Empirical Analysis of the Impact of Two Key Parameters of the Harmony Search Algorithm on Performance

Metaheuristic algorithms are widely utilized as effective tools for solving complex optimization problems. Among them, the Harmony Search (HS) algorithm has garnered significant attention for its simple structure and excellent performance. The efficacy of the HS algorithm is heavily dependent on the configuration of its internal parameters, with the Harmony Memory Considering Rate (HMCR) and Pitch Adjusting Rate (PAR) playing pivotal roles. These parameters determine the probabilities of using the Random Generation (RG), Harmony Memory Consideration (HMC), and Pitch Adjustment (PA) operators, thereby controlling the balance between exploration and exploitation. However, a systematic empirical analysis of the interaction between these parameters and the characteristics of the problem at hand remains insufficient. Thus, this study conducts a comprehensive empirical analysis of the performance sensitivity of the HS algorithm to variations in HMCR and PAR values. The analysis is performed on a suite of 23 benchmark functions, encompassing diverse characteristics such as unimodality/multimodality and separability/non-separability, along with 5 real-world optimization problems. Through extensive experimentation, the performance for each parameter combination was evaluated on a rank-based system and visualized using heatmaps. The results experimentally demonstrate that the algorithm’s performance is most sensitive to the HMCR value across all function types, establishing that setting a high HMCR value (≥0.9) is a prerequisite for securing stable performance. Conversely, the optimal PAR value showed a direct correlation with the topographical features of the problem landscape. For unimodal problems, a low PAR value between 0.1 and 0.3 was more effective, whereas for complex multimodal problems with numerous local optima, a relatively higher PAR value between 0.3 and 0.5 proved more efficient in searching for the global optimum. This research provides a guideline into the parameter settings of the HS algorithm and contributes to enhancing its practical applicability by proposing a systematic parameter tuning strategy based on problem characteristics.