Improved Smoothed Analysis of Multiobjective Optimization

Author:

Brunsch Tobias1,Röglin Heiko1

Affiliation:

1. University of Bonn, Bonn, Germany

Abstract

We present several new results about smoothed analysis of multiobjective optimization problems. Motivated by the discrepancy between worst-case analysis and practical experience, this line of research has gained a lot of attention in the last decade. We consider problems in which d linear and one arbitrary objective function are to be optimized over a set S ⊆ {0, 1} n of feasible solutions. We improve the previously best known bound for the smoothed number of Pareto-optimal solutions to O ( n 2 d φ d ), where φ denotes the perturbation parameter. Additionally, we show that for any constant c the c th moment of the smoothed number of Pareto-optimal solutions is bounded by O (( n 2 d φ d ) c ). This improves the previously best known bounds significantly. Furthermore, we address the criticism that the perturbations in smoothed analysis destroy the zero-structure of problems by showing that the smoothed number of Pareto-optimal solutions remains polynomially bounded even for zero-preserving perturbations. This broadens the class of problems captured by smoothed analysis and it has consequences for nonlinear objective functions. One corollary of our result is that the smoothed number of Pareto-optimal solutions is polynomially bounded for polynomial objective functions. Our results also extend to integer optimization problems.

Publisher

Association for Computing Machinery (ACM)

Subject

Artificial Intelligence,Hardware and Architecture,Information Systems,Control and Systems Engineering,Software

Reference22 articles.

1. René Beier. 2004. Probabilistic analysis of discrete optimization problems. Ph.D. dissertation. Universität des Saarlandes. René Beier. 2004. Probabilistic analysis of discrete optimization problems. Ph.D. dissertation. Universität des Saarlandes.

2. The Smoothed Number of Pareto Optimal Solutions in Bicriteria Integer Optimization

3. Random knapsack in expected polynomial time

4. Typical Properties of Winners and Losers [0.2ex] in Discrete Optimization

Cited by 7 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3