Differential Evolution Based on Fitness Euclidean-Distance Ratio for Multimodal Optimization

In this paper, fitness euclidean-distance ratio (FER) is incorprated into differential evolution to solve multimodal optimization problems. The prime target of multi-modal optimization is to finding multiple global and local optima of a problem in one single run. Though variants of differential evolution (DE) are highly effective in locating single global optimum, few DE algorithms perform well when solving multi-optima problems. This work uses the FER technique to enhance the DE’s ability of locating and maintaining multiple peaks. The proposed algorithm is tested on a number of benchmark test function and the experimental results show that the proposed simple algorithm performs better comparing with a number of state-of-the-art multimodal optimization approaches.

[1]  Xiaodong Li,et al.  Adaptively Choosing Neighbourhood Bests Using Species in a Particle Swarm Optimizer for Multimodal Function Optimization , 2004, GECCO.

[2]  P. N. Suganthan,et al.  Modified species-based differential evolution with self-adaptive radius for multi-modal optimization , 2010, International Conference on Computational Problem-Solving.

[3]  Xiaodong Li,et al.  Niching Without Niching Parameters: Particle Swarm Optimization Using a Ring Topology , 2010, IEEE Transactions on Evolutionary Computation.

[4]  Xiaodong Li,et al.  Efficient differential evolution using speciation for multimodal function optimization , 2005, GECCO '05.

[5]  James Kennedy,et al.  Particle swarm optimization , 1995, Proceedings of ICNN'95 - International Conference on Neural Networks.

[6]  Ponnuthurai N. Suganthan,et al.  Multi-objective evolutionary algorithms based on the summation of normalized objectives and diversified selection , 2010, Inf. Sci..

[7]  Zbigniew Michalewicz,et al.  Genetic Algorithms + Data Structures = Evolution Programs , 1996, Springer Berlin Heidelberg.

[8]  Georges R. Harik,et al.  Finding Multimodal Solutions Using Restricted Tournament Selection , 1995, ICGA.

[9]  P. John Clarkson,et al.  Erratum: A Species Conserving Genetic Algorithm for Multimodal Function Optimization , 2003, Evolutionary Computation.

[10]  R. Storn,et al.  Differential Evolution: A Practical Approach to Global Optimization (Natural Computing Series) , 2005 .

[11]  Ponnuthurai N. Suganthan,et al.  Dynamic Grouping Crowding Differential Evolution with Ensemble of Parameters for Multi-modal Optimization , 2010, SEMCCO.

[12]  Rainer Storn,et al.  Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces , 1997, J. Glob. Optim..

[13]  Ponnuthurai N. Suganthan,et al.  Current position-based Fitness Euclidean-distance Ratio Particle Swarm Optimizer for multi-modal optimization , 2010, 2010 Second World Congress on Nature and Biologically Inspired Computing (NaBIC).

[14]  Jing J. Liang,et al.  Memetic Fitness Euclidean-Distance Particle Swarm Optimization for Multi-modal Optimization , 2011, ICIC.

[15]  David E. Goldberg,et al.  Genetic Algorithms with Sharing for Multimodalfunction Optimization , 1987, ICGA.

[16]  Jing J. Liang,et al.  Niching particle swarm optimization with local search for multi-modal optimization , 2012, Inf. Sci..

[17]  Xiaodong Li,et al.  A multimodal particle swarm optimizer based on fitness Euclidean-distance ratio , 2007, GECCO '07.

[18]  René Thomsen,et al.  Multimodal optimization using crowding-based differential evolution , 2004, Proceedings of the 2004 Congress on Evolutionary Computation (IEEE Cat. No.04TH8753).