An efficient branch-and-cut algorithm for approximately submodular function maximization

Naoya Uematsu, Shunji Umetani, Yoshinobu Kawahara

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

When approaching problems in computer science, we often encounter situations where a subset of a finite set maximizing some utility function needs to be selected. Some of such utility functions are known to be approximately submodular. For the problem of maximizing an approximately submodular function (ASFM problem), a greedy algorithm quickly finds good feasible solutions for many instances while guaranteeing (1-e{-gamma})-approximation ratio for a given submodular ratio gamma. However, we still encounter its applications that ask more accurate or exactly optimal solutions within a reasonable computation time. In this paper, we present an efficient branch-and-cut algorithm for the non-decreasing ASFM problem based on its binary integer programming (BIP) formulation with an exponential number of constraints. To this end, we first derive a BIP formulation of the ASFM problem, and then we develop an improved constraint generation algorithm that starts from a reduced BIP problem with a small subset of constraints and repeats solving the reduced BIP problem while adding a promising set of constraints at each iteration. Moreover, we incorporate it into a branch-and-cut algorithm to attain good upper bounds while solving a smaller number of nodes of a search tree. The computational results for three types of well-known benchmark instances show that our algorithm performs better than the conventional exact algorithms.

Original languageEnglish
Title of host publication2019 IEEE International Conference on Systems, Man and Cybernetics, SMC 2019
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages3160-3167
Number of pages8
ISBN (Electronic)9781728145693
DOIs
Publication statusPublished - Oct 2019
Event2019 IEEE International Conference on Systems, Man and Cybernetics, SMC 2019 - Bari, Italy
Duration: Oct 6 2019Oct 9 2019

Publication series

NameConference Proceedings - IEEE International Conference on Systems, Man and Cybernetics
Volume2019-October
ISSN (Print)1062-922X

Conference

Conference2019 IEEE International Conference on Systems, Man and Cybernetics, SMC 2019
Country/TerritoryItaly
CityBari
Period10/6/1910/9/19

All Science Journal Classification (ASJC) codes

  • Electrical and Electronic Engineering
  • Control and Systems Engineering
  • Human-Computer Interaction

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