Abstract
The random drift particle swarm optimization (RDPSO) algorithm is an effective random search technique inspired by the trajectory analysis of the canonical PSO and the free electron model in metal conductors placed in an external electric field. However, like other PSO variants, the RDPSO algorithm also inevitably encounters premature convergence when solving multimodal problems. To address this issue, this paper proposes a novel diversity collaboratively guided (DCG) strategy for the RDPSO algorithm that enhances the search ability of the algorithm. In this strategy, two kinds of diversity measures are defined and modified in a collaborative manner. Specifically, the whole search process of the RDPSO is divided into three phases based on the changes in the two diversity measures. In each phase, different values are selected for the key parameters of the update equation in the RDPSO to make the particle swarm perform different search modes. Consequently, the improved RDPSO algorithm with the DCG strategy (DCG-RDPSO) can maintain its diversity dynamically at a certain level, and thus can search constantly without stagnation until the search process terminates. The performance evaluation of the proposed algorithm is done on the CEC-2013 benchmark suite, in comparison with several versions of RDPSO, different variants of PSO and several non-PSO evolutionary algorithms. Experimental results show that the proposed DCG strategy can significantly improve the performance and robustness of the RDPSO algorithm for most of the multimodal problems. Further experiments on economic dispatch problems also verify the effectiveness of the DCG strategy.
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References
Alomoush MI, Oweis ZB (2018) Environmental-economic dispatch using stochastic fractal search algorithm. Int Trans Electr Energy Syst 28(5):e2530
Assareh E, Behrang MA, Assari MR, Ghanbarzadeh A (2010) Application of PSO (particle swarm optimization) and GA (genetic algorithm) techniques on demand estimation of oil in Iran. Energy 35(12):5223–5229
Brits R, Engelbrecht AP, Van den Bergh F (2002) A niching particle swarm optimizer. In Proceedings of the 4th Asia-Pacific conference on simulated evolution and learning, Singapore: Orchid Country Club, vol 2, pp 692–696
Cao Y, Zhang H, Li W, Zhou M, Zhang Y, Chaovalitwongse WA (2018) Comprehensive learning particle swarm optimization algorithm with local search for multimodal functions. IEEE Trans Evol Comput 23(4):718–731
Chen PH, Chang HC (1995) Large-scale economic dispatch by genetic algorithm. IEEE Trans Power Syst 10(4):1919–1926
Chen HM, Liu BF, Huang HL, Hwang SF, Ho SY (2007) SODOCK: Swarm optimization for highly flexible protein–ligand docking. J Comput Chem 28(2):612–623
Chokpanyasuwan C (2009) Honey bee colony optimization to solve economic dispatch problem with generator constraints. In: 2009 6th international conference on electrical engineering/electronics, computer, telecommunications and information technology, IEEE, vol 1, pp 200–203
Chowdhury BH, Rahman S (1990) A review of recent advances in economic dispatch. IEEE Trans Power Syst 5(4):1248–1259
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
Cui L, Zhang K, Li G, Wang X, Yang S, Ming Z, Huang JZ, Lu N (2018) A smart artificial bee colony algorithm with distance-fitness-based neighbor search and its application. Future Gener Comput Syst 89:478–493
Du WB, Gao Y, Liu C, Zheng Z, Wang Z (2015) Adequate is better: particle swarm optimization with limited-information. Appl Math Comput 268:832–838
Hu J, Zeng J, Tan Y (2007) A diversity-guided particle swarm optimizer for dynamic environments. International conference on life system modeling and simulation. Springer, Berlin, pp 239–247
