Cellular Harmony Search for Optimization Problems

Structured population in evolutionary algorithms (EAs) is an important research track where an individual only interacts with its neighboring individuals in the breeding step. The main rationale behind this is to provide a high level of diversity to overcome the genetic drift. Cellular automata concepts have been embedded to the process of EA in order to provide a decentralized method in order to preserve the population structure. Harmony search (HS) is a recent EA that considers the whole individuals in the breeding step. In this paper, the cellular automata concepts are embedded into the HS algorithm to come up with a new version called cellular harmony search (cHS). In cHS, the population is arranged as a two-dimensional toroidal grid, where each individual in the grid is a cell and only interacts with its neighbors. The memory consideration and population update are modified according to cellular EA theory. The experimental results using benchmark functions show that embedding the cellular automata concepts with HS processes directly affects the performance. Finally, a parameter sensitivity analysis of the cHS variation is analyzed and a comparative evaluation shows the success of cHS.

[1]  Jing J. Liang,et al.  Dynamic multi-swarm particle swarm optimizer with local search , 2005, 2005 IEEE Congress on Evolutionary Computation.

[2]  Kalyanmoy Deb,et al.  A population-based, steady-state procedure for real-parameter optimization , 2005, 2005 IEEE Congress on Evolutionary Computation.

[3]  Gaige Wang,et al.  A Novel Hybrid Bat Algorithm with Harmony Search for Global Numerical Optimization , 2013, J. Appl. Math..

[4]  Marcus Gallagher,et al.  Experimental results for the special session on real-parameter optimization at CEC 2005: a simple, continuous EDA , 2005, 2005 IEEE Congress on Evolutionary Computation.

[5]  M. Fesanghary,et al.  An improved harmony search algorithm for solving optimization problems , 2007, Appl. Math. Comput..

[6]  L. Darrell Whitley,et al.  Evaluating Evolutionary Algorithms , 1996, Artif. Intell..

[7]  Nikolaus Hansen,et al.  A restart CMA evolution strategy with increasing population size , 2005, 2005 IEEE Congress on Evolutionary Computation.

[8]  Zong Woo Geem,et al.  Generalised Adaptive Harmony Search: A Comparative Analysis of Modern Harmony Search , 2013, J. Appl. Math..

[9]  Petr Posík,et al.  Real-parameter optimization using the mutation step co-evolution , 2005, 2005 IEEE Congress on Evolutionary Computation.

[10]  Pedro J. Ballester,et al.  Real-parameter optimization performance study on the CEC-2005 benchmark with SPC-PNX , 2005, 2005 IEEE Congress on Evolutionary Computation.

[11]  L. Darrell Whitley,et al.  GENITOR II: a distributed genetic algorithm , 1990, J. Exp. Theor. Artif. Intell..

[12]  Lipu Zhang,et al.  An Elite Decision Making Harmony Search Algorithm for Optimization Problem , 2012, J. Appl. Math..

[13]  Mahamed G. H. Omran,et al.  Global-best harmony search , 2008, Appl. Math. Comput..

[14]  Xin-She Yang.  Harmony Search as a Metaheuristic Algorithm , 2009 .

[15]  C. Fernandes,et al.  A study on non-random mating and varying population size in genetic algorithms using a royal road function , 2001, Proceedings of the 2001 Congress on Evolutionary Computation (IEEE Cat. No.01TH8546).

[16]  Francisco Herrera,et al.  Adaptive local search parameters for real-coded memetic algorithms , 2005, 2005 IEEE Congress on Evolutionary Computation.

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

[18]  Quan-Ke Pan,et al.  A local-best harmony search algorithm with dynamic subpopulations , 2010 .

[19]  Jacek Blazewicz,et al.  Scheduling a Divisible Task in a Two-dimensional Toroidal Mesh , 1999, Discret. Appl. Math..

[20]  A. Kai Qin,et al.  Self-adaptive differential evolution algorithm for numerical optimization , 2005, 2005 IEEE Congress on Evolutionary Computation.

[21]  Mohammed Azmi Al-Betar,et al.  University Course Timetabling Using a Hybrid Harmony Search Metaheuristic Algorithm , 2012, IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews).

[22]  Heinz Mühlenbein,et al.  The parallel genetic algorithm as function optimizer , 1991, Parallel Comput..

[23]  B. Schönfisch,et al.  Synchronous and asynchronous updating in cellular automata. , 1999, Bio Systems.

[24]  Xin Yao,et al.  Evolutionary programming made faster , 1999, IEEE Trans. Evol. Comput..

[25]  Mohammed A. Awadallah,et al.  Novel selection schemes for harmony search , 2012, Appl. Math. Comput..

[26]  Zong Woo Geem,et al.  An analysis of selection methods in memory consideration for harmony search , 2013, Appl. Math. Comput..

[27]  Ajith Abraham,et al.  Population-variance and explorative power of Harmony Search: An analysis , 2008, 2008 Third International Conference on Digital Information Management.

[28]  Zong Woo Geem,et al.  Novel derivative of harmony search algorithm for discrete design variables , 2008, Appl. Math. Comput..

[29]  Enrique Alba,et al.  The exploration/exploitation tradeoff in dynamic cellular genetic algorithms , 2005, IEEE Transactions on Evolutionary Computation.

[30]  Mohammed Azmi Al-Betar,et al.  Office-Space-Allocation Problem Using Harmony Search Algorithm , 2012, ICONIP.

[31]  Mohammed Azmi Al-Betar,et al.  Nurse Rostering Using Modified Harmony Search Algorithm , 2011, SEMCCO.

[32]  Mohammed Azmi Al-Betar,et al.  Selection mechanisms in memory consideration for examination timetabling with harmony search , 2010, GECCO '10.

[33]  Anne Auger,et al.  Performance evaluation of an advanced local search evolutionary algorithm , 2005, 2005 IEEE Congress on Evolutionary Computation.

[34]  Y. M. Cheng,et al.  An improved harmony search minimization algorithm using different slip surface generation methods for slope stability analysis , 2008 .

[35]  Enrique Alba,et al.  Hierarchical Cellular Genetic Algorithm , 2006, EvoCOP.

[36]  Saku Kukkonen,et al.  Real-parameter optimization with differential evolution , 2005, 2005 IEEE Congress on Evolutionary Computation.

[37]  Zong Woo Geem,et al.  A New Heuristic Optimization Algorithm: Harmony Search , 2001, Simul..

[38]  Mohammed Azmi Al-Betar,et al.  A harmony search algorithm for university course timetabling , 2010, Annals of Operations Research.

[39]  Carlos García-Martínez,et al.  Hybrid real-coded genetic algorithms with female and male differentiation , 2005, 2005 IEEE Congress on Evolutionary Computation.

[40]  Liang Gao,et al.  Cellular particle swarm optimization , 2011, Inf. Sci..

[41]  Christian Blum,et al.  Metaheuristics in combinatorial optimization: Overview and conceptual comparison , 2003, CSUR.

[42]  Ting Yee Lim.  Structured population genetic algorithms: a literature survey , 2012, Artificial Intelligence Review.

[43]  Zong Woo Geem,et al.  Economic Dispatch Using Parameter-Setting-Free Harmony Search , 2013, J. Appl. Math..