Abstract
Recently, there are a number of particle swarm optimization algorithms (PSOs) proposed for tackling multi-objective optimization problems (MOPs). Most of multi-objective PSOs (MOPSOs) were designed to speed up their convergence, which have been validated when tackling various kinds of MOPs. However, they may face some challenges for tackling some complicated MOPs, such as the UF test problems with complicated Pareto-optimal sets, mainly due to their neglect on the diversity. To solve the above problem, a novel hybrid MOPSO (called HMOPSO-ARA) is suggested in this paper with an adaptive resource allocation strategy, which shows a superior performance over most MOPSOs. Using the decomposition approach in HMOPSO-ARA, MOPs are transferred into a set of subproblems, each of which is accordingly optimized by one particle using a novel velocity update approach with the strengthened search capability. Then, an adaptive resource allocation strategy is employed based on the relevant improvement on the aggregated function, which can reasonably assign the computational resource to the particles according to their performance, so as to accelerate the convergence speed to the true Pareto-optimal front. Moreover, a decomposition-based clonal selection strategy is further used to enhance our performance, where the cloning process is run on the external archive based on the relevant fitness improvement. The experiments validate the superiority of HMOPSO-ARA over four competitive MOPSOs (SMPSO, CMPSO, dMOPSO and AgMOPSO) and four competitive multi-objective evolutionary algorithms (MOEA/D-ARA, MOEA/D-DE MOEA/D-GRA and EF_PD) when tackling thirty-five test problems (DTLZ1-DTLZ9, WFG1-WFG9, UF1-UF10 and F1-F9), in terms of two widely used performance indicators.
Highlights
In some real-world engineering problems, we often need to solve the optimization problems with several objectives, which are usually conflicted with each other
In order to enhance the robustness and performance of multi-objective particle swarm optimization (PSO) (MOPSOs), we propose a novel velocity update method in this paper, which can provide another new search direction from xpbesti to xgbesti to speed up the convergence, and can make more disturbances on the particles to improve the diversity, as defined below
Similar to the UF test problems, the F1-F9 test problems are first proposed in [31], which aim to estimate the ability of multi-objective evolutionary algorithms (MOEAs) in tackling complicated Pareto-optimal set (PS) shapes
Summary
In some real-world engineering problems, we often need to solve the optimization problems with several objectives, which are usually conflicted with each other. Multi-objective evolutionary algorithms (MOEAs) have been presented and shown promising performance in solving different kinds of MOPs [2]–[4]. Decomposition-based MOEAs solve MOPs by optimizing a set of subproblems on a collaborative manner. A collaborative resource allocation strategy was proposed in MOEA/D-CRA [14], which runs the resource allocation based on the contributions to produce the high-quality solutions for each subproblem. A novel indicator-based method was presented in DLS-MOEA [22], which designs an enhanced diversification mechanism and a new solution generator based on the external archive, while an enhanced inverted generational distance indicator was reported in VOLUME 7, 2019. A novel velocity update strategy for PSObased search and a decomposition-based clonal selection method are presented in our algorithm to further speed up the convergence and maintain the diversity. Xgbesti is randomly selected from top 10% particles with the lager improvement fitness values for i-th subproblem
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