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Adaptive multi-objective particle swarm optimization using three-stage strategy with decomposition

Abstract

Balancing the convergence and the diversity is one of the crucial researches in solving multi-objective problems (MOPs). However, the optimization algorithms are inefficient and require massive iterations. The convergence accuracy and the distribution of the obtained non-dominated solutions are defective in solving complex MOPs. To solve these problems, a novel adaptive multi-objective particle swarm optimization using a three-stage strategy (tssAMOPSO) is proposed in this paper. Firstly, an adaptive flight parameter adjustment is proposed to manage the states of the algorithm, switching between the global exploration and the local exploitation. Then, the three-stage strategy, including adaptive optimization, decomposition, and Gaussian attenuation mutation, is conducted by population in each iteration. The three-stage strategy remarkably promotes the diversity and efficiency of the optimization process. Furthermore, the convergence analysis of three-stage strategy is provided in detail. Finally, particles are equipped with memory interval to improve the reliability of personal best selection. In the maintenance of external archive, the proposed fusion index can enhance the quality of non-dominated solutions directly. A series of benchmark instances, ZDT and DTLZ test suits, are used to verify the performance of tssAMOPSO. Several classical and state-of-the-art algorithms are employed for experimental comparisons. Experimental results show that tssAMOPSO outperforms the other algorithms and achieves admirable comprehensive performance.

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References

  1. Abo-Hammour Z, Alsmadi O, Momani S, Abu Arqub O (2013) A genetic algorithm approach for prediction of linear dynamical systems. Math Probl Eng, p 831657

  2. Abualigah L, Diabat A (2021) Advances in sine cosine algorithm: a comprehensive survey. Artif Intell Rev 54(4):2567–2608

    Article  Google Scholar 

  3. Abualigah L, Diabat A, Mirjalili S, Abd Elaziz M, Gandomi AH (2021) The arithmetic optimization algorithm. Comput Methods Appl Mech Eng 376:113609

    MathSciNet  MATH  Article  Google Scholar 

  4. Arqub OA, Abo-Hammour Z (2014) Numerical solution of systems of second-order boundary value problems using continuous genetic algorithm. Inf Sci 279:396–415

    MathSciNet  MATH  Article  Google Scholar 

  5. Birattari M, Pellegrini P, Dorigo M (2007) On the invariance of ant colony optimization. IEEE Trans Evol Comput 11(6):732–742

    Article  Google Scholar 

  6. Bolufé-Röhler A, Chen S (2013) Minimum population search—lessons from building a heuristic technique with two population members. In: 2013 IEEE congress on evolutionary computation, pp 2061-2068

  7. Brockhoff D, Zitzler E (2009) Objective reduction in evolutionary multiobjective optimization: theory and applications. Evol Comput 17(2):135–166

    Article  Google Scholar 

  8. Chakraborty P, Das S, Roy GG, Abraham A (2011) On convergence of the multi-objective particle swarm optimizers. Inf Sci 181(8):1411–1425

    MathSciNet  MATH  Article  Google Scholar 

  9. Cheng R, Jin Y (2015) A competitive swarm optimizer for large scale optimization. IEEE Trans Cybern 45(2):191–204

    Article  Google Scholar 

  10. Clerc M, Kennedy J (2002) The particle swarm–explosion, stability, and convergence in a multidimensional complex space. IEEE Trans Evol Comput 6(1):58–73

    Article  Google Scholar 

  11. Coello CAC, Lechuga MS (2002) Mopso: a proposal for multiple objective particle swarm optimization. In: Proceedings of the 2002 congress on evolutionary computation. CEC’02 (Cat. No.02TH8600), vol 2, pp 1051–1056

  12. Coello CAC, Pulido GT, Lechuga MS (2004) Handling multiple objectives with particle swarm optimization. IEEE Trans Evol Comput 8(3):256–279

    Article  Google Scholar 

  13. Dai C, Wang Y, Ye M (2015) A new multi-objective particle swarm optimization algorithm based on decomposition. Inf Sci 325:541–557

    Article  Google Scholar 

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

    Article  Google Scholar 

  15. Fakhouri HN, Hudaib A, Sleit A (2020) Multivector particle swarm optimization algorithm. Soft Comput 24(15):11695–11713

    Article  Google Scholar 

  16. Fonseca CM, Fleming PJ (1998) Multiobjective optimization and multiple constraint handling with evolutionary algorithms. i. A unified formulation. IEEE Trans Syst Man Cybern Part A Syst Hum 28(1):26–37

  17. Gao H, Shi Y, Pun CM, Kwong S (2019) An improved artificial bee colony algorithm with its application. IEEE Trans Industr Inf 15(4):1853–1865

    Article  Google Scholar 

  18. Gong M, Cai Q, Chen X, Ma L (2014) Complex network clustering by multiobjective discrete particle swarm optimization based on decomposition. IEEE Trans Evol Comput 18(1):82–97

