Abstract
Recently, decomposition-based multiobjective evolutionary algorithms have good performances in the field of multiobjective optimization problems (MOPs) and have been paid attention by many scholars. Generally, a MOP is decomposed into a number of subproblems through a set of weight vectors with good uniformly and aggregate functions. The main role of weight vectors is to ensure the diversity and convergence of obtained solutions. However, these algorithms with uniformity of weight vectors cannot obtain a set of solutions with good diversity on some MOPs with complex Pareto optimal fronts (PFs) (i.e., PFs with a sharp peak or low tail or discontinuous PFs). To deal with this problem, an improved decomposition-based multiobjective evolutionary algorithm with adaptive weight adjustment (IMOEA/DA) is proposed. Firstly, a new method based on uniform design and crowding distance is used to generate a set of weight vectors with good uniformly. Secondly, according to the distances of obtained nondominated solutions, an adaptive weight vector adjustment strategy is proposed to redistribute the weight vectors of subobjective spaces. Thirdly, a selection strategy is used to help each subobjective space to obtain a nondominated solution (if have). Comparing with six efficient state-of-the-art algorithms, for example, NSGAII, MOEA/D, MOEA/D-AWA, EMOSA, RVEA, and KnEA on some benchmark functions, the proposed algorithm is able to find a set of solutions with better diversity and convergence.
Highlights
We study the effectiveness of IMOEA/ DA on multiobjective optimization problems (MOPs) with complex Pareto optimal fronts (PFs)
IMOEA/ DA can obtain a set of nondominated solutions with good uniformity. These results suggest that the weight adjustment of IMOEA/DA does improve multiobjective evolutionary algorithms (MOEAs)/D significantly in the terms of uniformity for the MOPs with complex PFs
The results of Wilcoxon rank-sum test show that IMOEA/DA outperforms IMOEA/D on all test problems; these indicate that the diversity of solutions obtained by IMOEA/DA is better than those obtained by IMOEA/D and the proposed adaptive weight vector adjustment strategy can help obtained solutions to maintain the diversity; in the form of the generational distance (GD) metric, the convergence of solutions obtained by IMOEA/DA is worse than those obtained by IMOEA/D, which is because that instability in search direction of IMOEA/DA leads to a decrease in convergence speed
Summary
In real-world applications, there are many problems needed to simultaneously optimize multiple objectives which are typically characterized by conflicting objectives. The two main advantages of MOEA/D are that it uses the neighbor strategy to improve the search efficiency and well maintain the diversity of obtained solutions by the given weight vectors. We develop an improved decompositionbased multiobjective evolutionary algorithm with adaptive weight vector adjustment (IMOEA/DA) to solve MOPs. The main contributions of this paper are as follows: firstly, a new method [36] based on uniform design and crowding distance [5] is used to generate a uniformity of weight vectors; secondly, some weight vectors are adaptively deleted or added according to the distances of obtained nondominated solutions to solve the problems with complex PF; thirdly, a selection strategy is used to help each subobjective space to obtain a nondominated solution (if have).
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