On the Harmony Search Using Quaternions
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 re
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Department of Computing, S˜ ao Paulo State University, S˜ ao Paulo, Brazil [email protected], [email protected] 2 School of Science and Technology, Middlesex University, London, UK [email protected]
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.
Keywords: Harmony Search
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· Quaternions · Optimization
Introduction
Function optimization plays an important role in a number of applications, ranging from simulation in aerodynamics to fine-tuning machine learning algorithms. Although one can find several problems that can be modeled by convex functions, most applications out there pose a bigger challenge, since they are usually encoded by non-convex functions, which means they may contain both local and global optima. In light of that, one may handle such sort of functions by means of two approaches: (i) the first one concerns with trying different optimization techniques, and (ii) the second one aims at finding a different representation of the search space in order to deal with smoother landscape functions. In the last decades, the scientific community has focused even more on optimization techniques based on the nature, the so-called meta-heuristics [23]. Such techniques are based on different mechanisms that address the problem of optimization, such as evolutionary processes, mimetism, and swarm intelligence, just to name a few. These techniques have been in the spotlight mainly due to their elegance and easiness of implementation, as well as solid results in a number of well-known problems in the literature [1]. c Springer International Publishing AG 2016 F. Schwenker et al. (Eds.): ANNPR 2016, LNAI 9896, pp. 126–137, 2016. DOI: 10.1007/978-3-319-46182-3 11
On the Harmony Search Using Quaternions
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Recently, Malan and Engelbrecht [11] presented an interesting study that aimed at predicting possible situations in which the well-known Particle Swarm Optimization (PSO) algorithm would fail based on the fitness landscape. Basically, depending on the “smoothness degree” of the fitness function landscape, one can expect a probable performance of the algorithm. Once again, the fitness function plays an important role in the optimization problem, and finding suitable representations of that function in differen
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