The Weighted-Tchebycheff Approach to Design Optimization

摘要

Bi-objective optimization is a useful mathematical method for the investigation of real-world problems withrnconflicting two objectives that arise in decision making in order to incorporate a tradeoff between the two objectives.rnIn most of such studies, an assumption of convexity on the problems has been made. However, the method to obtainrna non-convex Pareto frontier has not yet been fully explored. In many practical industrial situations, at least onernobjective function can be a higher-order than the second. Consequently, the associated Pareto frontier can bernnonconvex. In this situation, it is known that obtaining efficient solutions using the conventional weighted-sumrnmethod is unlikely because this method do not yield solutions that lie in nonconvex regions of the feasible designrnspace. In practice, this means that weighted-sum methods could miss potentially preferable solutions. For this reason,rnwe develop a weighted-Tchebycheff-based bi-objective optimization model to obtain all efficient solutions and arnnonconvex Pareto frontier. The weighted-Tchebycheff method is far more effective than any other method when arnfunction has higher-order terms or is neither convex nor concave. Our numerical example clearly shows thernadvantages of the proposed model.