A Multiobjective Discrete Optimization Model for Land Allocation

Abstract

A multiobjective integer programming model is presented for allocating an area of land for development. The objectives considered in the allocation are cost, proximity to desirable and undesirable land features and the shape of the area. An interactive multiobjective optimization algorithm is presented and applied to the model. The algorithm generates a subset of efficient solutions with some guidance from the decision maker at each iteration as to what constitutes a “preferred” efficient point. The algorithm calls for the frequent solution of subproblems which constrain all but one of the objectives while optimizing the remaining one. In the land allocation model, the subproblems are integer programs solved efficiently by specialized enumeration techniques. For some of the subproblems (namely, those using proximity as the single objective), the first feasible solution we enumerate is guaranteed optimal. For the other subproblems, we show that an algorithm with this fortunate property would require the solution of an NP-hard problem at each step of the enumeration. The model and algorithm were tested in locating potential sites for a 13-acre residential development within a 2250-acre study area near Norris, Tennessee.