPSO can be applied to solve diverse real-world optimization problems. Moreover, the velocity pausing concept can be easily integrated with new or existing metaheuristic algorithms to enhance their performances. The Matlab code of VPPSO is available at: https://uk.mathworks.com/matlabcentral/fileexchange/119633-vppso.

A Promotive Particle Swarm Optimizer With Double Hierarchical Structures

In this study, a novel promotive particle swarm optimizer with double hierarchical structures is proposed. It is inspired by successful mechanisms present in social and biological systems to make particles compete fairly. In the proposed method, the swarm is first divided into multiple independent subpopulations organized in a hierarchical promotion structure, which protects subpopulation at each hierarchy to search for the optima in parallel. A unidirectional communication strategy and a promotion operator are further implemented to allow excellent particles to be promoted from low-hierarchy subpopulations to high-hierarchy subpopulations. Furthermore, for the internal competition within each subpopulation of the hierarchical promotion structure, a hierarchical multiscale optimum controlled by a tiered architecture of particles is constructed for particles, in which each particle can synthesize a set of optima of its different scales. The hierarchical promotion structure can protect particles that just fly to promising regions and have low fitness from competing with the entire swarm. Also, the double hierarchical structures increase the diversity of searching. Numerical experiments and statistical analysis of results reported on 30 benchmark problems show that the proposed method improves the accuracy and convergence speed especially in solving complex problems when compared with several variations of particle swarm optimization.

Partial Oxidation of FeS Nanoparticles Enhances Cr(VI) Sequestration

Iron sulfide nanoparticles (nano-FeS) have shown great potential for in situ remediation of Cr(VI) pollution by reducing Cr(VI) to the less soluble and toxic Cr(III). However, material oxidation that inevitably occurs during storage and application alters its reactivity. Herein, we show that partial oxidation of nanoparticulate mackinawite (FeS) significantly enhances its capability in sequestering Cr(VI). Oxidation of nano-FeS increases its binding affinity to Cr(VI), likely due to preferential inner-sphere complexation of Cr(VI) oxyanions to ferric over ferrous iron in mackinawite/lepidocrocite (FeS/γ-FeOOH) nanocomposites. A trade-off is that oxidation mitigates Cr(VI) reduction by lowering the electron-donating potential of the material and the electron transfer at a solution-material interface and consequently hinders the transformation of adsorbed Cr(VI) to Cr(III). Notably, the rate-limiting step of Cr(VI) sequestration transitions from adsorption to reduction during oxidation, as demonstrated with batch experiments coupled with kinetic modeling. Thus, an optimum oxidation degree exists, wherein the gain in the overall performance from enhanced adsorption overcompensates the loss from inhibited reduction, resulting in maximum sequestration of aqueous Cr(VI) as solid-phase Cr(III). Our findings inform better assessment and design of nanomaterials for Cr(VI) remediation and may be extended to interactions of other oxyanions with natural and engineered nanoparticles during oxidative aging.

A Fast Hybrid Feature Selection Based on Correlation-Guided Clustering and Particle Swarm Optimization for High-Dimensional Data

The "curse of dimensionality" and the high computational cost have still limited the application of the evolutionary algorithm in high-dimensional feature selection (FS) problems. This article proposes a new three-phase hybrid FS algorithm based on correlation-guided clustering and particle swarm optimization (PSO) (HFS-C-P) to tackle the above two problems at the same time. To this end, three kinds of FS methods are effectively integrated into the proposed algorithm based on their respective advantages. In the first and second phases, a filter FS method and a feature clustering-based method with low computational cost are designed to reduce the search space used by the third phase. After that, the third phase applies oneself to finding an optimal feature subset by using an evolutionary algorithm with the global searchability. Moreover, a symmetric uncertainty-based feature deletion method, a fast correlation-guided feature clustering strategy, and an improved integer PSO are developed to improve the performance of the three phases, respectively. Finally, the proposed algorithm is validated on 18 publicly available real-world datasets in comparison with nine FS algorithms. Experimental results show that the proposed algorithm can obtain a good feature subset with the lowest computational cost.

