On the iterative convergence of harmony search algorithm and a proposed modification

Inspired by the improvisation process of music players, a population-based meta-heuristic algorithm-harmony search (HS) has been proposed recently. HS is good at exploitation, but it can be poor at exploration, and its convergence performance can also be an issue in some cases. To address these disadvantages, the distance bandwidth (bw) adjusting methods proposed in recent literatures are summarized and the exploration ability of HS improvisation is investigated in this paper. Further, the relationship between improvisation exploration and each parameter under asymmetric interval is derived, and an iterative convergence sufficiency of the iteration equation which consists of variance expectation and mean expectation is proven theoretically. Based on these analyses, a modified harmony search (MHS) algorithm is proposed. Moreover, the effects of the key parameters including HMS, PAR and HMCR on the performance of the MHS algorithm are discussed in depth. Experimental results reveal that the proposed MHS algorithm performs better than HS as well as its state-of-the-art variants and other classic excellent meta-heuristic approaches.