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Optimization Letters

, Volume 6, Issue 4, pp 605–619 | Cite as

A biased random-key genetic algorithm for the Steiner triple covering problem

  • Mauricio G. C. Resende
  • Rodrigo F. Toso
  • José Fernando Gonçalves
  • Ricardo M. A. Silva
Original Paper

Abstract

We present a biased random-key genetic algorithm (BRKGA) for finding small covers of computationally difficult set covering problems that arise in computing the 1-width of incidence matrices of Steiner triple systems. Using a parallel implementation of the BRKGA, we compute improved covers for the two largest instances in a standard set of test problems used to evaluate solution procedures for this problem. The new covers for instances A 405 and A 729 have sizes 335 and 617, respectively. On all other smaller instances our algorithm consistently produces covers of optimal size.

Keywords

Steiner triple covering Set covering Genetic algorithm Biased random-key genetic algorithm Random keys Combinatorial optimization Heuristics Metaheuristics 

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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • Mauricio G. C. Resende
    • 1
  • Rodrigo F. Toso
    • 2
  • José Fernando Gonçalves
    • 3
  • Ricardo M. A. Silva
    • 4
  1. 1.Algorithms and Optimization Research DepartmentAT&T Labs ResearchFlorham ParkUSA
  2. 2.Department of Computer ScienceRutgers UniversityPiscatawayUSA
  3. 3.Faculdade de Economia do Porto, NIAADPortoPortugal
  4. 4.Centro de Informática (CIn), Federal University of PernambucoRecifeBrazil

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