Development of interactive methods for the mathematical programming problem in multi-objective decision process

Abstract

When planning the allocation of resources, designing or controlling a system, one is often confronted with a need to simultaneously consider several objectives. The multi-objective decision problem arises when the decision-maker(DM) perceives the need to alter the course of the multi-objective system about which he/she is concerned. The inherent conflicting nature of objectives makes one impossible to obtain an optimal solution that simultaneously maximize all objectives. Instead of the optimal solution, the DM chooses the most preferred solution(MPS) based on his/her preference structure among the efficient solutions. Therefore the DM``s preference should be incorporated into the problem solving process. But the decision analyst may have difficulties for involving the DM``s preference, because the DM``s preference structure is not generally known explicitly. The main characteristic methodological aspects of the multi-objective decision problem is the process of eliciting the DM``s preference, suitable to the concerned multi-objective decision problems. Many researches have been carried out for developing methods based on different assumptions and approaches to measure or derive the utility function and solve the various types of Multi-Objective Programming(MOP) problems. In assessing the preference structure, the interactive approach is becoming popular and promising proved by many comparative studies. In this work, we develop an improved interactive method for the MOP problems, especially the multi-objective linear programming(MOLP) problem and the multi-objective integer linear programming(MOLP) probelm, together with development of a new preference representation scheme. In assessing the partial preference, queries of paired comparisons are posed to the DM, which gives to the DM less cognitive burden. For the MOLP problem, we will extend the notion of the Maximally Changeable Dominated Cone (MCDC), on which an interactive scheme is based. Hence, in solution...