A METHOD FOR GENERATING ALL THE EFFICIENT SOLUTIONS OF A 0-1 MULTI-OBJECTIVE LINEAR PROGRAMMING PROBLEM

Abstract

In this paper, a method using the concept of l1-norm is proposed to find all the efficient solutions of a 0-1 Multi-Objective Linear Programming (MOLP) problem. These solutions are specified without generating all feasible solutions. Corresponding to a feasible solution of a 0-1 MOLP problem, a vector is constructed, the components of which are the values of objective functions. The method consists of a one-stage algorithm. In each iteration of this algorithm a 0-1 single objective linear programming problem is solved. We have proved that optimal solutions of this 0-1 single objective linear programming problem are efficient solutions of the 0-1 MOLP problem. Corresponding to efficient solutions which are obtained in an iteration, some constraints are added to the 0-1 single objective linear programming problem of the next iteration. Using a theorem we guarantee that the proposed algorithm generates all the efficient solutions of the 0-1 MOLP problem. Numerical results are presented for an example taken from the literature to illustrate the proposed algorithm.