Decision Making Based on Approximate and Smoothed Pareto Curves

Abstract. We consider bicriteria optimization problems and investigate the relationship between two standard approaches to solving them: (i) computing the Pareto curve and (ii) the so-called decision maker’s approach in which both criteria are combined into a single (usually nonlinear) objective function. Previous work by Papadimitriou and Yannakakis showed how to efficiently approximate the Pareto curve for problems like Shortest Path, Spanning Tree, and Perfect Matching. We wish to determine for which classes of combined objective functions the approximate Pareto curve also yields an approximate solution to the decision maker’s problem. We show that an FPTAS for the Pareto curve also gives an FPTAS for the decision maker’s problem if the combined objective function is growth bounded like a quasi-polynomial function. If these functions, however, show exponential growth then the decision maker’s problem is NP-hard to approximate within any factor. In order to bypass these limit...

• Type: Conference
• Year: 2005
• Where: ISAAC
• Authors: Heiner Ackermann, Alantha Newman, Heiko Röglin, Berthold Vöcking
• Keywords: Decision Maker, Decision Maker Problem, ISAAC 2005, Pareto Curve