Global Optimization in Practice: An Application to Interactive Multiple Objective Linear Programming

A multiple objective linear programming problem (P) involves the simultaneous maximization of two or more conflicting linear objective functions over a nonempty polyhedron X. Many of the most popular methods for solving this type of problem, including many well-known interactive methods, involve searching the efficient set XE of the problem. Generally, however, XE is a complicated, nonconvex set. As a result, concepts and methods from global optimization may be useful in searching XE. In this paper, we will explain in theory, and show via an actual application to citrus rootstock selection in Florida, how the potential usefulness of the well-known interactive method STEM for solving problem (P) in this way, can depend crucially upon how accurately certain global optimization problems involving minimizations over XE are solved. In particular, we will show both in theory and in practice that the choice of whether to use the popular but unreliable ‘payoff table’ approach or to use one of the lesser known, more accurate global optimization methods to solve these problems can determine whether STEM succeeds or fails as a decision aid. Several lessons and conclusions of transferable value derived from this research are also given.