A procedure to find discrete representations of the efficient set with specified coverage errors

Abstract

An important issue in multiple objective mathematical programming is finding discrete representations of the efficient set. Because discrete points can be directly studied by a decision maker, a discrete representation can serve as the solution to the multiple objective problem at hand. However, the discrete representation must be of acceptable quality to ensure that a most-preferred solution identified by a decision maker is of acceptable quality. Recently, attributes for measuring the quality of discrete representations have been proposed. Although discrete representations can be obtained in many different ways, and their quality evaluated afterwards, the ultimate goal should be to find such representations so as to conform to specified quality standards. We present a method that can find discrete representations of the efficient set according to a specified level of quality. The procedure is based on mathematical programming tools and can be implemented relatively easily when the domain of interest is a polyhedron. The nonconvexity of the efficient set is dealt with through a coordinated decomposition approach. We conduct computational experiments and report results.