Informative SNP Selection Based on a Fuzzy Clustering and Improved Binary Particle Swarm Optimization Algorithm

Single-nucleotide polymorphism (SNP) involves the replacement of a single nucleotide in a deoxyribonucleic acid (DNA) sequence and is often linked to the development of specific diseases. Although current genotyping methods can tag SNP loci within biological samples to provide accurate genetic information for a disease associated, they have limited prediction accuracy. Furthermore, they are complex to perform and may result in the prediction of an excessive number of tag SNP loci, which may not always be associated with the disease. Therefore in this manuscript, we aimed to evaluate the impact of a newly optimized fuzzy clustering and binary particle swarm optimization algorithm (FCBPSO) on the accuracy and running time of informative SNP selection. Fuzzy clustering and FCBPSO were first applied to identify the equivalence relation and the candidate tag SNP set to reduce the redundancy between loci. The FCBPSO algorithm was then optimized and used to obtain the final tag SNP set. The prediction performance and running time of the newly developed model were compared with other traditional methods, including NMC, SPSO, and MCMR. The prediction accuracy of the FCBPSO algorithm was always higher than that of the other algorithms especially as the number of tag SNPs increased. However, when the number of tag SNPs was low, the prediction accuracy of FCBPSO was slightly lower than that of MCMR (add prediction accuracy values for each algorithm). However, the running time of the FCBPSO algorithm was always lower than that of MCMR. FCBPSO not only reduced the size and dimension of the optimization problem but also simplified the training of the prediction model. This improved the prediction accuracy of the model and reduced the running time when compared with other traditional methods.

A Hybrid Particle Swarm Optimization-Based Wavelet Threshold Denoising Algorithm for Acoustic Emission Signals

Acoustic emission (AE) as a non-destructive monitoring method is used to identify small damage in various materials effectively. However, AE signals acquired during the monitoring of oil and gas steel pipelines are always contaminated with noise. A noisy signal can be a threat to the reliability and accuracy of the findings. To address these shortcomings, this study offers a technique based on discrete wavelet transform to eliminate noise in these signals. The denoising performance is affected by several factors, including wavelet basis function, decomposition level, thresholding method, and the threshold selection criteria. Traditional threshold selection rules rely on statistical and empirical variables, which influence their performance in noise reduction under various conditions. To obtain the global best solution, a threshold selection approach is proposed by integrating particle swarm optimization and the late acceptance hill-climbing heuristic algorithms. By comparing five common approaches, the superiority of the suggested technique was validated by simulation results. The enhanced thresholding solution based on particle swarm optimization algorithm outperformed others in terms of signal-to-noise ratio and root-mean-square error of denoised AE signals, implying that it is more effective for the detection of AE sources in oil and gas steel pipelines.

Differential Elite Learning Particle Swarm Optimization for Global Numerical Optimization

Although particle swarm optimization (PSO) has been successfully applied to solve optimization problems, its optimization performance still encounters challenges when dealing with complicated optimization problems, especially those with many interacting variables and many wide and flat local basins. To alleviate this issue, this paper proposes a differential elite learning particle swarm optimization (DELPSO) by differentiating the two guiding exemplars as much as possible to direct the update of each particle. Specifically, in this optimizer, particles in the current swarm are divided into two groups, namely the elite group and non-elite group, based on their fitness. Then, particles in the non-elite group are updated by learning from those in the elite group, while particles in the elite group are not updated and directly enter the next generation. To comprise fast convergence and high diversity at the particle level, we let each particle in the non-elite group learn from two differential elites in the elite group. In this way, the learning effectiveness and the learning diversity of particles is expectedly improved to a large extent. To alleviate the sensitivity of the proposed DELPSO to the newly introduced parameters, dynamic adjustment strategies for parameters were further designed. With the above two main components, the proposed DELPSO is expected to compromise the search intensification and diversification well to explore and exploit the solution space properly to obtain promising performance. Extensive experiments conducted on the widely used CEC 2017 benchmark set with three different dimension sizes demonstrated that the proposed DELPSO achieves highly competitive or even much better performance than state-of-the-art PSO variants.

