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Top1. Introduction
Harmony Search (HS) is a population-based phenomenon-mimicking algorithm (PMA) which imitates the improvisation process of musicians (Geem et al., 2001). Unlike traditional gradient-based optimization algorithms which have performed well only for continuous-valued variables, HS has performed well for both continuous-valued and discrete-valued variables because it possesses a new stochastic derivative (Geem, 2008) which is a new-paradigm derivative based on musicians’ experiences. In this derivative, the searching direction to the optimal solution can be stochastically determined based on musicians’ historical preferences.
HS has also considered various theoretical factors such as correlation among decision variables, theoretical background of best fret width (bw), global searching by suppressing local prematureness, global searching by managing multiple harmony memories, adaptive parameter setting along the iteration, and so forth (Geem, 2006a, 2009a; Mukhopadhyay et al., 2008). The algorithm has been also hybridized with other techniques such as genetic algorithm, simulated annealing, ant colony optimization, particle swarm optimization, chaos theory, fuzzy theory, artificial neural network, simplex method, Taguchi method, sequential quadratic programming, and commercial optimization module.
In line with the above-mentioned various theoretical backgrounds, the HS algorithm has been successfully applied to various optimization problems such as project scheduling, text mining, image tracking, robotics, power system design, structural design, water infrastructure design, dam scheduling, hydrologic model calibration, groundwater management, geotechnical stability analysis, ecological conservation, vehicle routing, heat exchanger design, offshore structure anchoring, bioinformatics, medical physics, medical imaging, etc. (Kim et al., 2001; Geem et al., 2002, 2005; Lee & Geem, 2004, 2005; Geem, 2006b; Jang et al., 2008; Coelho & Bernerta, 2009). For more details, readers can refer to several books on the HS algorithms (e.g., Geem, 2009a).
In fact, HS is very efficient if the number of parameters to be optimized is small (<25). However, some researchers (Omran & Mahdavi, 2008; Cheng et al., 2008) claimed that HS did not work well for relatively large problems although this is not always the case, since Geem (2009b) showed that the original HS is much better than GA, Simulated Annealing and Tabu Search when applied to 454-variable water network problem.
A new class of optimization methods is Probabilistic algorithms. Probabilistic methods search a problem space using a probabilistic model of potential solutions. They explicitly use probability models in problem solving. Thus, in probabilistic methods a population is approximated with a probability distribution and new potential solutions are generated by sampling this distribution. Two representative probabilistic algorithms are the Estimation of Distribution Algorithm (EDA) (Larranaga & Lozano, 2002) and the more recent Cross-Entropy (CE) method (Rubinstein & Kroese, 2004). Probabilistic algorithms have been successfully applied to a wide range of optimization problems (Pelikan et al., 2006).
In this paper, we propose a probabilistic harmony search (PHS) method that explicitly uses a probability model to enhance the performance of HS. Several well-known benchmark problems are used to compare the proposed approach against HS and other recent methods.