research-article

A hybridization between memetic algorithm and semidefinite relaxation for the max-cut problem

Authors:

Victor LiAuthors Info & Claims

GECCO '12: Proceedings of the 14th annual conference on Genetic and evolutionary computation

Pages 425 - 432

https://doi.org/10.1145/2330163.2330224

Published: 07 July 2012 Publication History

Abstract

The Max-Cut problem is a classical NP-hard combinatorial optimization problem. It consists of dividing the vertices of a weighted graph into two subsets, such that the sum of the weights of the edges connecting the two subsets is maximized. Although semidefinite relaxation algorithms for Max-Cut have been proved to be of high quality and offer performance guarantees, in practice, metaheuristic algorithms are still the first option to solve large Max-Cut instances. In this paper, we present the first effort at combining semidefinite programming (SDP) with metaheuristic algorithm (Memetic Algorithm) to solve the Max-Cut problem. Based on the solution of semidefinite relaxation, we use Goemans-Williamson Algorithm to seed high quality solutions to the initial population for the memetic algorithm. Experimental results on well-known benchmark problems show that our new hybrid algorithm is capable of obtaining better solutions in the initial population generation stage than previous algorithms, and the overall performance of our algorithm is better than one of the best existing algorithms. Besides, new best solutions for 14 benchmark problems were found by our algorithm.

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Cited By

Choi HKim JMoon BArnold D(2014)A hybrid incremental genetic algorithm for subgraph isomorphism problemProceedings of the 2014 Annual Conference on Genetic and Evolutionary Computation10.1145/2576768.2598382(445-452)Online publication date: 12-Jul-2014
https://dl.acm.org/doi/10.1145/2576768.2598382
Yun HHa MMcKay R(2014)VLR: A Memory-Based Optimization HeuristicParallel Problem Solving from Nature – PPSN XIII10.1007/978-3-319-10762-2_15(151-160)Online publication date: 2014
https://doi.org/10.1007/978-3-319-10762-2_15

Index Terms

A hybridization between memetic algorithm and semidefinite relaxation for the max-cut problem
1. Computing methodologies
  1. Artificial intelligence
    1. Search methodologies
      1. Heuristic function construction

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cover image ACM Conferences

GECCO '12: Proceedings of the 14th annual conference on Genetic and evolutionary computation

July 2012

1396 pages

ISBN:9781450311779

DOI:10.1145/2330163

Editor:
Terence Soule
University of Idaho, USA
,
General Chair:
Jason H. Moore
Dartmouth College, USA

Copyright © 2012 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Published: 07 July 2012

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GECCO '12: Genetic and Evolutionary Computation Conference

July 7 - 11, 2012

Pennsylvania, Philadelphia, USA

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Cited By

Choi HKim JMoon BArnold D(2014)A hybrid incremental genetic algorithm for subgraph isomorphism problemProceedings of the 2014 Annual Conference on Genetic and Evolutionary Computation10.1145/2576768.2598382(445-452)Online publication date: 12-Jul-2014
https://dl.acm.org/doi/10.1145/2576768.2598382
Yun HHa MMcKay R(2014)VLR: A Memory-Based Optimization HeuristicParallel Problem Solving from Nature – PPSN XIII10.1007/978-3-319-10762-2_15(151-160)Online publication date: 2014
https://doi.org/10.1007/978-3-319-10762-2_15

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