Abstract
Comprehensive learning particle swarm optimization (CLPSO) is a powerful state-of-the-art single-objective metaheuristic. Extending from CLPSO, this paper proposes multiswarm CLPSO (MSCLPSO) for multiobjective optimization. MSCLPSO involves multiple swarms, with each swarm associated with a separate original objective. Each particle’s personal best position is determined just according to the corresponding single objective. Elitists are stored externally. MSCLPSO differs from existing multiobjective particle swarm optimizers in three aspects. First, each swarm focuses on optimizing the associated objective using CLPSO, without learning from the elitists or any other swarm. Second, mutation is applied to the elitists and the mutation strategy appropriately exploits the personal best positions and elitists. Third, a modified differential evolution (DE) strategy is applied to some extreme and least crowded elitists. The DE strategy updates an elitist based on the differences of the elitists. The personal best positions carry useful information about the Pareto set, and the mutation and DE strategies help MSCLPSO discover the true Pareto front. Experiments conducted on various benchmark problems demonstrate that MSCLPSO can find nondominated solutions distributed reasonably over the true Pareto front in a single run.
Highlights
Multiobjective optimization deals with multiple objectives that often conflict with each other
multiswarm CLPSO (MSCLPSO), coevolutionary multiswarm PSO (CMPSO), Multiobjective evolutionary algorithm based on decomposition (MOEA/D), and Nondominated sorting genetic algorithm II (NSGA-II) are ranked according to their mean inverted generational distance (IGD) results and the multiobjective metaheuristics (MOMHs) are compared using the wellknown Wilcoxon rank sum test with the significance level 0.05
The final nondominated solutions obtained by MSCLPSO and some literature MOMHs on all the benchmark multiobjective optimization problems (MOPs) are illustrated in Figs 3 and 4
Summary
Multiobjective optimization deals with multiple objectives that often conflict with each other. Multiobjective optimization methods are either generating or preferences-based [1]. The preferences-based methods, with the preferences of the objectives known in advance, convert the multiple objectives into a single objective through techniques such as weighting and ε-constraint; the single-objective problem can be solved using a single-objective optimizer. It has been noted in [3] that the weighting technique cannot find a nondominated solution on PLOS ONE | DOI:10.1371/journal.pone.0172033. Let kmax be the predefined maximum number of generations, in each generation k, w is updated according to Eq (3)
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