Cosine Harmony Search (CHS) for Static Optimization

Abstract

Harmony Search (HS) is the behaviour imitation of a musician looking for a balanced harmony. HS has difficulty finding the best tuning parameter, especially for Pitch Adjustment Rate (PAR). PAR plays a crucial role in selecting historical solution and adjusting it using Bandwidth (BW) value. PAR in HS requires a constant value to be initialized. Furthermore, there is a delay in convergence speed due to the disproportion of global and local search capabilities. Although some HS variants have claimed to overcome this shortcoming by introducing the self-modification of PAR, these justifications have been found to be imprecise and require more extensive experiments. Local Opposition-Based Learning Self-Adaptation Global Harmony Search (LHS) implements a heuristic factor, η for self-modification of PAR. It (η) manages the probability for selecting the adaptive step, either global adaptive step or worst adaptive step. If the value of η is large, the prospects of selecting the global adaptive step is higher, thereby allowing the algorithm to exploit a better harmony value. Conversely, if η is small, the worst adaptive step is prone to selection, therefore the algorithm is closed to the best global solution. In this paper, in addressing the existing HS obstacle, we introduce a Cosine Harmony Search (CHS) which incorporates an additional strategy rule. This additional strategy employs the η inspired by LHS and contains the cosine parameter. This allows for self-modification of pitch tuning to enlarge the exploitation capabilities. We test our proposed CHS on twelve standard static benchmark functions and compare it with basic HS and five state-of-the-art HS variants. Our proposed method and these state-of-the-art algorithms are executed using 30 and 50 dimensions. The numerical results demonstrated that the CHS has outperformed other state-of-the-art algorithms in terms of accuracy and convergence speed evaluations.

Similarity Detection for Hadith of Fiqh of Women using Cosine Similarity and Boyer Moore Method

“…The principle of similarity shows that the same object will be seen together as a group, this can be determined through shape, color, direction, and size [24], [25]. Following is the pseudo-code of this algorithm: The dot product is a value that expresses the angle between two vectors.…”