Jacobian matrix singularity based pareto front identification for multi-objective problems

Abstract

This paper presents a new structured method to effectively determine the complete boundary, including the Pareto frontier, of a multi-objective optimization problem. The proposed technique identifies the boundary in the cost space by systematically searching the design parameter space for points which make the Jacobian matrix of the cost vector singular. This corresponds to the identifying a manifold in parameter space which results in a reduced dimensional manifold in the cost space. Since the boundary of the cost space implies a reduced dimensional manifold, a systematic approach is now available for exact identification of the boundary in the cost space. The efficacy of the proposed method is demonstrated on one optimization and one optimal control problem, in this paper.