Ecological Optimization Using Harmony Search ZONG WOO GEEM, JUSTIN C. WILLIAMS Environmental Planning & Management Program Johns Hopkins University Baltimore, Maryland, USA zwgeem@gmail.com, jcwjr@jhu.edu Abstract: - The music-inspired meta-heuristic algorithm, harmony search, was applied to a natural reserve selection problem for preserving species and their habitats. The problem was formulated as an optimization problem (maximal covering species problem; MCSP) to maximize covered species with minimal efforts. Then, it was solved by an improved harmony search (HS) algorithm which includes problem-specific operations. When applied to real-world problem in the state of Oregon, USA, the harmony search algorithm found better solutions than those of another meta-heuristic algorithm, simulated annealing. Key-Words: - Harmony search, Optimization, Maximal covering species problem, Evolutionary algorithm, Meta-heuristics, Soft computing 1 Introduction In modern industrial and urbanized life, conserving ecosystem and its species is very important. In order to do so, quantitative optimization techniques have been developed and utilized for the nature reserve site selection problem. In the light of the optimization, ReVelle et al. [1] reviewed five classes of the reserve selection problem: (1) species set covering problem (SSCP); (2) maximal covering species problem (MCSP); (3) backup and redundant covering problem (Maximal Multiple-Representation Species Problem; MMRSP); (4) chance constrained covering problem; and (5) expected covering problem. Out of the above-mentioned five classes, the MCSP was especially tackled by various algorithms [2-4]. In this study, we apply a recently-developed harmony search (HS) algorithm to the MCSP and to compare our results with those of another meta-heuristic algorithm, simulated annealing (SA), from the literature [2]. 2 Problem Formulation Of the five classes of reserve selection problems discussed in [1], SSCP and MCSP are especially popular forms. The SSCP is to find the least number of parcels while covering every species. The mathematical formulation of the SSCP model is as follows:  J j j x Min (1)     i M j j I i all x t s . , 1 . . (2) where j and J are the index and set of land parcels, respectively; i and I are the index and set of species, respectively; i M is the set of parcels j that include species i ; and j x is a binary variable for parcel selection (it has 1 if parcel is selected, and has 0 otherwise). The MCSP is to find the maximal number of species while limiting the number of selected parcels to P . The mathematical formulation of the MCSP model is as follows:  I i i y Max (3)     i M j i j I i all y x t s , , . . (4)    J j j P x . (5) where i y is a binary variable for species covering (it has 1 if species i is covered, and has 0 otherwise). AMERICAN CONFERENCE ON APPLIED MATHEMATICS (MATH '08), Harvard, Massachusetts, USA, March 24-26, 2008 ISSN: 1790-5117 148 ISBN: 978-960-6766-47-3