##
**Novel derivative of harmony search algorithm for discrete design variables.**
*(English)*
Zbl 1146.90501

Summary: Calculus has widespread applications in science and engineering. Optimization is one of its major subjects, where a problem can be mathematically formulated and its optimal solution is determined by using derivatives. However, this calculus-based derivative technique can only be applied to real-valued or continuous-valued functions rather than discrete-valued functions while there are many situations where design variables contain not continuous values but discrete values by nature. In order to consider these realistic design situations, this study proposes a novel derivative for discrete design variables based on a harmony search algorithm. Detailed analysis shows how this new stochastic derivative works in the bench-mark function and fluid-transport network design. Hopefully this new derivative, as a fundamental technology, will be utilized in various science and engineering problems.

### MSC:

90C27 | Combinatorial optimization |

90C59 | Approximation methods and heuristics in mathematical programming |

### Keywords:

stochastic derivative; harmony search; discrete variable; combinatorial optimization; evolutionary algorithm; soft computing; meta-heuristics
PDFBibTeX
XMLCite

\textit{Z. W. Geem}, Appl. Math. Comput. 199, No. 1, 223--230 (2008; Zbl 1146.90501)

Full Text:
DOI

### References:

[1] | Ayvaz, M. T., Simultaneous determination of aquifer parameters and zone structures with fuzzy C-means clustering and meta-heuristic harmony search algorithm, Advances in Water Resources, 30, 11, 2326-2338 (2007) |

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

[3] | Geem, Z. W., Improved harmony search from ensemble of music players, Lecture Notes in Artificial Intelligence, 4251, 86-93 (2006) |

[4] | Geem, Z. W., Optimal scheduling of multiple dam system using harmony search algorithm, Lecture Notes in Computer Science, 4507, 316-323 (2007) |

[5] | Geem, Z. W., Harmony search algorithm for solving Sudoku, Lecture Notes in Artificial Intelligence, 4692, 371-378 (2007) |

[6] | Geem, Z. W.; Choi, J. Y., Music composition using harmony search algorithm, Lecture Notes in Computer Science, 4448, 593-600 (2007) |

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

[8] | Geem, Z. W.; Lee, K. S.; Park, Y., Application of harmony search to vehicle routing, American Journal of Applied Sciences, 2, 12, 1552-1557 (2005) |

[9] | Geem, Z. W.; Tseng, C.-L.; Park, Y., Harmony search for generalized orienteering problem: best touring in China, Lecture Notes in Computer Science, 3612, 741-750 (2005) |

[10] | Lee, K. S.; Geem, Z. W., A new meta-heuristic algorithm for continuous engineering optimization: harmony search theory and practice, Computer Methods in Applied Mechanics and Engineering, 194, 36-38, 3902-3933 (2005) · Zbl 1096.74042 |

[11] | Lee, K. S.; Geem, Z. W.; Lee, S.-H.; Bae, K.-W., The harmony search heuristic algorithm for discrete structural optimization, Engineering Optimization, 37, 7, 663-684 (2005) |

[12] | Li, L.; Chi, S.-C.; Chu, X.-S., Location of non-circular slip surface using the modified harmony search method based on correcting strategy, Rock and Soil Mechanics, 27, 10, 1714-1718 (2006) |

[13] | Mahdavi, M.; Fesanghary, M.; Damangir, E., An improved harmony search algorithm for solving optimization problems, Applied Mathematics and Computation, 188, 2, 1567-1579 (2007) · Zbl 1119.65053 |

[14] | Mays, L. W.; Tung, Y.-K., Hydrosystems Engineering and Management (1992), McGraw-Hill: McGraw-Hill NY |

[15] | Ryu, S.; Duggal, A. S.; Heyl, C. N.; Geem, Z. W., Mooring cost optimization via harmony search, Proceedings of the 26th International Conference on Offshore Mechanics and Arctic Engineering (OMAE 2007), June 10-15, 2007 (2007), ASME: ASME San Diego, CA, USA |

[16] | A. Vasebi, M. Fesanghary, S.M.T. Bathaeea, Combined heat and power economic dispatch by harmony search algorithm, International Journal of Electrical Power & Energy Systems, in press, doi:10.1016/j.ijepes.2007.06.006; A. Vasebi, M. Fesanghary, S.M.T. Bathaeea, Combined heat and power economic dispatch by harmony search algorithm, International Journal of Electrical Power & Energy Systems, in press, doi:10.1016/j.ijepes.2007.06.006 |

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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.