A New Robustness Index for Multi-Objective Optimization based on a User Perspective
Christoffer Cromvik, Peter Lindroth, Michael Patriksson, Ann‐Brith Strömberg · Chalmers Publication Library (Chalmers University of Technology) · 2011
Abstract Solving practical optimization problems that are sensitive to small changes in thevariables or model parameters requires special attention regarding the robustnessof solutions. We present a definition of a new robustness index for multi-objectiveoptimization problems. The definition is based on an approximation of the un-derlying utility function for a single decision maker. We further demonstrate anefficient computational procedure to evaluate robustness. The procedure is ap-plied to two numerical examples: one analytic test problem and one real-worldproblem in antenna design. The results show that the robustness varies over thePareto front and that it can be improved if the decision maker is willing to sacri-fice in optimality of the solution. Keywords: multi-objective optimization, vector optimization, robustness, multi-criteria deci-sion making, utility theory 1 Introduction Many applications of optimization comprise several more or less conflicting objec-tives, such as cost versus quality and expected return versus risk. These are to be op-timized simultaneously and the aim is to find the most appropriate balance betweenall of the objectives. Mathematically, such a problem is denoted a