{"id":157475,"date":"2009-04-02T00:00:00","date_gmt":"2009-04-02T00:00:00","guid":{"rendered":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/msr-research-item\/smoothed-analysis-of-multiobjective-optimization\/"},"modified":"2018-10-16T21:57:11","modified_gmt":"2018-10-17T04:57:11","slug":"smoothed-analysis-of-multiobjective-optimization","status":"publish","type":"msr-research-item","link":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/publication\/smoothed-analysis-of-multiobjective-optimization\/","title":{"rendered":"Smoothed Analysis of Multiobjective Optimization"},"content":{"rendered":"<div class=\"asset-content\">\n<p>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 Rene Beier. Moreover, we give polynomial bounds on all finite moments of the number of Pareto-otpimal 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 Vocking.<\/p>\n<\/div>\n<p><!-- .asset-content --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>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 Rene Beier. Moreover, we give polynomial bounds on all finite moments of the number of Pareto-otpimal solutions, which yields the 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