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

M.G.C. Resende(mgcr***at***research.att.com)
R.F. Toso(rtoso***at***cs.rutgers.edu)
J.F. Gonçalves(jfgoncal***at***fep.up.pt)
R.M.A. Silva(rmas***at***dcc.ufla.br)

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 A405 and A729 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.

Category 1: Combinatorial Optimization

Category 2: Combinatorial Optimization (Meta Heuristics )

Category 3: Optimization Software and Modeling Systems (Parallel Algorithms )

Citation: AT&T Labs Research Technical Report, Florham Park, New Jersey, Oct. 2010

Download: [PDF]

Entry Submitted: 11/12/2010
Entry Accepted: 11/12/2010
Entry Last Modified: 11/12/2010

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