    Article  Google Scholar 

  19. Han H, Lu W, Qiao J (2017) An adaptive multiobjective particle swarm optimization based on multiple adaptive methods. IEEE Trans Cybern 47(9):2754–2767

    Article  Google Scholar 

  20. Han H, Lu W, Zhang L, Qiao J (2018) Adaptive gradient multiobjective particle swarm optimization. IEEE Trans Cybern 48(11):3067–3079

    Article  Google Scholar 

  21. Hu W, Yen GG (2015) Adaptive multiobjective particle swarm optimization based on parallel cell coordinate system. IEEE Trans Evol Comput 19(1):1–18

    Article  Google Scholar 

  22. Huang H, Lv L, Ye S, Hao Z (2019) Particle swarm optimization with convergence speed controller for large-scale numerical optimization. Soft Comput Fusion Founda Methodol Appl 23:4421–4437

    Google Scholar 

  23. Jara EC (2014) Multi-objective optimization by using evolutionary algorithms: the p-optimality criteria. IEEE Trans Evol Comput 18(2):167–179

  24. Kennedy J, Eberhart R (1995) Particle swarm optimization. In: Proceedings of ICNN’95—international conference on neural networks, vol 4, pp 1942–1948

  25. Kumar RS, Kondapaneni K, Dixit V, Goswami A, Thakur LS, Tiwari MK (2015) Multi-objective modeling of production and pollution routing problem with time window: a self-learning particle swarm optimization approach. Comput Ind Eng, p S0360835215002879

  26. Lee K, Kim J (2013) Multiobjective particle swarm optimization with preference-based sort and its application to path following footstep optimization for humanoid robots. IEEE Trans Evol Comput 17(6):755–766

    Article  Google Scholar 

  27. Leong W, Yen GG (2008) Pso-based multiobjective optimization with dynamic population size and adaptive local archives. IEEE Trans Syst Man Cybern Part B (Cybern) 38(5):1270–1293

    Article  Google Scholar 

  28. Li H, Zhang Q (2009) Multiobjective optimization problems with complicated pareto sets, moea/d and nsga-ii. IEEE Trans Evol Comput 13(2):284–302

    Article  Google Scholar 

  29. Li C, Yang S, Nguyen TT (2012) A self-learning particle swarm optimizer for global optimization problems. IEEE Trans Syst Man Cybern Part B (Cybern) 42(3):627–646

    Article  Google Scholar 

  30. Li L, Wang W, Li W, Xu X, Zhao Y (2016) A novel ranking-based optimal guides selection strategy in mopso. Proc Comput Sci 91:1001–1010, promoting Business Analytics and Quantitative Management of Technology: 4th International Conference on Information Technology and Quantitative Management (ITQM 2016)

  31. Lin Q, Li J, Du Z, Chen J, Ming Z (2015) A novel multi-objective particle swarm optimization with multiple search strategies. Eur J Oper Res 247(3):732–744

    MathSciNet  MATH  Article  Google Scholar 

  32. Liu J, Liu J (2019) Applying multi-objective ant colony optimization algorithm for solving the unequal area facility layout problems. Appl Soft Comput 74:167–189

    Article  Google Scholar 

  33. Maghawry A, Hodhod R, Omar Y, Kholief M (2021) An approach for optimizing multi-objective problems using hybrid genetic algorithms. Soft Comput 25:389–405

    Article  Google Scholar 

  34. Martín-Moreno R, Vega-Rodríguez MA (2018) Multi-objective artificial bee colony algorithm applied to the bi-objective orienteering problem. Knowl Based Syst 154:93–101

    Article  Google Scholar 

  35. Meza J, Espitia H, Montenegro C, Giménez E, González-Crespo R (2017) Movpso: Vortex multi-objective particle swarm optimization. Appl Soft Comput 52:1042–1057

    Article  Google Scholar 

  36. Mirjalili S, Lewis A (2016) The whale optimization algorithm. Adv Eng Softw 95:51–67

    Article  Google Scholar 

  37. Moubayed NA, Petrovski A, Mccall J (2014) D2mopso: Mopso based on decomposition and dominance with archiving using crowding distance in objective and solution spaces. Evol Comput 22(1):47–77

    Article  Google Scholar 

  38. Nebro AJ, Durillo JJ, Garcia-Nieto J, Coello Coello CA, Luna F, Alba E (2009) Smpso: a new pso-based metaheuristic for multi-objective optimization. In: 2009 IEEE symposium on computational intelligence in multi-criteria decision-making (MCDM), pp 66–73

  39. Ogata K (1995) Discrete-time control systems, 2nd edn. Prentice-Hall, New York

    Google Scholar 

  40. Peng W, Zhang Q (2008) A decomposition-based multi-objective particle swarm optimization algorithm for continuous optimization problems. In: 2008 IEEE international conference on granular computing, pp 534–537

