An Improved Harmony Search Algorithm with Differential Mutation Operator

Harmony Search (HS) is a recently developed stochastic algorithm which imitates the music improvisation process. In this process, the musicians improvise their instrument pitches searching for the perfect state of harmony. Practical experiences, however, suggest that the algorithm suffers from the problems of slow and/or premature convergence over multimodal and rough fitness landscapes. This paper presents an attempt to improve the search performance of HS by hybridizing it with Differential Evolution (DE) algorithm. The performance of the resulting hybrid algorithm has been compared with classical HS, the global best HS, and a very popular variant of DE over a test-suite of six well known benchmark functions and one interesting practical optimization problem. The comparison is based on the following performance indices - (i) accuracy of final result, (ii) computational speed, and (iii) frequency of hitting the optima.

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

[2]  Jeffrey Horn,et al.  Handbook of evolutionary computation , 1997 .

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

[4]  Peter J. Angeline,et al.  Evolutionary Optimization Versus Particle Swarm Optimization: Philosophy and Performance Differences , 1998, Evolutionary Programming.

[5]  Barbara Webb,et al.  Swarm Intelligence: From Natural to Artificial Systems , 2002, Connect. Sci..

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

[7]  Zbigniew Michalewicz,et al.  Evolutionary Algorithms for Constrained Parameter Optimization Problems , 1996, Evolutionary Computation.

[8]  Ioannis B. Theocharis,et al.  Microgenetic algorithms as generalized hill-climbing operators for GA optimization , 2001, IEEE Trans. Evol. Comput..

[9]  Andries Petrus Engelbrecht,et al.  Fundamentals of Computational Swarm Intelligence , 2005 .

[10]  Zbigniew Michalewicz,et al.  Evolutionary Algorithms, Homomorphous Mappings, and Constrained Parameter Optimization , 1999, Evolutionary Computation.

[11]  A. E. Eiben,et al.  On Evolutionary Exploration and Exploitation , 1998, Fundam. Informaticae.

[12]  Z. Michalewicz,et al.  Genocop III: a co-evolutionary algorithm for numerical optimization problems with nonlinear constraints , 1995, Proceedings of 1995 IEEE International Conference on Evolutionary Computation.

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

[14]  R. Parncutt.  Harmony: A Psychoacoustical Approach , 1989 .

[15]  R. Storn,et al.  Differential Evolution - A simple and efficient adaptive scheme for global optimization over continuous spaces , 2004 .

[16]  Z. Geem.  Music-Inspired Harmony Search Algorithm: Theory and Applications , 2009 .

[17]  Mirjana Cangalovic,et al.  Solving spread spectrum radar polyphase code design problem by tabu search and variable neighbourhood search , 2003, Eur. J. Oper. Res..

[18]  Zbigniew Michalewicz,et al.  Parameter Control in Evolutionary Algorithms , 2007, Parameter Setting in Evolutionary Algorithms.

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

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

[21]  M. Mahdavi,et al.  ARTICLE IN PRESS Available online at www.sciencedirect.com , 2007 .

[22]  M. Fesanghary,et al.  Combined heat and power economic dispatch by harmony search algorithm , 2007 .

[23]  Zong Woo Geem,et al.  Harmony Search Optimization: Application to Pipe Network Design , 2002 .

[24]  K. Lee,et al.  A new meta-heuristic algorithm for continuous engineering optimization: harmony search theory and practice , 2005 .

[25]  K. Lee,et al.  A new structural optimization method based on the harmony search algorithm , 2004 .

[26]  Hans-Paul Schwefel,et al.  Evolution strategies – A comprehensive introduction , 2002, Natural Computing.

[27]  Xin Yao,et al.  Stochastic ranking for constrained evolutionary optimization , 2000, IEEE Trans. Evol. Comput..

[28]  Zong Woo Geem,et al.  Application of Harmony Search to Vehicle Routing , 2005 .

[29]  Mauro Birattari,et al.  Swarm Intelligence , 2012, Lecture Notes in Computer Science.

[30]  Yangyang Li,et al.  Quantum-Inspired Immune Clonal Algorithm for Global Optimization , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[31]  Paul T. Boggs,et al.  Sequential Quadratic Programming , 1995, Acta Numerica.

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

[33]  Zong Woo Geem,et al.  Optimal Scheduling of Multiple Dam System Using Harmony Search Algorithm , 2007, IWANN.

[34]  Daniel A. Ashlock,et al.  Evolutionary computation for modeling and optimization , 2005 .

[35]  Marco Dorigo,et al.  Swarm intelligence: from natural to artificial systems , 1999 .