Compromise point incorporating trade-off ratio in multi-objective optimization

The aims of multi-objective optimization are (1) to find pareto-optimal solutions and (2) to analyze the trade-off between conflicting objectives. This paper proposes an interactive method for solving multi-objective optimization problems using the satisficing trade-off method (STOM). In particular, we introduce a trade-off matrix to quantitatively analyze the trade-off between conflicting objectives. Each element of the trade-off matrix consists of a projection matrix of active constraints and gradients of objective functions. In addition, the compromise point and the compromise solution incorporating the trade-off ratio that the decision-maker desires are defined in this paper. The technique to obtain the compromise point is proposed in this paper. Through numerical examples, the validity proposed method is examined. (C) 2012 Elsevier B.V. All rights reserved.