Measuring the quality of discrete representations of efficient sets in multiple objective mathematical programming

Abstract.

One way of solving multiple objective mathematical programming problems is finding discrete representations of the efficient set. A modified goal of finding good discrete representations of the efficient set would contribute to the practicality of vector maximization algorithms. We define coverage, uniformity and cardinality as the three attributes of quality of discrete representations and introduce a framework that includes these attributes in which discrete representations can be evaluated, compared to each other, and judged satisfactory or unsatisfactory by a Decision Maker. We provide simple mathematical programming formulations that can be used to compute the coverage error of a given discrete representation. Our formulations are practically implementable when the problem under study is a multiobjective linear programming problem. We believe that the interactive algorithms along with the vector maximization methods can make use of our framework and its tools.