Novel derivative of harmony search algorithm for discrete design variables.

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

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##### References:

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