Integer Programming Methods for Reserve Selection and Design

Abstract

Abstract How many nature reserves should there be? Where should they be located? Which places have highest priority for protection? Conservation biologists, economists, and operations researchers have been developing quantitative methods to address these questions since the 1980s. The first formulations (Kirkpatrick 1983; Margules et al. 1988; Chapters 3 and 19) focused on species protection and efficiency – select the minimum number of reserves from a list of candidate sites to represent all species – and were solved using iterative heuristics, which guarantee only an approximation of the optimal solution (Chapter 5). Researchers later formulated the problem as a 0–1 linear integer programming (IP) model and found mathematically proven optimal solutions using the branch and bound (B&B) method available in commercial optimization software (Saetersdal et al. 1993; Underhill 1994). The main advantage of formulating a reserve selection problem as an IP model is the availability of solution methods such as B&B that guarantee finding the optimal solution. Researchers quickly recognized this advantage and have formulated reserve selection problems with a remarkable array of objectives and constraints.