USING WEIGHTED-SUM FUNCTIONS TO COMPUTE NONSUPPORTED EFFICIENT SOLUTIONS IN MULTIOBJECTIVE COMBINATORIAL-{0,1} PROBLEMS

In multiobjective linear programming, the weighted-sum functions can be used to characterize the entire set of efficient solutions, but in multiobjective combinatorial-{0,1} problems these functions can only determine a small subset of efficient solutions, called supported efficient solutions. In this paper, we show how the entire set of efficient solutions can be found with the same technique by modifying the original problem. An algorithm is proposed. Some results are presented and the effect of some parameters of the proposed algorithm is illustrated with the multiobjective {0,1}-knapsack problem.