A harmony search algorithm for high-dimensional multimodal optimization problems

• DDRA strategy for avoiding generating invalid solutions.
• Dynamic fret width (fw) strategy of two phases for balance global exploration and local exploitation.
• DIHS algorithm for improving the solution quality and search efficiency.
• Take-one strategy for a fast convergence to globally optimal solution is analyzed.

Harmony search (HS) and its variants have been found successful applications, however with poor solution accuracy and convergence performance for high-dimensional (≥200) multimodal optimization problems. The reason is mainly huge search space and multiple local minima. To tackle the problem, we present a new HS algorithm called DIHS, which is based on Dynamic-Dimensionality-Reduction-Adjustment (DDRA) and dynamic fret width (fw) strategy. The former is for avoiding generating invalid solutions and the latter is to balance global exploration and local exploitation. Theoretical analysis on the DDRA strategy for success rate of update operation is given and influence of related parameters on solution accuracy is investigated. Our experiments include comparison on solution accuracy and CPU time with seven typical HS algorithms and four widely used evolutionary algorithms (SaDE, CoDE, CMAES and CLPSO) and statistical comparison by the Wilcoxon Signed-Rank Test with the seven HS algorithms and four evolutionary algorithms. The problems in experiments include twelve multimodal and four complex uni-modal functions with high-dimensionality.Experimental results indicate that the proposed approach can provide significant improvement on solution accuracy with less CPU time in solving high-dimensional multimodal optimization problems, and the more dimensionality that the optimization problem is, the more benefits it provides.