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A new monarch butterfly optimization with an improved crossover operator

Abstract

Recently, by examining and simulating the migration behavior of monarch butterflies in nature, Wang et al. proposed a new swarm intelligence-based metaheuristic algorithm, called monarch butterfly optimization (MBO), for addressing various global optimization tasks. The effectiveness of MBO was verified by benchmark evaluation on an array of unimodal and multimodal test functions in comparison with the five state-of-the-art metaheuristic algorithms on most benchmarks. However, MBO failed to come up with satisfactory performance (Std values and mean fitness) on some benchmarks. In order to overcome this, a new version of MBO algorithm, incorporating crossover operator is presented in this paper. A variant of the original MBO, the proposed one is essentially a self-adaptive crossover (SAC) operator. A kind of greedy strategy is also utilized. It ensures that only the better monarch butterfly individuals, satisfying a certain criterion, are allowed to pass to the next generation, instead of all the updated monarch butterfly individuals, as was done in the basic MBO. In other words, the proposed methodology is essentially a new version of the original MBO, supplemented with Greedy strategy and self-adaptive Crossover operator (GCMBO). In GCMBO, the SAC operator can significantly improve the diversity of population during the later run phase of the search. In butterfly adjusting operator, the greedy strategy is used to select only those monarch butterfly individuals, possessing improved fitness and hence can aid towards accelerating convergence. Finally, the proposed GCMBO method is benchmarked by twenty-five standard unimodal and multimodal test functions. The results clearly demonstrate the capability of GCMBO in significantly outperforming the basic MBO method for almost all the test cases. The MATLAB code used in the paper can be found in the website: http://www.mathworks.com/matlabcentral/fileexchange/55339-gcmbo.

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Acknowledgments

This work was supported by Jiangsu Province Science Foundation for Youths (No. BK20150239) and National Natural Science Foundation of China (No. 61375066 and No. 61503165).

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Correspondence to Gai-Ge Wang.

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Wang, GG., Deb, S., Zhao, X. et al. A new monarch butterfly optimization with an improved crossover operator. Oper Res Int J 18, 731–755 (2018). https://doi.org/10.1007/s12351-016-0251-z

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Keywords

  • Monarch butterfly optimization
  • Migration
  • Butterfly adjusting operator
  • Greedy strategy
  • Crossover
  • Benchmark problems