Stochastic Triad Topology Based Particle Swarm Optimization for Global Numerical Optimization

Particle swarm optimization (PSO) has exhibited well-known feasibility in problem optimization. However, its optimization performance still encounters challenges when confronted with complicated optimization problems with many local areas. In PSO, the interaction among particles and utilization of the communication information play crucial roles in improving the learning effectiveness and learning diversity of particles. To promote the communication effectiveness among particles, this paper proposes a stochastic triad topology to allow each particle to communicate with two random ones in the swarm via their personal best positions. Then, unlike existing studies that employ the personal best positions of the updated particle and the neighboring best position of the topology to direct its update, this paper adopts the best one and the mean position of the three personal best positions in the associated triad topology as the two guiding exemplars to direct the update of each particle. To further promote the interaction diversity among particles, an archive is maintained to store the obsolete personal best positions of particles and is then used to interact with particles in the triad topology. To enhance the chance of escaping from local regions, a random restart strategy is probabilistically triggered to introduce initialized solutions to the archive. To alleviate sensitivity to parameters, dynamic adjustment strategies are designed to dynamically adjust the associated parameter settings during the evolution. Integrating the above mechanism, a stochastic triad topology-based PSO (STTPSO) is developed to effectively search complex solution space. With the above techniques, the learning diversity and learning effectiveness of particles are largely promoted and thus the developed STTPSO is expected to explore and exploit the solution space appropriately to find high-quality solutions. Extensive experiments conducted on the commonly used CEC 2017 benchmark problem set with different dimension sizes substantiate that the proposed STTPSO achieves highly competitive or even much better performance than state-of-the-art and representative PSO variants.

Lévy flight-based inverse adaptive comprehensive learning particle swarm optimization

In the traditional particle swarm optimization algorithm, the particles always choose to learn from the well-behaved particles in the population during the population iteration. Nevertheless, according to the principles of particle swarm optimization, we know that the motion of each particle has an impact on other individuals, and even poorly behaved particles can provide valuable information. Based on this consideration, we propose Lévy flight-based inverse adaptive comprehensive learning particle swarm optimization, called LFIACL-PSO. In the LFIACL-PSO algorithm, First, when the particle is trapped in the local optimum and cannot jump out, inverse learning is used, and the learning step size is obtained through the Lévy flight. Second, to increase the diversity of the algorithm and prevent it from prematurely converging, a comprehensive learning strategy and Ring-type topology are used as part of the learning paradigm. In addition, use the adaptive update to update the acceleration coefficients for each learning paradigm. Finally, the comprehensive performance of LFIACL-PSO is measured using 16 benchmark functions and a real engineering application problem and compared with seven other classical particle swarm optimization algorithms. Experimental comparison results show that the comprehensive performance of the LFIACL-PSO outperforms comparative PSO variants.

Stochastic Cognitive Dominance Leading Particle Swarm Optimization for Multimodal Problems

Optimization problems become increasingly complicated in the era of big data and Internet of Things, which significantly challenges the effectiveness and efficiency of existing optimization methods. To effectively solve this kind of problems, this paper puts forward a stochastic cognitive dominance leading particle swarm optimization algorithm (SCDLPSO). Specifically, for each particle, two personal cognitive best positions are first randomly selected from those of all particles. Then, only when the cognitive best position of the particle is dominated by at least one of the two selected ones, this particle is updated by cognitively learning from the better personal positions; otherwise, this particle is not updated and directly enters the next generation. With this stochastic cognitive dominance leading mechanism, it is expected that the learning diversity and the learning efficiency of particles in the proposed optimizer could be promoted, and thus the optimizer is expected to explore and exploit the solution space properly. At last, extensive experiments are conducted on a widely acknowledged benchmark problem set with different dimension sizes to evaluate the effectiveness of the proposed SCDLPSO. Experimental results demonstrate that the devised optimizer achieves highly competitive or even much better performance than several state-of-the-art PSO variants.

Dynamic Population Cooperative

Particle swarm optimization (PSO) has attracted wide attention in the recent decade. Although PSO is an efficient and simple evolutionary algorithm and has been successfully applied to solve optimization problems in many real-world fields, premature maturation and poor local search capability remain two critical issues for PSO. Therefore, to alleviate these disadvantages, a dynamic population cooperative particle swarm optimization for global optimization problems (DPCPSO) is proposed. Firstly, to enhance local search capability, an elite neighborhood learning strategy is constructed by leveraging information from elite particles. Meanwhile, to make the particle easily jump out of the local optimum, a crossover-mutation mechanism is utilized. Finally, a dynamic population partitioning mechanism is designed to balance exploration and exploitation capabilities. 16 classic benchmark functions and 1 real-world optimization problem are used to test the proposed algorithm against with 6 typical PSO algorithms. The experimental results show that DPCPSO is statistically and significantly better than the compared algorithms for most of the test problems. Moreover, the convergence speed and convergence accuracy of DPCPSO are also significantly improved. Therefore, the algorithm is highly competitive in solving global optimization problems.

