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A tri-stage competitive swarm optimizer for constrained multi-objective optimization

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Abstract

Objective optimization and constraint satisfaction should be considered simultaneously when dealing with constrained multi-objective optimization problems (CMOPs). But it is difficult for existing constraint multi-objective evolutionary algorithms (CMOEAs) to strike a good balance between them, especially for CMOPs with complex constraints. To address this issue, this paper proposes a tri-stage competitive swarm optimizer (CSO), namely TSCSO, where objective optimization and constraint satisfaction receive different attention in different stages. In Stage-I, the population converges to the vicinity of the unconstrained Pareto front (PF) without considering any constraints. In Stage-II, a balance strategy and ranking approach based on convergence, diversity, and feasibility are proposed to enhance the diversity of the population and explore more feasible regions. An external archive is used to store the feasible solutions explored during the evolutionary process. In Stage-III, the population is first initialized by the feasible solutions in the archive, and the CSO operator with efficient search is used to search for the feasible regions omitted in Stage-II. Statistical results on two benchmark suites with twenty-eight problems and five real-world problems indicate that the proposed algorithm performs better than other state-of-the-art CMOEAs overall.

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Data Availability

The datasets generated and analyzed during the current study are available in the PlatEMO [47] (https://github.com/BIMK/PlatEMO

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Authors and Affiliations

  1. School of Computer Science, China University of Geosciences, Jincheng, Wuhan, 430074, Hubei, China

    Jun Dong, Wenyin Gong & Fei Ming

Authors
  1. Jun Dong
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  2. Wenyin Gong
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  3. Fei Ming
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Correspondence to Wenyin Gong.

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Appendices

Appendix

Extended Data

Table 5 HV values of TSCSO and PPS, LMOCSO, CMOPSO, MOEAD-DAE, CMOEA-MS, MSCMO, ToP, TiGE-2 on the LIR-CMOP benchmark suite
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Table 6 HV values of TSCSO and PPS, LMOCSO, CMOPSO, MOEAD-DAE, CMOEA-MS, MSCMO, ToP, TiGE-2 on the MW benchmark suite
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Table 7 HV values of TSCSO and its three transfigurations on the LIR-CMOP benchmark suite
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Table 8 IGD values of TSCSO and its four transfigurations (TSCSO-A, TSCSO-B, TSCSO-C, TSCSO-D) on the MW benchmark suite. The proportion between Stage-I, Stage-II and Stage-III of these four transfigurations are: TSCSO-A (10%, 45%, 45%), TSCSO-B (30%, 35%, 35%), TSCSO-C (40%, 30%, 30%), TSCSO-D (50%, 25%, 25%)
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Table 9 HV values of TSCSO and its four transfigurations (TSCSO-A, TSCSO-B, TSCSO-C, TSCSO-D) on the MW benchmark suite. The proportion between Stage-I, Stage-II and Stage-III of these four transfigurations are: TSCSO-A (10%, 45%, 45%), TSCSO-B (30%, 35%, 35%), TSCSO-C (40%, 30%, 30%), TSCSO-D (50%, 25%, 25%)
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Table 10 IGD values of TSCSO and its four transfigurations (TSCSO-A, TSCSO-B, TSCSO-C, TSCSO-D) on the LIRCMOP benchmark suite. The proportion between Stage-I, Stage-II and Stage-III of these four transfigurations are: TSCSO-A (10%, 45%, 45%), TSCSO-B (30%, 35%, 35%), TSCSO-C (40%, 30%, 30%), TSCSO-D (50%, 25%, 25%)
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Table 11 HV values of TSCSO and its four transfigurations (TSCSO-A, TSCSO-B, TSCSO-C, TSCSO-D) on the LIRCMOP benchmark suite. The proportion between Stage-I, Stage-II and Stage-III of these four transfigurations are: TSCSO-A (10%, 45%, 45%), TSCSO-B (30%, 35%, 35%), TSCSO-C (40%, 30%, 30%), TSCSO-D (50%, 25%, 25%)
Full size table

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Dong, J., Gong, W. & Ming, F. A tri-stage competitive swarm optimizer for constrained multi-objective optimization. Appl Intell 53, 7892–7916 (2023). https://doi.org/10.1007/s10489-022-03874-w

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