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A coevolution algorithm based on two-staged strategy for constrained multi-objective problems

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Abstract

Constrained Multiobjective Problem (CMOP) is widely used in engineering applications, but the current constrained Multiobjective Optimization algorithms (CMOEA) often fails to effectively balance convergence and diversity. For this purpose, a two-stage co-evolution constrained multi-objective optimization evolutionary algorithm (TSC-CMOEA) is presented to solve constrained multi-objective optimization problems. This method divides the search process into two phases: in the first stage, the synchronous co-evolution is used, and the population corresponding to the help problem and the population corresponding to the raw problem cooperate with each other and share the offspring to produce better solutions, so as to quickly cross the infeasible region and approach the Pareto front; The second stage discards the help problem when it fails and maintains only the evolution of the main population to save computing resources and enhance convergence. The combination of synchronous co-evolution and staged strategy allows the population to traverse infeasible regions more efficiently and converge quickly to feasible and non-dominant regions. The test results on benchmark CMOPs show that the convergence and population distribution of TSC-CMOEA is significantly better than those of NSGA-II, NSGA-III, C-MOEA/D, PPS, ToP and CCMO.

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References

  1. Tan B, Ma H, Mei Y, Zhang M (2018) Evolutionary multi-objective optimization for web service location allocation problem. IEEE Trans Serv Comput

  2. Farzin H, Fotuhi-Firuzabad M, Moeini-Aghtaie M (2016) A stochastic multi-objective framework for optimal scheduling of energy storage systems in microgrids. IEEE Trans Smart Grid 8(1):117–127

    Article  Google Scholar 

  3. Gong M, Wang Z, Zhu Z, Jiao L (2017) A similarity-based multiobjective evolutionary algorithm for deployment optimization of near space communication system. IEEE Trans Evol Comput 21(6):878–897

    Article  Google Scholar 

  4. Deb K, Jain H (2014) An evolutionary many-objective optimization algorithm using reference-point-based nondominated sorting approach, part i: Solving problems with box constraints. IEEE Trans Evol Comput 18(4):577–601

    Article  Google Scholar 

  5. Zhu Q, Zhang Q, Lin Q (2020) A constrained multiobjective evolutionary algorithm with detect-and-escape strategy. IEEE Trans Evol Comput 24(5):938–947

    Article  Google Scholar 

  6. Garg H (2016) A hybrid pso-ga algorithm for constrained optimization problems. Appl Math Comput 274:292–305

    MathSciNet  MATH  Google Scholar 

  7. Qiao J, Zhou H, Yang C, Yang S (2019) A decomposition-based multiobjective evolutionary algorithm with angle-based adaptive penalty. Appl Soft Comput 74:190–205

    Article  Google Scholar 

  8. Woldesenbet YG, Yen GG, Tessema BG (2009) Constraint handling in multiobjective evolutionary optimization. IEEE Trans Evol Comput 13(3):514–525

    Article  Google Scholar 

  9. Fan Z, Li W, Cai X, Li H, Wei C, Zhang Q, Deb K, Goodman E (2019) Push and pull search for solving constrained multi-objective optimization problems. Swarm Evol Comput 44:665–679

    Article  Google Scholar 

  10. Runarsson TP, Yao X (2000) Stochastic ranking for constrained evolutionary optimization. IEEE Trans Evol Comput 4(3):284–294

    Article  Google Scholar 

  11. Deb K, Pratap A, Agarwal S, Meyarivan TAMT (2002) A fast and elitist multiobjective genetic algorithm: Nsga-ii. IEEE Trans Evol Comput 6(2):182–197

    Article  Google Scholar 

  12. Yi W, Gao L, Pei Z, Lu J, Chen Y (2021) ε constrained differential evolution using halfspace partition for optimization problems. J Intell Manuf 32(1):157–178

    Article  Google Scholar 

  13. Fan Z, Li W, Cai X, Hu K, Lin H, Li H (2016) Angle-based constrained dominance principle in moea/d for constrained multi-objective optimization problems. In: 2016 IEEE Congress on evolutionary computation (CEC), IEEE, pp 460–467

  14. Xia M, Dong M (2021) A novel two-archive evolutionary algorithm for constrained multi-objective optimization with small feasible regions. Knowl-Based Syst,, pp 107693

  15. Liu ZZ, Wang BC, Tang K (2021) Handling constrained multiobjective optimization problems via bidirectional coevolution. IEEE Trans Cybern PP(99):1–14

    Google Scholar 

  16. Wang B-C, Li H-X, Zhang Q, Wang Y (2018) Decomposition-based multiobjective optimization for constrained evolutionary optimization. IEEE Transactions on systems, man, and cybernetics: systems

  17. Tian Y, Zhang T, Xiao J, Zhang X, Jin Y (2020) A coevolutionary framework for constrained multi-objective optimization problems. IEEE Transactions on systems, man, and cybernetics: systems

  18. Yu K, Liang J, Qu B, Yue C (2021) Purpose-directed two-phase multiobjective differential evolution for constrained multiobjective optimization. Swarm Evol Comput 60:100799

    Article  Google Scholar 

  19. Panda A, Pani S (2016) A symbiotic organisms search algorithm with adaptive penalty function to solve multi-objective constrained optimization problems. Appl Soft Comput 46(C):344–360

    Article  Google Scholar 

  20. Peng C, Liu HL, Gu F (2017) An evolutionary algorithm with directed weights for constrained multi-objective optimization. Appl Soft Comput 60:613–622. https://doi.org/10.1016/j.asoc.2017.06.053, https://www.sciencedirect.com/science/article/pii/S1568494617303964

