Harmony search

In operations research, harmony search is a phenomenon-mimicking metaheuristic introduced in 2001 by Zong Woo Geem, Joong Hoon Kim, and G. V. Loganathan. Harmony search is inspired by the improvisation process of jazz musicians.

In the HS algorithm, each musician (= decision variable) plays (= generates) a note (= a value) for finding a best harmony (= global optimum) all together.

Harmony search tries to find a vector ${\displaystyle \mathbf {x} }$ which optimizes (minimizes or maximizes) a certain objective function.

The algorithm has the following steps:

Step 1: Generate random vectors (${\displaystyle \mathbf {x} ^{1},\ldots ,\mathbf {x} ^{hms}}$) as many as ${\displaystyle hms}$ (harmony memory size), then store them in harmony memory (HM).

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