Efficient Mutation Strategies Embedded in Laplacian-Biogeography-Based Optimization Algorithm for Unconstrained Function Minimization

Efficient Mutation Strategies Embedded in Laplacian-Biogeography-Based Optimization Algorithm for Unconstrained Function Minimization

Vanita Garg (Department of Mathematics, Indian Institute of Technology, Roorkee, India) and Kusum Deep (Department of Mathematics, Indian Institute of Technology, Roorkee, India)
Copyright: © 2016 |Pages: 33
DOI: 10.4018/IJAEC.2016040102
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Abstract

Biogeography-Based optimization (BBO) is a nature inspired optimization technique that has excellent exploitation ability but the exploration ability needs to be improved to make it more robust. With this objective in mind, Garg and Deep proposed Laplacian BBO (LX-BBO) based on the Laplace Crossover which is a Real Coded Genetic Crossover Operator. It was concluded that LX- BBO outperforms its competitors. A natural question is to incorporate real coded mutation strategies into LX-BBO in order to improve its diversity. Therefore, in this paper, the exploring ability of LX-BBO is further investigated by using six different types of mutation operators present in literature. Gaussian, Cauchy, Levy, Power, Polynomial and Random mutation are used to test which mutation works best for LX-BBO. The performance of all these versions of BBO are measured on the benchmark problem set proposed in CEC 2014. On the basis of the criteria lay down by CEC, analysis of numerical and graphical results and statistical tests it is concluded that LX-BBO works best with Random and Cauchy Mutation.
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2. Biogeography-Based Optimization

Biogeography Based Optimization is based on the idea of migration, speciation and extinction of species. The idea of biogeography theory is given by McArthur and E. Wilson (1963). The idea of Biogeography give rise to Biogeography based Optimization Algorithm which is proposed by Dan Simon in 2008. In Biogeography Based Optimization, a candidate solution is improved using two operators. These operators are given as follows:

  • Migration: The information sharing between the solutions (habitats) is termed as Migration. This information is shared probabilistically. If a solution Si is selected to be modified, then its immigration rate λi is used probabilistically to decide whether each SIV of the solution is to be modified or not. If a given SIV in a given solution is selected to be modified, then the emigration rate μi of the other solution is used to decide which of the solutions is to migrate a randomly selected SIV to solution Si:

where:

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