Contiguity Constraints for Single‐Region Site Search Problems

This paper proposes an explicit set of constraints as a general approach to the contiguity problem in site search modeling. Site search models address the challenging problem of identifying the best area in a study region for a particular land use, given that there are no candidate sites. Criteria that commonly arise in a search include a site's area, suitability, cost, shape, and proximity to surrounding geographic features. An unsolved problem in this modeling arena is the identification of a general set of mathematical programming constraints that can guarantee a contiguous solution (site) for any 0–1 integer‐programming site search formulation. The constraints proposed herein address this problem, and we evaluate their efficacy and efficiency in the context of a regular and irregular tessellation of geographic space. An especially efficient constraint form is derived from a more general form and similarly evaluated. The results demonstrate that the proposed constraints represent a viable, general approach to the contiguity problem.