Smoothed Analysis of Multiobjective Optimization

Abstract— We prove that the number of Pareto-optimal solutions in any multiobjective binary optimization problem with a finite number of linear objective functions is polynomial in the model of smoothed analysis. This resolves a conjecture of Ren´e Beier [5]. Moreover, we give polynomial bounds on all finite moments of the number of Pareto-optimal solutions, which yields the first non-trivial concentration bound for this quantity. Using our new technique, we give a complete characterization of polynomial smoothed complexity for binary optimization problems, which strengthens an earlier result due to Beier and V¨ocking [8]. Keywords-multiobjective optimization; Pareto-optimal solutions; smoothed analysis

• Type: Conference
• Year: 2009
• Where: FOCS
• Authors: Heiko Röglin, Shang-Hua Teng
• Keywords: Binary Optimization Problems, FOCS 2009, Pareto-optimal Solutions, Smoothed Analysis, Theoretical Computer Science