Generation-Level Parallelism for Evolutionary Computation: A Pipeline-Based Parallel Particle Swarm Optimization

Due to the population-based and iterative-based characteristics of evolutionary computation (EC) algorithms, parallel techniques have been widely used to speed up the EC algorithms. However, the parallelism usually performs in the population level where multiple populations (or subpopulations) run in parallel or in the individual level where the individuals are distributed to multiple resources. That is, different populations or different individuals can be executed simultaneously to reduce running time. However, the research into generation-level parallelism for EC algorithms has seldom been reported. In this article, we propose a new paradigm of the parallel EC algorithm by making the first attempt to parallelize the algorithm in the generation level. This idea is inspired by the industrial pipeline technique. Specifically, a kind of EC algorithm called local version particle swarm optimization (PSO) is adopted to implement a pipeline-based parallel PSO (PPPSO, i.e., P³SO). Due to the generation-level parallelism in P³SO, when some particles still perform their evolutionary operations in the current generation, some other particles can simultaneously go to the next generation to carry out the new evolutionary operations, or even go to further next generation(s). The experimental results show that the problem-solving ability of P³SO is not affected while the evolutionary speed has been substantially accelerated in a significant fashion. Therefore, generation-level parallelism is possible in EC algorithms and may have significant potential applications in time-consumption optimization problems.

A multi-sample particle swarm optimization algorithm based on electric field force

Aiming at the premature convergence problem of particle swarm optimization algorithm, a multi-sample particle swarm optimization (MSPSO) algorithm based on electric field force is proposed. Firstly, we introduce the concept of the electric field into the particle swarm optimization algorithm. The particles are affected by the electric field force, which makes the particles exhibit diverse behaviors. Secondly, MSPSO constructs multiple samples through two new strategies to guide particle learning. An electric field force-based comprehensive learning strategy (EFCLS) is proposed to build attractive samples and repulsive samples, thus improving search efficiency. To further enhance the convergence accuracy of the algorithm, a segment-based weighted learning strategy (SWLS) is employed to construct a global learning sample so that the particles learn more comprehensive information. In addition, the parameters of the model are adjusted adaptively to adapt to the population status in different periods. We have verified the effectiveness of these newly proposed strategies through experiments. Sixteen benchmark functions and eight well-known particle swarm optimization algorithm variants are employed to prove the superiority of MSPSO. The comparison results show that MSPSO has better performance in terms of accuracy, especially for high-dimensional spaces, while maintaining a faster convergence rate. Besides, a real-world problem also verified that MSPSO has practical application value.

Control system research in wave compensation based on particle swarm optimization

For the offshore wave compensation control system, its controller setting will directly affect the platform's compensation effect. In order to study the wave compensation control system and optimization strategy, we build and simulate the wave compensation control model by using particle swarm optimization (PSO) to optimize the controller's control parameters and compare the results with other intelligent algorithms. Then we compare the response errors of the wave compensation platform under different PID controllers; and compare the particle swarm algorithm's response results and the genetic algorithm to the system controller optimization. The results show that the particle swarm algorithm is 63.94% lower than the genetic algorithm overshoot, and the peak time is 0.26 s lower, the adjustment time is 1.4 s lower than the genetic algorithm. It shows that the control effect of the wave compensation control system has a great relationship with the controller's parameter selection. Meanwhile, the particle swarm optimization algorithm's optimization can set the wave compensation PID control system, and it has the optimization effect of small overshoot and fast response time. This paper proposes the application of the particle swarm algorithm to the wave compensation system. It verifies the superiority of the method after application, and provides a new research reference for the subsequent research on the wave compensation control systems.

Feature Selection Using Enhanced Particle Swarm Optimisation for Classification Models

In this research, we propose two Particle Swarm Optimisation (PSO) variants to undertake feature selection tasks. The aim is to overcome two major shortcomings of the original PSO model, i.e., premature convergence and weak exploitation around the near optimal solutions. The first proposed PSO variant incorporates four key operations, including a modified PSO operation with rectified personal and global best signals, spiral search based local exploitation, Gaussian distribution-based swarm leader enhancement, and mirroring and mutation operations for worst solution improvement. The second proposed PSO model enhances the first one through four new strategies, i.e., an adaptive exemplar breeding mechanism incorporating multiple optimal signals, nonlinear function oriented search coefficients, exponential and scattering schemes for swarm leader, and worst solution enhancement, respectively. In comparison with a set of 15 classical and advanced search methods, the proposed models illustrate statistical superiority for discriminative feature selection for a total of 13 data sets.

