Effects of initial memory and identical harmony in global optimization using harmony search algorithm Zong Woo Geem ⇑ Department of Energy IT, Gachon University, South Korea Environmental Planning and Management Program, Johns Hopkins University, United States article info Keywords: Harmony search Global optimization Phenomenon-mimicking algorithm abstract Since the harmony search algorithm searches solution space stochastically, it can find local optima and also global optimum. For the purpose of enhancing the frequency and reaching global optimum, this study introduces two new features that increase the diversity of solu- tions stored in the harmony memory. The first feature generates initial harmonies more than harmony memory size, and the second limits the number of identical harmonies stored in the harmony memory. After performing extensive simulation, it was shown that limiting the number of identical harmonies in the harmony memory enhanced the solution quality in terms of global optimum frequency and objective function value. It was also shown that generating more initial harmonies did not affect the solution quality signifi- cantly. Thus, the technique limiting identical harmonies can be utilized in future applica- tions in order to more optimize the solution quality. Ó 2012 Elsevier Inc. All rights reserved. 1. Introduction The harmony search (HS) algorithm is an optimization technique for finding a global optimum (GO) for a given domain, that is the highest or lowest value based on an objective function. HS tends to find GO [1,2] or near-global optima [3–5] for many applications although it is sometimes inefficient for finding the absolute optimum with continuous-valued decision variables [6]. HS searches solution space stochastically [7]. This helps maintain the diversity of the solutions while preventing prema- ture convergence. Diversity is an important factor in HS because memory-considering or pitch-adjusting a homogeneous harmony memory (HM) does not produce new and good solutions. One technique to maintain diversity in HS is to limit the number of similar solutions [8]. The goal of this study is to further investigate how to diversify the solutions stored in HM and how to search for a GO more frequently. In order to do so, this study shows extensive computing results obtained by using different numbers of initially generated harmonies and different numbers of allowable identical harmonies in HM. 2. Structure of harmony search algorithm In Step 1, the HS algorithm prepares a rectangular array of numbers, identified as harmony memory (HM), which mimics the memories of musicians as follows [9]: 0096-3003/$ - see front matter Ó 2012 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.amc.2012.04.070 ⇑ Address: Department of Energy IT, Gachon University, Seongnam, Zip 461-701, South Korea. E-mail addresses: geem@gachon.ac.kr, geem@jhu.edu Applied Mathematics and Computation 218 (2012) 11337–11343 Contents lists available at SciVerse ScienceDirect Applied Mathematics and Computation journal homepage: www.elsevier.com/locate/amc