Global Optimization of Combined Region Aggregation and Leveling Model

Abstract

The advent and widespread use of innovative spatial analysis technologies, such as geographic information systems (GIS), computer aided design (CAD) systems, and global positioning systems (GPS), have prompted great interest in spatial optimization. The tasks of selecting an optimal subregion from a larger region—region aggregation—and determining an optimal strategy for cutting and filling that subregion to a uniform elevation—land leveling—are examples of spatial analyses that can benefit from these powerful computer technologies. The combined region aggregation and leveling problem is a complex spatial problem that often involves the comprehensive consideration of multiple, incommensurate, and often conflicting objectives, while at the same time satisfying a set of prespecified physical and logical constraints. Traditionally, these two problems are solved separately, often precluding the identification of global optima. Through this research, a multiobjective integer programming model that considers these problems simultaneously is formulated, a computational algorithm for solving the model is presented, and numerical results that demonstrate the efficiency and effectiveness of this procedure are discussed. Computational experiments report polynomial complexity of the heuristic procedure against exponential worst-case complexity of traditional enumerative methods.