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Zbl 1146.90501
Geem, Zong Woo
Novel derivative of harmony search algorithm for discrete design variables. (English)
[J] Appl. Math. Comput. 199, No. 1, 223-230 (2008). ISSN 0096-3003

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 2000:: *90C27 Combinatorial programming
90C59 Approximation methods and heuristics

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

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