Finding all optimal solutions to the reserve site selection problem: formulation and computational analysis

The problem of selecting nature reserves has received increased attention in the literature during the past decade, and a variety of approaches have been promoted for selecting those sites to include in a reserve network. One set of techniques employs heuristic algorithms and thus provides possibly sub-optimal solutions. Another set of models and accompanying algorithms uses an integer programming formulation of the problem, resulting in an optimization problem known as the Maximal Covering Problem, or MCP. Solution of the MCP provides an optimal solution to the reserve site selection problem, and while various algorithms can be employed for solving the MCP they all suffer from the disadvantage of providing a single optimal solution dictating the selection of areas for conservation. In order to provide complete information to decision makers, the determination of all alternate optimal solutions is necessary. This paper explores two procedures for finding all such solutions. We describe the formulation and motivation of each method. A computational analysis on a data set describing native terrestrial vertebrates in the state of Oregon illustrates the effectiveness of each approach.