Janostik J, Pluhacek M, Senkerik R, Zelinka I (2016) Particle swarm optimizer with diversity measure based on swarm representation in complex network. In: Proceedings of the Second International Afro-European Conference for Industrial Advancement AECIA 2015, Springer, Champaign, pp 561–569
Kao YT, Zahara E (2008) A hybrid genetic algorithm and particle swarm optimization for multimodal functions. Appl Soft Comput 8(2):849–857
Kennedy J (2006) Swarm intelligence. Handbook of nature-inspired and innovative computing. Springer, Boston, pp 187–219
Kennedy J, Eberhart R (1995) Particle swarm optimization. In: Proceedings of ICNN'95-international conference on neural networks, IEEE, vol 4, pp 1942–1948
Kittel C, Kroemer H (1998) Thermal physics, 2nd edn. Freeman, San Francisco
Li X (2007) A multimodal particle swarm optimizer based on fitness Euclidean-distance ratio. In: Proceedings of the 9th annual conference on Genetic and evolutionary computation, pp 78–85
Li X (2009) Niching without niching parameters: particle swarm optimization using a ring topology. IEEE Trans Evol Comput 14(1):150–169
Li Z, Ngambusabongsopa R, Mohammed E, Eustache N (2011) A novel diversity guided particle swarm multi-objective optimization algorithm. Int J Digit Content Technol Appl 5(1):269–278
Li Y, Zhan ZH, Lin S, Zhang J, Luo X (2015) Competitive and cooperative particle swarm optimization with information sharing mechanism for global optimization problems. Inf Sci 293:370–382
Liang JJ, Qin AK, Suganthan PN, Baskar S (2006) Comprehensive learning particle swarm optimizer for global optimization of multimodal functions. IEEE Trans Evol Comput 10(3):281–295
Liang JJ, Qu BY, Suganthan PN, Hernández-Díaz, AG (2013) Problem definitions and evaluation criteria for the CEC 2013 special session on real-parameter optimization, vol 34. Computational Intelligence Laboratory, Zhengzhou University, Zhengzhou, China and Nanyang Technological University, Singapore, Technical Report, 201212, pp 281–295
Liu Q, Du S, van Wyk BJ, Sun Y (2020) Niching particle swarm optimization based on Euclidean distance and hierarchical clustering for multimodal optimization. Nonlinear Dyn 99(3):2459–2477
Liu J, Ma D, Ma TB, Zhang W (2017) Ecosystem particle swarm optimization. Soft Comput 21(7):1667–1691
Luo K, Ma J, Zhao Q (2019) Enhanced self-adaptive global-best harmony search without any extra statistic and external archive. Inf Sci 482:228–247
Mendes R, Kennedy J, Neves J (2004) The fully informed particle swarm: simpler, maybe better. IEEE Trans Evol Comput 8(3):204–210
Meng A, Hu H, Yin H, Peng X, Guo Z (2015) Crisscross optimization algorithm for large-scale dynamic economic dispatch problem with valve-point effects. Energy 93:2175–2190
Mohammadi F, Abdi H (2018) A modified crow search algorithm (MCSA) for solving economic load dispatch problem. Appl Soft Comput 71:51–65
Morris GM, Goodsell DS, Halliday RS, Huey R, Hart WE, Belew RK, Olson AJ (1998) Automated docking using a Lamarckian genetic algorithm and an empirical binding free energy function. J Comput Chem 19(14):1639–1662
Omar MA (1975) Elementary solid state physics: principles and applications. Pearson Education India, New Delhi
Pant M, Radha T, Singh V P (2007) A simple diversity guided particle swarm optimization. In: 2007 IEEE congress on evolutionary computation, IEEE, pp 3294–3299
Park JB, Jeong YW, Shin JR, Lee KY (2009) An improved particle swarm optimization for nonconvex economic dispatch problems. IEEE Trans Power Syst 25(1):156–166
Riget J, Vesterstrøm JS (2002) A diversity-guided particle swarm optimizer-the ARPSO, vol 2. Department of Computer Science, University of Aarhus, Aarhus, Denmark, Technical report
Ruxton GD (2006) The unequal variance t-test is an underused alternative to Student’s t-test and the Mann–Whitney U test. Behav Ecol 17(4):688–690