    Article  Google Scholar 

  21. Liu R, Li J, Mu C, Jiao L, et al. (2017) A coevolutionary technique based on multi-swarm particle swarm optimization for dynamic multi-objective optimization. Eur J Oper Res 261(3):1028– 1051

    Article  MathSciNet  MATH  Google Scholar 

  22. Peng X, Liu K, Jin Y (2016) A dynamic optimization approach to the design of cooperative co-evolutionary algorithms. Knowl-Based Syst 109:174–186

    Article  Google Scholar 

  23. Zhang X-Y, Gong Y-J, Lin Y, Zhang J, Kwong S, Zhang J (2019) Dynamic cooperative coevolution for large scale optimization. IEEE Trans Evol Comput 23(6):935–948

    Article  Google Scholar 

  24. Mohamed AW (2018) A novel differential evolution algorithm for solving constrained engineering optimization problems. J Intell Manuf 29(3):659–692

    Article  Google Scholar 

  25. Zhou J, Zou J, Yang S, Zheng J, Pei T (2021) Niche-based and angle-based selection strategies for many-objective evolutionary optimization. Information Sciences

  26. Yang N, Liu HL (2021) Adaptively allocating constraint-handling techniques for constrained multi-objective optimization problems. Int J Pattern Recognit Artif Intell

  27. Wang J, Liang G, Zhang J (2018) Cooperative differential evolution framework for constrained multiobjective optimization. IEEE Trans Cybern 49(6):2060–2072

    Article  Google Scholar 

  28. Li K, Chen R, Fu G, Yao X (2018) Two-archive evolutionary algorithm for constrained multiobjective optimization. IEEE Trans Evol Comput 23(2):303–315

    Article  Google Scholar 

  29. Wang J, Li Y, Zhang Q, Zhang Z, Gao S (2021) Cooperative multiobjective evolutionary algorithm with propulsive population for constrained multiobjective optimization. IEEE Trans Syst Man Cybern: Syst PP(99):1–16

    Google Scholar 

  30. Liu ZZ, Wang Y (2019) Handling constrained multiobjective optimization problems with constraints in both the decision and objective spaces. IEEE Trans Evol Comput 23(5):870– 884

    Article  Google Scholar 

  31. Tian Y, Cheng R, Zhang X, Jin Y (2017) Platemo: A matlab platform for evolutionary multi-objective optimization [educational forum]. IEEE Comput Intell Mag 12(4):73–87

    Article  Google Scholar 

  32. Ma Z, Wang Y (2019) Evolutionary constrained multiobjective optimization: Test suite construction and performance comparisons. IEEE Trans Evol Comput 23(6):972–986

    Article  MathSciNet  Google Scholar 

  33. Fan Z, Li W, Cai X, Huang H, Fang Y, You Y, Mo J, Wei C, Goodman E (2019) An improved epsilon constraint-handling method in moea/d for cmops with large infeasible regions. Soft Comput 23(23):12491–12510

    Article  Google Scholar 

  34. a JD, b SG, C DM, A FH (2011) A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms. Swarm Evol Comput 1 (1):3–18

    Article  Google Scholar 

  35. Tian Y, Xiang X, Zhang X, Cheng R, Jin Y (2018) Sampling reference points on the pareto fronts of benchmark multi-objective optimization problems. In: 2018 IEEE congress on evolutionary computation (CEC), pp 1–6 (2018). IEEE

Download references

Acknowledgments

The authors are very grateful to the anonymous reviewers for their valuable comments on improving this article. Additionally, this work is supported by Hunan Provincial Natural Science Foundation of China (No. 2020JJ4587), Guangdong Basic and Applied Basic Research Foundation (No. 2019A1515110423), Open Fund Project of Key Laboratory of Advanced Perception and Intelligent Control of High-end Equipment of Ministry of Education (No. GDSC202020), and Open Fund Project of Fujian Provincial Key Laboratory of Data Intensive Computing (No. BD202004). Supported by the Open Research Fund of AnHui Key Laboratory of Detection Technology and Energy Saving Devices (No. JCKJ2021B05).

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Authors and Affiliations

  1. School of Computer Science, Xiangtan University, Xiangtan, 411105, Hunan, China

    Chaodong Fan, Jiawei Wang & Zhenhuan Zeng

  2. Foshan Green Intelligent Manufacturing Research Institute of Xiangtan University, Foshan, 528000, GuangDong, China

    Chaodong Fan & Jiawei Wang

  3. Key Laboratory of Advanced Perception and Intelligent Control of High-end Equipment of Ministry of Education, Anhui Polytechnic University, Wuhu, 241000, Anhui, China

    Chaodong Fan, Leyi Xiao & Fanyong Cheng

  4. School of Information Technology and Management, Hunan University of Finance and Economics, Changsha, 410205, Hunan, China

    Chaodong Fan & Leyi Xiao

  5. AnHui Key Laboratory of Detection Technology and Energy Saving Devices, AnHui Polytechnic University, Wuhu, 241000, Anhui, China

    Leyi Xiao

  6. College of Foreign Languages; Inter-disciplinary Research Center of Language Intelligence and Cultural Heritages, Hunan University, Changsha, 410082, Hunan, China

    Zhaoyang Ai

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  1. Chaodong Fan
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  2. Jiawei Wang
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  3. Leyi Xiao
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Correspondence to Leyi Xiao.

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Fan, C., Wang, J., Xiao, L. et al. A coevolution algorithm based on two-staged strategy for constrained multi-objective problems. Appl Intell 52, 17954–17973 (2022). https://doi.org/10.1007/s10489-022-03421-7

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