Global-best harmony search.

*(English)*Zbl 1146.90091Summary: Harmony search (HS) 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. A new variant of HS, called global-best harmony search (GHS), is proposed in this paper where concepts from swarm intelligence are borrowed to enhance the performance of HS. The performance of the GHS is investigated and compared with HS and a recently developed variation of HS. The experiments conducted show that the GHS generally outperformed the other approaches when applied to ten benchmark problems. The effect of noise on the performance of the three HS variants is investigated and a scalability study is conducted. The effect of the GHS parameters is analyzed. Finally, the three HS variants are compared on several integer programming test problems. The results show that the three approaches seem to be an efficient alternative for solving integer programming problems.

##### MSC:

90C59 | Approximation methods and heuristics in mathematical programming |

PDF
BibTeX
XML
Cite

\textit{M. G. H. Omran} and \textit{M. Mahdavi}, Appl. Math. Comput. 198, No. 2, 643--656 (2008; Zbl 1146.90091)

Full Text:
DOI

##### References:

[1] | T. Bäck, F. Hoffmeister, H. Schwefel, A Survey of evolution strategies. In: Proceedings of the Fourth International Conference on Genetic Algorithms and their Applications, vols. 2-9, 1991. |

[2] | R. Eberhart, J. Kennedy, A new optimizer using particle swarm theory, in: Proceedings of the Sixth International Symposium on Micromachine and Human Science, pp. 39-43, 1995. |

[3] | Fogel, L., Evolutionary programming in perspective: the top-down view, () |

[4] | Z. Geem, Optimal design of water distribution networks using harmony search. PhD Thesis, Korea University, Seoul, Korea, 2000. |

[5] | Geem, Z., Optimal cost design of water distribution networks using harmony search, Engineering optimization, 38, 3, 259-280, (2006) |

[6] | Geem, Z.; Kim, J.; Loganathan, G., A new heuristic optimization algorithm: harmony search, Simulation, 76, 2, 60-68, (2001) |

[7] | Geem, Z.; Kim, J.; Loganathan, G., Harmony search optimization: application to pipe network design, International journal of model simulation, 22, 2, 125-133, (2002) |

[8] | Z. Geem, C. Tseng, Y. Park, Harmony search for generalized orienteering problem: best touring in China, in: Springer Lecture Notes in Computer Science 3412 (2005) 741-750. |

[9] | Goldberg, D., Genetic algorithms in search, optimization and machine learning, (1989), Addison-Wesley · Zbl 0721.68056 |

[10] | J. Kennedy, R.C. Eberhart, Particle swarm optimization, in: Proceedings of the IEEE International Joint Conference on Neural Networks, IEEE Press, 1995. pp. 1942-1948. |

[11] | Kim, J.; Geem, Z.; Kim, E., Parameter estimation of the nonlinear muskingum model using harmony search, Journal of American water resource association, 37, 5, 1131-1138, (2001) |

[12] | Koza, J., Genetic programming: on the programming of computers by means of natural selection, (1992), MIT Press Cambridge, MA · Zbl 0850.68161 |

[13] | Koza, J.; Poli, R., Genetic programming, (), 127-164, Chapter 5 |

[14] | E. Laskari, K. Parsopoulos, M. Vrahatis, Particle swarm optimization for integer programming, in: Proceedings of the 2002 Congress on Evolutionary Computation (2) (2002) 1582-1587. |

[15] | Lee, K.; Geem, Z., A new structural optimization method based on the harmony search algorithm, Computer and structures, 82, 9-10, 781-798, (2004) |

[16] | Lee, K.; Geem, Z., A new meta-heuristic algorithm for continuous engineering optimization: harmony search theory and practice, Computer methods in applied mechanics and engineering, 194, 2005, 3902-3933, (2005) · Zbl 1096.74042 |

[17] | Mahdavi, M.; Fesanghary, M.; Damangir, E., An improved harmony search algorithm for solving optimization problems, Applied mathematics and computation, 188, 2007, 1567-1579, (2007) · Zbl 1119.65053 |

[18] | Michalewicz, Z.; Fogel, D., How to solve it: modern heuristics, (2000), Springer-Verlag Berlin · Zbl 0943.90002 |

[19] | R. Storn, K. Price, Differential evolution – a simple and efficient adaptive scheme for global optimization over continuous spaces, Technical Report TR-95-012, International Computer Science Institute, Berkeley, CA, 1995. · Zbl 0888.90135 |

[20] | Van Laarhoven, P.; Aarts, E., Simulated annealing: theory and applications, (1987), Kluwer Academic Publishers · Zbl 0643.65028 |

[21] | Yao, X.; Liu, Y.; Lin, G., Evolutionary programming made faster, IEEE transactions on evolutionary computation, 3, 2, 82-102, (1999) |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.