An Estimation Method of the Range of Weighting Coefficients where the Solution Prefered by an Operator is Optimal in Multi-Objective Optimization

Hirokazu Kobayashi, Ryosuke Tachi, Hisashi Tamaki

In the weight method, which is known as one of solutions to the multi-objective optimization problem, it is possible to obtain Pareto optimal solutions by repeating the different weighting coefficients from previous ones and solving by using them. In this research, as a reverse procedure to the above, when a solution preferred by an operator is given, a method of estimating the range of the weighting coefficients where this solution becomes optimal is proposed. We regard a target problem as a mathematical programming problem and estimate the range of weighting coefficients for each purpose based on the basic idea of simplex method. Through some examples, the effectiveness of the proposed approach is examined, and it is confirmed that we can estimate the range of weighting coefficients where the solution preferred by the operator becomes optimal, when this solution exists in feasible region.