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Author Brunsch, Tobias ♦ Rglin, Heiko
Source ACM Digital Library
Content type Text
Publisher Association for Computing Machinery (ACM)
File Format PDF
Copyright Year ©2015
Language English
Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Subject Keyword Multiobjective optimization ♦ Smoothed analysis
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 $\textit{d}$ linear and one arbitrary objective function are to be optimized over a set $\textit{S}$ ⊆ {0, $1}^{n}$ of feasible solutions. We improve the previously best known bound for the smoothed number of Pareto-optimal solutions to $O(n^{2d}$ $&phis;^{d}),$ where &phis; denotes the perturbation parameter. Additionally, we show that for any constant $\textit{c}$ the $\textit{c}th$ moment of the smoothed number of Pareto-optimal solutions is bounded by $O((n^{2d}$ $&phis;^{d})^{c}).$ 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.
ISSN 00045411
Age Range 18 to 22 years ♦ above 22 year
Educational Use Research
Education Level UG and PG
Learning Resource Type Article
Publisher Date 2015-03-02
Publisher Place New York
e-ISSN 1557735X
Journal Journal of the ACM (JACM)
Volume Number 62
Issue Number 1
Page Count 58
Starting Page 1
Ending Page 58


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Source: ACM Digital Library