An efficient particle swarm optimization with homotopy strategy for global numerical optimization

Particle swarm optimization (PSO) as a successful optimization algorithm is widely used in many practical applications due to its advantages in fast convergence speed and convenient implementation. As a population optimization algorithm, the quality of initial population plays an important role in the performance of PSO. However, random initialization is used in population initialization for PSO. Using the solution of the solved problem as prior knowledge will help to improve the quality of the initial population solution. In this paper, we use homotopy analysis method (HAM) to build a bridge between the solved problems and the problems to be solved. Therefore, an improved PSO framework based on HAM, called HAM-PSO, is proposed. The framework of HAM-PSO includes four main processes. It contains obtaining the prior knowledge, constructing homotopy function, generating initial solution and solving the to be solved by PSO. In fact, the framework does not change the PSO, but replaces the random population initialization. The basic PSO algorithm and three others typical PSO algorithms are used to verify the feasibility and effectiveness of this framework. The experimental results show that the four PSO using this framework are better than those without this framework.

Elite Exploitation: A Combination of Mathematical Concept and EMO Approach for Multi-Objective Decision Making

This paper explores the combination of a classic mathematical function named “hyperbolic tangent” with a metaheuristic algorithm, and proposes a novel hybrid genetic algorithm called NSGA-II-BnF for multi-objective decision making. Recently, many metaheuristic evolutionary algorithms have been proposed for tackling multi-objective optimization problems (MOPs). These algorithms demonstrate excellent capabilities and offer available solutions to decision makers. However, their convergence performance may be challenged by some MOPs with elaborate Pareto fronts such as CFs, WFGs, and UFs, primarily due to the neglect of diversity. We solve this problem by proposing an algorithm with elite exploitation strategy, which contains two parts: first, we design a biased elite allocation strategy, which allocates computation resources appropriately to elites of the population by crowding distance-based roulette. Second, we propose a self-guided fast individual exploitation approach, which guides elites to generate neighbors by a symmetry exploitation operator, which is based on mathematical hyperbolic tangent function. Furthermore, we designed a mechanism to emphasize the algorithm’s applicability, which allows decision makers to adjust the exploitation intensity with their preferences. We compare our proposed NSGA-II-BnF with four other improved versions of NSGA-II (NSGA-IIconflict, rNSGA-II, RPDNSGA-II, and NSGA-II-SDR) and four competitive and widely-used algorithms (MOEA/D-DE, dMOPSO, SPEA-II, and SMPSO) on 36 test problems (DTLZ1–DTLZ7, WGF1–WFG9, UF1–UF10, and CF1–CF10), and measured using two widely used indicators—inverted generational distance (IGD) and hypervolume (HV). Experiment results demonstrate that NSGA-II-BnF exhibits superior performance to most of the algorithms on all test problems.

Triple Archives Particle Swarm Optimization

There are two common challenges in particle swarm optimization (PSO) research, that is, selecting proper exemplars and designing an efficient learning model for a particle. In this article, we propose a triple archives PSO (TAPSO), in which particles in three archives are used to deal with the above two challenges. First, particles who have better fitness (i.e., elites) are recorded in one archive while other particles who offer faster progress, called profiteers in this article, are saved in another archive. Second, when breeding each dimension of a potential exemplar for a particle, we choose a pair of elite and profiteer from corresponding archives as two parents to generate the dimension value by ordinary genetic operators. Third, each particle carries out a specific learning model according to the fitness of its potential exemplars. Furthermore, there is no acceleration coefficient in TAPSO aiming to simplify the learning models. Finally, if an exemplar has excellent performance, it will be regarded as an outstanding exemplar and saved in the third archive, which can be reused by inferior particles aiming to enhance the exploitation and to save computing resources. The experimental results and comparisons between TAPSO and other eight PSOs on 30 benchmark functions and four real applications suggest that TAPSO attains very promising performance in different types of functions, contributing to both higher solution accuracy and faster convergence speed. Furthermore, the effectiveness and efficiency of these new proposed strategies are discussed based on extensive experiments.