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Journal of Industrial and Management Optimization (JIMO)
 

The set covering problem revisited: An empirical study of the value of dual information

Pages: 575 - 594, Volume 11, Issue 2, April 2015      doi:10.3934/jimo.2015.11.575

 
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Belma Yelbay - Sabancl University, Manufacturing Systems and Industrial Engineering, Orhanl1-Tuzla, 34956 Istanbul, Turkey (email)
Ş. İlker Birbil - Sabanci University, Manufacturing Systems and Industrial Engineering, Orhanli-Tuzla, 34956 Istanbul, Turkey (email)
Kerem Bülbül - Sabanci University, Manufacturing Systems and Industrial Engineering, Orhanli-Tuzla, 34956 Istanbul, Turkey (email)

Abstract: This paper investigates the role of dual information on the performances of heuristics designed for solving the set covering problem. After solving the linear programming relaxation of the problem, the dual information is used to obtain the two main approaches proposed here: (i) The size of the original problem is reduced and then the resulting model is solved with exact methods. We demonstrate the effectiveness of this approach on a rich set of benchmark instances compiled from the literature. We conclude that set covering problems of various characteristics and sizes may reliably be solved to near optimality without resorting to custom solution methods. (ii) The dual information is embedded into an existing heuristic. This approach is demonstrated on a well-known local search based heuristic that was reported to obtain successful results on the set covering problem. Our results demonstrate that the use of dual information significantly improves the efficacy of the heuristic in terms of both solution time and accuracy.

Keywords:  Heuristics, set covering, primal-dual heuristic, LP relaxation, dual information.
Mathematics Subject Classification:  Primary: 90C27; Secondary: 68T20.

Received: September 2013;      Revised: April 2014;      Available Online: September 2014.

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