On the selection of solutions for mutation in differential evolution
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Differential evolution (DE) is a kind of evolutionary algorithms, which is suitable for solving complex optimization problems. Mutation is a crucial step in DE that generates new solutions from old ones. It was argued and has been commonly adopted in DE that the solutions selected for mutation should have mutually different indices. This restrained condition, however, has not been verified either theoretically or empirically yet. In this paper, we empirically investigate the selection of solutions for mutation in DE. From the observation of the extensive experiments, we suggest that the restrained condition could be relaxed for some classical DE versions as well as some advanced DE variants. Moreover, relaxing the restrained condition may also be useful in designing better future DE algorithms.
Keywordsdifferential evolution mutation the selection of solutions for mutation evolutionary algorithms
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The authors would like to thank the anonymous reviewers for their very constructive and helpful suggestions. This work was supported in part by the National Basic Research Program (973 Program) of China (2011CB013104), in part by the Innovation-driven Plan in Central South University (2015CXS012 and 2015CX007), in part by the National Natural Science Foundation of China (Grant Nos. 61273314 and 61673397), in part by the EU Horizon 2020 Marie Skłodowska-Curie Individual Fellowships (Project ID: 661327), in part by the Hunan Provincial Natural Science Fund for Distinguished Young Scholars (2016JJ1018), in part by the Program for New Century Excellent Talents in University (NCET-13-0596), and in part by State Key Laboratory of Intelligent Control and Decision of Complex Systems, Beijing Institute of Technology.
- 1.Storn R, Price K. Differential evolution — a simple and efficient adaptive scheme for global optimization over continuous spaces. Berkeley, CA: International Computer Science Institute. Technical Report TR-95-012. 1995Google Scholar
- 18.Wang Y, Wang B C, Li H X, Yen G G. Incorporating objective function information into the feasibility rule for constrained evolutionary optimization. IEEE Transactions on Cybernetics, 2016, doi: 10.1109/TCYB.2015.2493239Google Scholar
- 20.Tvrdík J. Modifications of differential evolution with composite trial vector generation strategies. In: Snášel V, Abraham A, Corchado E S, eds. Soft Computing Models in Industrial and Environmental Applications. Advances in Intelligent Systems and Computing, Vol 188. Berlin: Springer,2013, 113–122CrossRefGoogle Scholar
- 22.Liu H, Huang H, Liu S S. Explore influence of differential operator in DE mutation with unrestrained method to generate mutant vector. In: Rutkowski L, Korytkowski M, Scherer R, et al. eds. Swarm and Evolutionary Computation. Lecture Notes in Computer Science, Vol 7269. Berlin: Springer, 2012, 292–300CrossRefGoogle Scholar
- 23.Suganthan P N, Hansen N, Liang J, Deb K, Chen Y P, Auger A, Tiwari S. Problem definitions and evaluation criteria for the CEC 2005 special session on real-parameter optimization. KanGAL Report 2005005. 2005Google Scholar
- 24.Liang J J, Qu B Y, Suganthan P N, Hernández-Diaz A. Problem definitions and evaluation criteria for the CEC 2013 special session and competition on real-parameter optimization. Zhengzhou: Zhengzhou University. Technical Report. 2013Google Scholar
- 25.Tanabe R, Fukunaga A. Improving the search performance of shade using linear population size reduction. In: Proceeding of IEEE Congress on Evolutionary Computation. 2014, 1658–1665Google Scholar