A new multi-objective particle swarm optimisation algorithm based on R2 indicator selection mechanism

Wei, Lixin; Li, Xin; Fan, Rui

doi:10.1080/00207721.2019.1645914

Cited by 11 publications

(10 citation statements)

References 27 publications

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“…Wei et al [99] proposed a many-objective particle swarm optimizer based on the R2 indicator to achieve better convergence, which maximizes the internal density of a population. This method employs a bi-level archive-maintaining strategy based on the R2 indicator and objective space decomposition to maintain well-distributed solutions, which maximizes the dynamic similarity of a population.…”

Section: ) R2 Indicator-based Methodsmentioning

confidence: 99%

Methods That Optimize Multi-Objective Problems: A Survey and Experimental Evaluation

Taha

2020

IEEE Access

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Most current multi-optimization survey papers classify methods into broad objective categories and do not draw clear boundaries between the specific techniques employed by these methods. This may lead to the misclassification of unrelated methods/techniques into the same objective category. Moreover, most of these survey papers classify algorithms as independent of the specific techniques they employ. Toward this end, we introduce in this survey paper a methodology-based taxonomy that classifies multi-optimization methods into hierarchically nested, fine-grained, and specific classes. We provide a methodological taxonomy to classify methods into the following hierarchical fashion: objective categories© objective functions©optimization methods©optimization sub-methods. We introduce a comprehensive survey on the methods that are contained under each optimization method, the optimization methods contained under each objective function, and objective functions contained under each objective category. We selected the objective functions that should be maximized for solving most real-word multi-objective optimization problems, which are pairs of the following: partitions separability, internal density, dynamic similarity, and structural similarity. For each optimization method, we surveyed the various algorithms in literature that pertain to the method. We experimentally compared and ranked the optimization methods that fall under each objective function, the objective functions that fall under each objective category, and the objective categories used for solving a specific optimization problem.INDEX TERMS Multi-objective optimization, multi-objective problem, multi-objective evolutionary algorithm, objective function.Our methodology-based taxonomy enables a researcher reader to gain knowledge about the following:1) The very specific method under which the researcher's proposed algorithm falls.2) The objective's category and function under which the researcher's proposed method falls.3) The advantages and limitations of the method, objective category, and objective function under which the researcher's proposed algorithm falls. 4) The research works in literature that are the most comparable with the researcher's proposed algorithm. B. CURRENT SURVEY PAPERS ON THE TOPICCurrent survey papers can be classified into the following broad categories: multi-objective and many-objective methods. Multi-objective papers can be further classified into evolutionary-based and decomposition-based methods. In this Subsection, we outline the most notable survey papers based on the mentioned classifications.

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Section: ) R2 Indicator-based Methodsmentioning

confidence: 99%

Methods That Optimize Multi-Objective Problems: A Survey and Experimental Evaluation

Taha

2020

IEEE Access

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“…The number of function evaluations (NFE) is chosen as the termination criterion. NFEs are defined based on recent articles [35]- [38]. Regarding the two-objective test problems of ZDT and CEC09 (UF1-UF7), the maximum NFE is selected at 10k and 60k, respectively.…”

Section: Igd(s Zmentioning

confidence: 99%

R2-HMEWO: Hybrid multi-objective evolutionary algorithm based on the Equilibrium Optimizer and Whale Optimization Algorithm

Tahernezhad-Javazm

Rankin

Coyle

2022

2022 IEEE Congress on Evolutionary Computation (CEC)

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Multi-objective evolutionary algorithms can be categorized into three basic groups: domination-based, decomposition-based, and indicator-based algorithms. Hybrid multi-objective evolutionary algorithms, which combine algorithms from these groups, are gaining increased popularity in recent years. This is because hybrid algorithms can compensate for the drawbacks of the basic algorithms by adding different operators and structures that complement each other. This paper introduces a hybrid-multi objective evolutionary algorithm (R2-HMEWO) that applies hybridization in the form of structure and operators. R2-HMEWO is based on the whale optimization algorithm (WOA) and equilibrium optimizer (EO). Elite individuals of WOA and EO are selected from a repository based on the R2-indicator and shifted density estimationbased method. In order to improve solutions' diversity, a reference points method is devised to select next-generation individuals. The proposed multi-objective algorithm is evaluated on 19 benchmark test problems (ZDT, DTLZ, and CEC009) and compared with six state-of-the-art (SOTA) algorithms (NSGA-III, NSGA-II, MOEA/D, MOMBI-II, MOEA/IGD-NS, and dMOPSO). Based on the inverted generational distance (IGD) metric (mean of 25 independent runs), R2-HMEWO outperformed other algorithms on 14 out of 19 test problems and revealed a highly competitive performance on the other test problems. Also, R2-HMEWO performed statistically significant better than MOEA/D and dMOPSO in 15/19 and 14/19 test problems, respectively (p<0.05), and reached significant performance in 4 test problems (from ZDT and CEC09) compared to other algorithms.

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“…The parameter setting for ESMOPSO algorithm are used in the process of polynomial mutation including probability of crossover p c = 0.5 and probability of mutation p m = 1/V . During the process of particle update, the inertia weight is adaptively adjusted by cosine function [37], the social learning factor is c 1 = 1.2, the individual learning factor is c 2 = 1. The performance of the algorithm can be intuitively shown in the form of data and graphs.…”

Section: Experimental Settingsmentioning

confidence: 99%

A Multi-Objective Particle Swarm Optimization Algorithm Based on Enhanced Selection

Wang

2019

IEEE Access

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Most multi-objective particle swarm optimization algorithms, which have demonstrated their good performance on various practical problems involving two or three objectives, face significant challenges in complex problems. For overcoming this challenges, a multi-objective particle swarm optimization algorithm based on enhanced selection(ESMOPSO) is proposed. In order to increase the ability of exploration and exploitation, enhanced selection strategy is designed to update personal optimal particles, and objective function weighting is used to update global optimal particle adaptively. In addition, R2 indicator is incorporated into the achievement scalarizing function to layer particles in archive, which promotes the archive update. Besides, Gaussian mutation strategy is designed to avoid particles falling into local optimum, and polynomial mutation is applied in archive to increase the diversity of elite solutions. The performance of the proposed algorithm is validated and compared with some state-of-the-art algorithms on a number of test problems. Experimental results demonstrate that ESMOPSO algorithm shows very competitive performance when dealing with complex MOPs.

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A new multi-objective particle swarm optimisation algorithm based on R2 indicator selection mechanism

Cited by 11 publications

References 27 publications

Methods That Optimize Multi-Objective Problems: A Survey and Experimental Evaluation

Methods That Optimize Multi-Objective Problems: A Survey and Experimental Evaluation

R2-HMEWO: Hybrid multi-objective evolutionary algorithm based on the Equilibrium Optimizer and Whale Optimization Algorithm

A Multi-Objective Particle Swarm Optimization Algorithm Based on Enhanced Selection

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