Epsilon Dominance and Constraint Partitioning in Multiple Objective Problems

In this paper we consider efficient sets of multiple objective problems, in which the feasible action set is the intersection of two other sets, and where one of these sets has a special structure, such as an assignment or transportation structure. The objective is to find the efficient set of the special structure set, and its intersection with the other set, and to examine how good an approximation this set is to the desired efficient set. The approximation set is called an ε-efficient solution set. Some theoretical partition results are given for a special constraint structure with upper bounds on the objective function levels. For the case of 0-efficient solution sets, and finite explicit sets, a computational cost analysis of two computational sequences is given. We also consider two other 0-efficient solution set cases. Then ε-efficiency is considered for linear problems. Finally, the approach is illustrated by a special multiple objective transportation problem.