On the Harmony Search Using Quaternions

Abstract

Euclidean-based search spaces have been extensively studied to drive optimization techniques to the search for better solutions. However, in high dimensional spaces, non-convex functions might become too tricky to be optimized, thus requiring different representations aiming at smoother fitness landscapes. In this paper, we present a variant of the Harmony Search algorithm based on quaternions, which extend complex numbers and have been shown to be suitable to handle optimization problems in high dimensional spaces. The experimental results in a number of benchmark functions against standard Harmony Search, Improved Harmony Search and Particle Swarm Optimization showed the robustness of the proposed approach. Additionally, we demonstrated the robustness of the proposed approach in the context of fine-tuning parameters in Restricted Boltzmann Machines.