Abstract
A harmony search (HS) algorithm for solving high-dimensional multimodal optimization problems (named DIHS) was proposed in 2015 and showed good performance, in which a dynamic-dimensionality-reduction strategy is employed to maintain a high update success rate of harmony memory (HM). However, an extreme assumption was adopted in the DIHS that is not reasonable, and its analysis for the update success rate is not sufficiently accurate. In this study, we reanalyzed the update success rate of HS and now present a more valid method for analyzing the update success rate of HS. In the new analysis, take-k and take-all strategies that are employed to generate new solutions are compared to the update success rate, and the average convergence rate of algorithms is also analyzed. The experimental results demonstrate that the HS based on the take-k strategy is efficient and effective at solving some complex high-dimensional optimization problems.
Highlights
Harmony search (HS) [1,2,3,4,5], which is a meta-heuristic search algorithm that mimics the process of improvising a musical harmony, has been extensively employed in the fields of complex scientific computing and engineering optimization
Tuo et al proposed a hybrid algorithm based on HS and teaching-learning-based optimization (TLBO) for solving complex high-dimensional optimization problems; the algorithm showed efficient performance [7]
We identified a key analysis error in the article of DIHS, when the dimension D
Summary
Harmony search (HS) [1,2,3,4,5], which is a meta-heuristic search algorithm that mimics the process of improvising a musical harmony, has been extensively employed in the fields of complex scientific computing and engineering optimization. Various variants of HS were proposed to improve the performance for solving complex optimization problems [17,18,19,20,21,22,23,24], such as accelerating search speed, enhancing the power of global exploration and balancing the tradeoff between diversification and intensification. In 2015, an HS algorithm named “A harmony search algorithm for high-dimensional multimodal optimization problems (DIHS) [4]” was proposed. In DIHS, to determine why the standard HS has low efficiency and low precision in solving high-dimensional optimization problems, the take-one search strategy and take-all search strategy were compared to analyze the success rate of newly generated solutions for updating the worst solution in harmony memory (HM).
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