  41. Qiao J, Li F, Yang S, Yang C, Li W, Gu K (2020) An adaptive hybrid evolutionary immune multi-objective algorithm based on uniform distribution selection. Inf Sci 512:446–470

    MathSciNet  MATH  Article  Google Scholar 

  42. Qu B, Li C, Liang J, Yan L, Yu K, Zhu Y (2020) A self-organized speciation based multi-objective particle swarm optimizer for multimodal multi-objective problems. Appl Soft Comput 86:105886

    Article  Google Scholar 

  43. Rajani Kumar D, Kumar V (2020) Impact of controlling parameters on the performance of mopso algorithm. Proc Comput Sci 167:2132–2139

    Article  Google Scholar 

  44. Raquel CR, Naval PC (2005) An effective use of crowding distance in multiobjective particle swarm optimization. In: Proceedings of the 7th annual conference on genetic and evolutionary computation, Association for Computing Machinery, New York, NY, USA, GECCO, pp 257–264

  45. Srinivas N, Deb K (1994) Multiobjective optimization using nondominated sorting in genetic algorithms. Evol Comput 2(3):221–248

    Article  Google Scholar 

  46. Tan KC, Lee TH, Khor EF (2001) Evolutionary algorithms with dynamic population size and local exploration for multiobjective optimization. IEEE Trans Evol Comput 5(6):565–588

    Article  Google Scholar 

  47. Tao X, Guo W, Li Q, Ren C, Liu R (2020) Multiple scale self-adaptive cooperation mutation strategy-based particle swarm optimization. Appl Soft Comput 89:106124

    Article  Google Scholar 

  48. Wang D, Tan D, Liu L (2018) Particle swarm optimization algorithm: an overview. Soft Comput 22(2):387–408

    Article  Google Scholar 

  49. Wei B, Xia X, Yu F, Zhang Y, Xu X, Wu H, Gui L, He G (2020) Multiple adaptive strategies based particle swarm optimization algorithm. Swarm Evol Comput 57:100731

    Article  Google Scholar 

  50. Yen GG, Haiming Lu (2003) Dynamic multiobjective evolutionary algorithm: adaptive cell-based rank and density estimation. IEEE Trans Evol Comput 7(3):253–274

    Article  Google Scholar 

  51. Zhang Q, Li H (2007) Moea/d: a multiobjective evolutionary algorithm based on decomposition. IEEE Trans Evol Comput 11(6):712–731

    Article  Google Scholar 

  52. Zhang X, Tian Y, Cheng R, Jin Y (2015) An efficient approach to nondominated sorting for evolutionary multiobjective optimization. IEEE Trans Evol Comput 19(2):201–213

    Article  Google Scholar 

  53. Zhang H, Zhou A, Song S, Zhang Q, Gao X, Zhang J (2016) A self-organizing multiobjective evolutionary algorithm. IEEE Trans Evol Comput 20(5):792–806

    Article  Google Scholar 

  54. Zhang X, Zheng X, Cheng R, Qiu J, Jin Y (2018) A competitive mechanism based multi-objective particle swarm optimizer with fast convergence. Inf Sci 427:63–76

    MathSciNet  Article  Google Scholar 

  55. Zhu F, Chen D, Zou F (2021) A novel hybrid dynamic fireworks algorithm with particle swarm optimization. Soft Comput 25:2371–2398

    Article  Google Scholar 

  56. Zitzler E, Thiele L (1999) Multiobjective evolutionary algorithms: a comparative case study and the strength pareto approach. IEEE Trans Evol Comput 3(4):257–271

    Article  Google Scholar 

  57. Zitzler E, Laumanns M, Thiele L (2001) Spea2: improving the strength pareto evolutionary algorithm. TIK-Report 103

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Acknowledgements

This research was supported by National Natural Science Foundation of China under Grants (61703145); Scientific and technological innovation team of colleges and universities in Henan Province under Grants (20IRTSTHN019). In addition, we are grateful to the anonymous reviewers and editors for their valuable suggestions and comments on the initial version of the manuscript.

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W. M. Huang and W. Zhang jointly put forward the conception of this study. W. M. Huang designed and completed the experimental studies. Both W. M. Huang and W. Zhang participated in the analysis and interpretation of experimental results. W. M. Huang drafted the first edition of the manuscript. W. Zhang critically revised the important intellectual content of the manuscript. W. M. Huang and W. Zhang approved the final version of the manuscript together.

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Correspondence to Wei Zhang.

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Huang, W., Zhang, W. Adaptive multi-objective particle swarm optimization using three-stage strategy with decomposition. Soft Comput 25, 14645–14672 (2021). https://doi.org/10.1007/s00500-021-06262-7

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Keywords

  • Multi-objective optimization
  • Particle swarm optimization
  • Adaptive
  • Three-stage strategy
  • Decomposition