A hybrid optimization algorithm based on chaotic differential evolution and estimation of distribution
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A hybrid optimization algorithm based on chaotic differential evolution and estimation of distribution Fuqing Zhao1,2 · Zhongshi Shao1 · Junbiao Wang2 · Chuck Zhang3
Received: 31 December 2013 / Revised: 27 April 2015 / Accepted: 28 April 2015 © SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2015
Abstract Estimation of distribution algorithms (EDAs) and differential evolution (DE) are two types of evolutionary algorithms. The former has fast convergence rate and strong global search capability, but is easily trapped in local optimum. The latter has good local search capability with slower convergence speed. Therefore, a new hybrid optimization algorithm which combines the merits of both algorithms, a hybrid optimization algorithm based on chaotic differential evolution and estimation of distribution (cDE/EDA) was proposed. Due to its effective nature of harmonizing the global search of EDA with the local search of DE, the proposed algorithm can discover the optimal solution in a fast and reliable manner. Chaotic policy was used to strengthen the search ability of DE. Meantime the global convergence of algorithm was analyzed with the aid of limit theorem of monotone bounded sequence. The proposed algorithm was tested through a set of typical benchmark problems. The results demonstrate the effectiveness and efficiency of the proposed cDE/EDA algorithm. Keywords Hybrid optimization · Estimation of distribution algorithm · Chaotic differential evolution algorithm · Convergence · Global optimization Mathematics Subject Classification
90B40
Communicated by Natasa Krejic.
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Fuqing Zhao [email protected]
1
School of Computer and Communication Technology, Lanzhou University of Technology, Lanzhou 730050, China
2
Key Laboratory of Contemporary Design and Integrated Manufacturing Technology, Ministry of Education, Northwestern Polytechnical University, 710072 Xi’an, China
3
H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA
123
F. Zhao et al.
1 Introduction Estimation of distribution algorithms (EDAs) is one of the most popular evolutionary algorithms (Larrañaga and Lozano 2002). EDAs explicitly learn and build a probabilistic model to capture the parental distribution, and then sample new solutions from the probabilistic model (Pelikan et al. 2002). EDAs are good at the automatic discovery and exploitation of problem regularities. A population evolves with intensive communication among all of the promising individuals, readily extracting promising region of search space and discovering the global optimum (Pelikan et al. 2002; Ahn 2006). Thus, EDAs are regarded as a strong-cooperative search method. Many researchers have already done much research in the field of combining EDAs with other optimum algorithms in recent years. Liu et al. (2011) has introduced the thought of EDA to BFA to increase the diversity of the population and improve the convergence speed. Liu et al. (2008) introduced People-based Incremental Learn
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