A Constrained Decomposition Approach With Grids for Evolutionary Multiobjective Optimization

Decomposition-based multiobjective evolutionary algorithms (MOEAs) decompose a multiobjective optimization problem (MOP) into a set of scalar objective subproblems and solve them in a collaborative way. Commonly used decomposition approaches originate from mathematical programming and the direct use...

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Bibliographic Details
Published in:IEEE transactions on evolutionary computation 2018-08, Vol.22 (4), p.564-577
Main Authors: Cai, Xinye, Mei, Zhiwei, Fan, Zhun, Zhang, Qingfu
Format: Article
Language:English
Subjects:
Algorithms
Computer science
Constrained decomposition
Decomposition
Electronic mail
Evolutionary algorithms
evolutionary multiobjective optimization
grids
Linear programming
Mathematical programming
Mopping
Multiple objective analysis
Optimization
Pareto optimization
robust to Pareto front (PF)
Robustness
Robustness (mathematics)
Shape
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Summary:Decomposition-based multiobjective evolutionary algorithms (MOEAs) decompose a multiobjective optimization problem (MOP) into a set of scalar objective subproblems and solve them in a collaborative way. Commonly used decomposition approaches originate from mathematical programming and the direct use of them may not suit MOEAs due to their population-based property. For instance, these decomposition approaches used in MOEAs may cause the loss of diversity and/or be very sensitive to the shapes of Pareto fronts (PFs). This paper proposes a constrained decomposition with grids (CDG) that can better address these two issues thus more suitable for MOEAs. In addition, different subproblems in CDG defined by the constrained decomposition constitute a grid system. The grids have an inherent property of reflecting the information of neighborhood structures among the solutions, which is a desirable property for restricted mating selection in MOEAs. Based on CDG, a constrained decomposition MOEA with grid (CDG-MOEA) is further proposed. Extensive experiments are conducted to compare CDG-MOEA with the domination-based, indicator-based, and state-of-the-art decomposition-based MOEAs. The experimental results show that CDG-MOEA outperforms the compared algorithms in terms of both the convergence and diversity. More importantly, it is robust to the shapes of PFs and can still be very effective on MOPs with complex PFs (e.g., extremely convex, or with disparately scaled objectives).
ISSN:1089-778X
1941-0026
DOI:10.1109/TEVC.2017.2744674