MOEA/D with adaptive weight adjustment

Yutao Qi, Xiaoliang Ma, Fang Liu, Licheng Jiao, Jianyong Sun, Jianshe Wu

Research output: Contribution to journalArticle

201 Citations (Scopus)

Abstract

Recently, MOEA/D (multi-objective evolutionary algorithm based on decomposition) has achieved great success in the field of evolutionary multi-objective optimization and has attracted a lot of attention. It decomposes a multi-objective optimization problem (MOP) into a set of scalar subproblems using uniformly distributed aggregation weight vectors and provides an excellent general algorithmic framework of evolutionary multi-objective optimization. Generally, the uniformity of weight vectors in MOEA/D can ensure the diversity of the Pareto optimal solutions, however, it cannot work as well when the target MOP has a complex Pareto front (PF; i.e., discontinuous PF or PF with sharp peak or low tail). To remedy this, we propose an improved MOEA/D with adaptive weight vector adjustment (MOEA/D-AWA). According to the analysis of the geometric relationship between the weight vectors and the optimal solutions under the Chebyshev decomposition scheme, a new weight vector initialization method and an adaptive weight vector adjustment strategy are introduced in MOEA/D-AWA. The weights are adjusted periodically so that the weights of subproblems can be redistributed adaptively to obtain better uniformity of solutions. Meanwhile, computing efforts devoted to subproblems with duplicate optimal solution can be saved. Moreover, an external elite population is introduced to help adding new subproblems into real sparse regions rather than pseudo sparse regions of the complex PF, that is, discontinuous regions of the PF. MOEA/D-AWA has been compared with four state of the art MOEAs, namely the original MOEA/D, Adaptive-MOEA/D, paλ -MOEA/D, and NSGA-II on 10 widely used test problems, two newly constructed complex problems, and two many-objective problems. Experimental results indicate that MOEA/D-AWA outperforms the benchmark algorithms in terms of the IGD metric, particularly when the PF of the MOP is complex.
Original languageEnglish
Pages (from-to)231-264
Number of pages34
JournalEvolutionary Computation
Volume22
Issue number2
DOIs
Publication statusPublished - 2014
Externally publishedYes

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Multi-objective Evolutionary Algorithm
Evolutionary algorithms
Adjustment
Decomposition
Decompose
Multiobjective optimization
Multiobjective Optimization Problems
Evolutionary multiobjective Optimization
Uniformity
Optimal Solution
NSGA-II
Pareto Optimal Solution
Pareto Front
Chebyshev
Initialization
Test Problems
Agglomeration
Tail
Aggregation
Scalar

Cite this

Qi, Y., Ma, X., Liu, F., Jiao, L., Sun, J., & Wu, J. (2014). MOEA/D with adaptive weight adjustment. Evolutionary Computation, 22(2), 231-264. https://doi.org/10.1162/EVCO_a_00109
Qi, Yutao ; Ma, Xiaoliang ; Liu, Fang ; Jiao, Licheng ; Sun, Jianyong ; Wu, Jianshe. / MOEA/D with adaptive weight adjustment. In: Evolutionary Computation. 2014 ; Vol. 22, No. 2. pp. 231-264.
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Qi, Y, Ma, X, Liu, F, Jiao, L, Sun, J & Wu, J 2014, 'MOEA/D with adaptive weight adjustment', Evolutionary Computation, vol. 22, no. 2, pp. 231-264. https://doi.org/10.1162/EVCO_a_00109

MOEA/D with adaptive weight adjustment. / Qi, Yutao; Ma, Xiaoliang; Liu, Fang; Jiao, Licheng; Sun, Jianyong; Wu, Jianshe.

In: Evolutionary Computation, Vol. 22, No. 2, 2014, p. 231-264.

Research output: Contribution to journalArticle

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T1 - MOEA/D with adaptive weight adjustment

AU - Qi, Yutao

AU - Ma, Xiaoliang

AU - Liu, Fang

AU - Jiao, Licheng

AU - Sun, Jianyong

AU - Wu, Jianshe

PY - 2014

Y1 - 2014

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AB - Recently, MOEA/D (multi-objective evolutionary algorithm based on decomposition) has achieved great success in the field of evolutionary multi-objective optimization and has attracted a lot of attention. It decomposes a multi-objective optimization problem (MOP) into a set of scalar subproblems using uniformly distributed aggregation weight vectors and provides an excellent general algorithmic framework of evolutionary multi-objective optimization. Generally, the uniformity of weight vectors in MOEA/D can ensure the diversity of the Pareto optimal solutions, however, it cannot work as well when the target MOP has a complex Pareto front (PF; i.e., discontinuous PF or PF with sharp peak or low tail). To remedy this, we propose an improved MOEA/D with adaptive weight vector adjustment (MOEA/D-AWA). According to the analysis of the geometric relationship between the weight vectors and the optimal solutions under the Chebyshev decomposition scheme, a new weight vector initialization method and an adaptive weight vector adjustment strategy are introduced in MOEA/D-AWA. The weights are adjusted periodically so that the weights of subproblems can be redistributed adaptively to obtain better uniformity of solutions. Meanwhile, computing efforts devoted to subproblems with duplicate optimal solution can be saved. Moreover, an external elite population is introduced to help adding new subproblems into real sparse regions rather than pseudo sparse regions of the complex PF, that is, discontinuous regions of the PF. MOEA/D-AWA has been compared with four state of the art MOEAs, namely the original MOEA/D, Adaptive-MOEA/D, paλ -MOEA/D, and NSGA-II on 10 widely used test problems, two newly constructed complex problems, and two many-objective problems. Experimental results indicate that MOEA/D-AWA outperforms the benchmark algorithms in terms of the IGD metric, particularly when the PF of the MOP is complex.

U2 - 10.1162/EVCO_a_00109

DO - 10.1162/EVCO_a_00109

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