Modified Harmony Search Algorithm for Unconstrained Numerical Optimization Problems

Abstract:

Harmony search algorithm is a new meta-heuristic optimization method imitating the music improvisation process where musicians improvise their instruments’ pitches searching for a perfect state of harmony. To enable the harmony search algorithm to transcend its limited capability of local optimum, a modified harmony search algorithm is proposed in this paper. In the modified harmony search algorithm, the mutation operation of differential evolution algorithm is introduced into MHS algorithm, which improves its convergence. Several standard benchmark optimization functions are to be test and compare the performance of the MHS. The results revealed the superiority of the proposed method to the HS and recently developed variants.

• Periodical: Advanced Materials Research (Volumes 989-994)
• Pages: 2528-2531
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.989-994.2528
• Online since: July 2014
• Authors: Hong Gang Xia*, Qing Zhou Wang
• Keywords: Convergence, Harmony Search Algorithm, Modified Harmony Search, Mutation Operation

References

[1] He Y H, Hui C W. A binary coding genetic algorithm for multi-purpose process scheduling: A case study [J], Chemical Engineering Science, 2010, 65(16): 4816-4828.

DOI: 10.1016/j.ces.2010.05.032

[2] Shi H X. Solution to 0/1 knapsack problem based on improved ant colony algorithm [C], in: International Conference on Information Acquisition, 2006, 1062-1066.

DOI: 10.1109/icia.2006.305887

[3] Coelho L S. An efficient particle swarm approach for mixed-integer programming in reliability–redundancy optimization applications [J], Reliability Engineering & System Safety, 2009, 94(4): 830-837.

DOI: 10.1016/j.ress.2008.09.001

[4] Onwubolu G, Davendra D. Scheduling flow shops using differential evolution algorithm [J], European Journal of Operational Research, 2006, 171(2): 674-692.

DOI: 10.1016/j.ejor.2004.08.043

[5] Geem Z W, Kim J H, Loganathan G V. A new heuristic optimization algorithm: Harmony search [J], Simulation, 2001, 76(2): 60-68.

DOI: 10.1177/003754970107600201

[6] Lee K S, Geem Z W. A new structural optimization method based on the harmony search algorithm [J], Computers and Structures, 2004, 82(9/10): 781-798.

DOI: 10.1016/j.compstruc.2004.01.002

[7] Honggang XIA, Dongling CHEN, Liqun GAO. Modified Harmony Search Algorithm for Power Economic Load Dispatch [J], Journal of Computational Information Systems, 2013, 9(5): 2103-2110.

[8] Sharma K D, Chatterjee A, Rakshit A. Design of a Hybrid Stable Adaptive Fuzzy Controller Employing Lyapunov Theory and Harmony Search Algorithm [J], IEEE Transactions on Control Systems Technology, 2010, PP(99): 1-8.

DOI: 10.1109/tcst.2009.2039138

[9] Mahdavi M, Fesanghary M, Damangir E. An improved harmony search algorithm for solving optimization problems [J], Applied Mathematics and Computation, 2007, 188(2): 1567–1579.

DOI: 10.1016/j.amc.2006.11.033

[10] Chia-Ming Wang, Yin-Fu Huang. Self-adaptive harmony search algorithm for optimization. Expert Systems with Applications, 2010, 37(4): 2826-2837.

DOI: 10.1016/j.eswa.2009.09.008

[11] Omran M G H, Mahdavi M. Global-best harmony search [J], Applied Mathematics and Computation, 2008, 198(2): 643-656.

DOI: 10.1016/j.amc.2007.09.004

[12] Zou D X, Gao L Q, Wu J H, Li S. Novel global harmony search algorithm for unconstrained problems [J], Neurocomputing, 2010, 73(16-18): 3308-3318.

DOI: 10.1016/j.neucom.2010.07.010

[13] Storn, R., Price, K., Differential evolution: a simple and efficient adaptive scheme for global optimization over continuous spaces. Technical Report TR-95-012, Berkeley, USA: International Computer Science Institute, (1995).