A Beam-Search Approach to the Set Covering Problem
In this work we present a beam-search approach applied to the Set Covering Problem. The goal of this problem is to choose a subset of columns of minimal cost covering every row. Beam Search constructs a search tree by using a breadth-first search strategy, however only a fixed number of nodes are kept and the rest are discarded. Even though original beam search has a deterministic nature, our proposal has some elements that makes it stochastic. This approach has been tested with a well-known set of 45 SCP benchmark instances from OR-Library showing promising results.
KeywordsSCP Beam search Branch-and-Bound Greedy
Victor Reyes is supported by grant INF-PUCV 2015, Ricardo Soto is supported by grant CONICYT/FONDECYT/INICIACION/11130459, Broderick Crawford is supported by grant CONICYT/FONDECYT/REGULAR/1140897, and Ignacio Araya is supported by grant CONICYT/FONDECYT/INICIACION/11121366.
- 1.Balas, E., et al.: A class of location, distribution and scheduling problems: modeling and solution methods (1982)Google Scholar
- 9.Michael, R.G., David, S.J.: Computers and intractability: a guide to the theory of np-completeness. San Francisco, p. 1979. Freeman, LA (1979)Google Scholar
- 10.Haouari, M, Chaouachi, J.S.: A probabilistic greedy search algorithm for combinatorial optimisation with application to the set covering problem. J. Oper. Res. Soc. 792–799 (2002)Google Scholar
- 15.Norvig, P.: Paradigms of Artificial Intelligence Programming: Case Studies in Common LISP. Morgan Kaufmann (1992)Google Scholar