Sareni B, Krahenbuhl L (1998) Fitness sharing and niching methods revisited. IEEE Trans Evol Comput 2(3):97–106
Shi Y, Eberhart R (1998) A modified particle swarm optimizer. In: 1998 IEEE international conference on evolutionary computation proceedings. IEEE world congress on computational intelligence, IEEE, pp 69–73
Sinha N, Chakrabarti R, Chattopadhyay PK (2003) Evolutionary programming techniques for economic load dispatch. IEEE Trans Evol Computat 7(1):83–94
Subbaraj P, Rengaraj R, Salivahanan S (2009) Enhancement of combined heat and power economic dispatch using self adaptive real-coded genetic algorithm. Appl Energy 86(6):915–921
Sun J, Palade V, Wu XJ, Fang W, Wang Z (2013) Solving the power economic dispatch problem with generator constraints by random drift particle swarm optimization. IEEE Trans Industr Inform 10(1):222–232
Sun J, Wu X, Palade V, Fang W, Shi Y (2015) Random drift particle swarm optimization algorithm: convergence analysis and parameter selection. Mach Learn 101(1–3):345–376
Sun J, Zhao J, Wu X, Fang W, Cai Y, Xu W (2010) Parameter estimation for chaotic systems with a drift particle swarm optimization method. Phys Lett A 374(28):2816–2822
Swarup KS, Yamashiro S (2002) Unit commitment solution methodology using genetic algorithm. IEEE Trans Power Syst 17(1):87–91
Tanweer MR, Suresh S, Sundararajan N (2015) Self regulating particle swarm optimization algorithm. Inf Sci 294:182–202
Ursem RK (2002) Diversity-guided evolutionary algorithms. International conference on parallel problem solving from nature. Springer, Berlin, pp 462–471
Vitela JE, Castaños O (2008) A real-coded niching memetic algorithm for continuous multimodal function optimization. In: 2008 IEEE congress on evolutionary computation (IEEE World Congress on Computational Intelligence), IEEE, pp 2170–2177
Wang H, Sun H, Li C, Rahnamayan S, Pan JS (2013) Diversity enhanced particle swarm optimization with neighborhood search. Inf Sci 223:119–135
Wood AJ, Wollenberg BF (2003) Power generation, operation, and control. Tsinghua University Press, Beijing, p 195
Zhan ZH, Li J, Cao J, Zhang J, Chung HSH, Shi YH (2013) Multiple populations for multiple objectives: a coevolutionary technique for solving multiobjective optimization problems. IEEE Trans Cybern 43(2):445–463
Zhao J, Liu S, Zhou M, Guo X, Qi L (2018) Modified cuckoo search algorithm to solve economic power dispatch optimization problems. IEEE/CAA J Autom Sinica 5(4):794–806
Zou J, Deng Q, Zheng J, Yang S (2020) A close neighbor mobility method using particle swarm optimizer for solving multimodal optimization problems. Inf Sci 519:332–347
Zou D, Li S, Kong X, Ouyang H, Li Z (2018) Solving the dynamic economic dispatch by a memory-based global differential evolution and a repair technique of constraint handling. Energy 147:59–80
Acknowledgements
This work was supported in part by the National Natural Science Foundation of China (Projects Numbers: 61673194, 61672263, 61672265), and in part by the national first-class discipline program of Light Industry Technology and Engineering (Project Number: LITE2018-25).
Funding
This work was supported in part by the National Natural Science Foundation of China (Projects Numbers: 61673194, 61672263, 61672265), and in part by the national first-class discipline program of Light Industry Technology and Engineering (Project Number: LITE2018-25).
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Li, C., Sun, J., Palade, V. et al. Diversity collaboratively guided random drift particle swarm optimization. Int. J. Mach. Learn. & Cyber. 12, 2617–2638 (2021). https://doi.org/10.1007/s13042-021-01345-1
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DOI: https://doi.org/10.1007/s13042-021-01345-1