A simulated weed colony system with subregional differential evolution for multimodal optimization

This article proposes a two-stage hybrid multimodal optimizer based on invasive weed optimization (IWO) and differential evolution (DE) algorithms for locating and preserving multiple optima of a real-parameter functional landscape in a single run. Both IWO and DE have been modified from their original forms to meet the demands of the multimodal problems used in this work. A p-best crossover operation is introduced in the subregional DEs to improve their exploitative behaviour. The performance of the proposed algorithm is compared with a number of state-of-the-art multimodal optimization algorithms over a benchmark suite comprising 21 basic multimodal problems and seven composite multimodal problems. Experimental results suggest that the proposed technique is able to provide better and more consistent performance over the existing well-known multimodal algorithms for the majority of test problems without incurring any serious computational burden.

[1]  Xiaodong Yin,et al.  A Fast Genetic Algorithm with Sharing Scheme Using Cluster Analysis Methods in Multimodal Function Optimization , 1993 .

[2]  Ofer M. Shir,et al.  Niching in evolution strategies , 2005, GECCO '05.

[3]  Francisco Herrera,et al.  A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms , 2011, Swarm Evol. Comput..

[4]  Frans van den Bergh,et al.  A NICHING PARTICLE SWARM OPTIMIZER , 2002 .

[5]  Ponnuthurai Nagaratnam Suganthan,et al.  Benchmark Functions for the CEC'2013 Special Session and Competition on Large-Scale Global Optimization , 2008 .

[6]  Kalyanmoy Deb,et al.  Comparison of multi-modal optimization algorithms based on evolutionary algorithms , 2006, GECCO.

[7]  P. John Clarkson,et al.  A Species Conserving Genetic Algorithm for Multimodal Function Optimization , 2002, Evolutionary Computation.

[8]  Bijaya K. Panigrahi,et al.  On population variance and explorative power of invasive weed optimization algorithm , 2009, 2009 World Congress on Nature & Biologically Inspired Computing (NaBIC).

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

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

[11]  A. E. Eiben,et al.  Introduction to Evolutionary Computing , 2003, Natural Computing Series.

[12]  Daniela Zaharie A MULTIPOPULATION DIFFERENTIAL EVOLUTION ALGORITHM FOR MULTIMODAL OPTIMIZATION , 2004 .

[13]  Patrick Siarry,et al.  Island Model Cooperating with Speciation for Multimodal Optimization , 2000, PPSN.

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

[15]  C. Lucas,et al.  A novel numerical optimization algorithm inspired from weed colonization , 2006, Ecol. Informatics.

[16]  Jing J. Liang,et al.  Differential Evolution With Neighborhood Mutation for Multimodal Optimization , 2012, IEEE Transactions on Evolutionary Computation.

[17]  Kevin Warwick,et al.  A Variable Radius Niching Technique for Speciation in Genetic Algorithms , 2000, GECCO.

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

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

[20]  Jie Yao,et al.  Bi-Objective Multipopulation Genetic Algorithm for Multimodal Function Optimization , 2010, IEEE Transactions on Evolutionary Computation.

[21]  Ofer M. Shir,et al.  Adaptive Niche Radii and Niche Shapes Approaches for Niching with the CMA-ES , 2010, Evolutionary Computation.

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

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

[24]  F. Wilcoxon Individual Comparisons by Ranking Methods , 1945 .

[25]  Zachary V. Hendershot A Differential Evolution Algorithm for Automatically Discovering Multiple Global Optima in Multidimensional, Discontinuous Spaces , 2004, MAICS.

[26]  Kalyanmoy Deb,et al.  An Investigation of Niche and Species Formation in Genetic Function Optimization , 1989, ICGA.

[27]  Ponnuthurai N. Suganthan,et al.  Real-parameter evolutionary multimodal optimization - A survey of the state-of-the-art , 2011, Swarm Evol. Comput..

[28]  Alain Pétrowski,et al.  A clearing procedure as a niching method for genetic algorithms , 1996, Proceedings of IEEE International Conference on Evolutionary Computation.

[29]  Michael N. Vrahatis,et al.  On the computation of all global minimizers through particle swarm optimization , 2004, IEEE Transactions on Evolutionary Computation.

[30]  Hyun-Kyo Jung,et al.  A novel algorithm for multimodal function optimization based on evolution strategy , 2004, IEEE Transactions on Magnetics.

[31]  Michael N. Vrahatis,et al.  Modification of the Particle Swarm Optimizer for Locating All the Global Minima , 2001 .

[32]  R. Storn,et al.  Differential evolution a simple and efficient adaptive scheme for global optimization over continu , 1997 .

[33]  Xiaodong Li,et al.  Benchmark Functions for the CEC'2010 Special Session and Competition on Large-Scale , 2009 .

[34]  Ponnuthurai N. Suganthan,et al.  Novel multimodal problems and differential evolution with ensemble of restricted tournament selection , 2010, IEEE Congress on Evolutionary Computation.

[35]  T. Warren Liao,et al.  Two hybrid differential evolution algorithms for engineering design optimization , 2010, Appl. Soft Comput..

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

[37]  K. Dejong,et al.  An analysis of the behavior of a class of genetic adaptive systems , 1975 .

[38]  P. N. Suganthan,et al.  Differential Evolution: A Survey of the State-of-the-Art , 2011, IEEE Transactions on Evolutionary Computation.

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

[40]  Abdelhakim Ameur El Imrani,et al.  Dielectric composite multimodal optimization using a multipopulation cultural algorithm , 2008, Intell. Data Anal..

[41]  Samir W. Mahfoud Niching methods for genetic algorithms , 1996 .

[42]  R. K. Ursem Multinational evolutionary algorithms , 1999, Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406).

[43]  Jing J. Liang,et al.  Problem Definitions and Evaluation Criteria for the CEC 2005 Special Session on Real-Parameter Optimization , 2005 .

[44]  Chang-Hwan Im,et al.  A novel algorithm for multimodal function optimization based on evolution strategy , 2004 .

[45]  Ralph R. Martin,et al.  A Sequential Niche Technique for Multimodal Function Optimization , 1993, Evolutionary Computation.

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