A constraint handling technique using compound distance for solving constrained multi-objective optimization problems

Jiawei Yuan; Jiawei Yuan

doi:10.3934/math.2021365

AIMS Mathematics

2021, Volume 6, Issue 6: 6220-6241. doi: 10.3934/math.2021365

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A constraint handling technique using compound distance for solving constrained multi-objective optimization problems

Jiawei Yuan ^,

Guangdong University of Technology, Guangdong, China

Received: 06 March 2021 Accepted: 07 April 2021 Published: 09 April 2021
MSC : 90C29, 58E17, 11Y16

Guiding the working population to evenly explore the valuable areas which are not dominated by feasible solutions is important in the process of dealing with constrained multi-objective optimization problems (CMOPs). To this end, according to the angular distance and $ \ell_p $-norm, this paper introduces a new compound distance to measure individual's search diameter in the objective space. After that, we propose a constraint handling technique using the compound distance and embed it in evolutionary algorithm for solving CMOPs. In the proposed algorithm, the individuals with large search diameters in the valuable areas are given priority to be preserved. This can prevent the working population from getting stuck in the local areas and then find the optimal solutions for CMOPs more effectively. A series of numerical experiments show that the proposed algorithm has better performance and robustness than several existing state-of-the-art constrained multi-objective evolutionary algorithms in dealing with different CMOPs.
- compound distance,
- constraint handling,
- multi-objective optimization,
- evolutionary algorithm
Citation: Jiawei Yuan. A constraint handling technique using compound distance for solving constrained multi-objective optimization problems[J]. AIMS Mathematics, 2021, 6(6): 6220-6241. doi: 10.3934/math.2021365

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Abstract

Guiding the working population to evenly explore the valuable areas which are not dominated by feasible solutions is important in the process of dealing with constrained multi-objective optimization problems (CMOPs). To this end, according to the angular distance and $ \ell_p $-norm, this paper introduces a new compound distance to measure individual's search diameter in the objective space. After that, we propose a constraint handling technique using the compound distance and embed it in evolutionary algorithm for solving CMOPs. In the proposed algorithm, the individuals with large search diameters in the valuable areas are given priority to be preserved. This can prevent the working population from getting stuck in the local areas and then find the optimal solutions for CMOPs more effectively. A series of numerical experiments show that the proposed algorithm has better performance and robustness than several existing state-of-the-art constrained multi-objective evolutionary algorithms in dealing with different CMOPs.

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