Abstract
The set covering problem is a classic benchmark that has many real applications such as positioning of communications systems, logical analysis, steel production, vehicle routing, and service allocation in general. In this paper, we present an improved firefly algorithm to the efficient resolution of this problem. The firefly algorithm is a recent metaheuristic based on the flashing characteristics of fireflies that attract each other by using their brightness. We improve this approach by incorporating pre-processing and an heuristic feasibility operator resulting in an interesting solver able to clearly outperform the previously reported results obtained from firefly algorithms.
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Balas, E., Carrera, M.C.: A dynamic subgradient-based branch-and-bound procedure for set covering. Oper. Res. 44(6), 875–890 (1996)
Beasley, J.E., Chu, P.C.: A genetic algorithm for the set covering problem. Eur. J. Oper. Res. 94(2) (1996)
Beasley, J.E.: A Lagrangian heuristic for set covering problems. Naval Res. Logistics 37(1), 151–164 (1990)
Beasley, J.E., Chu, P.C.: A genetic algorithm for the set covering problem. Eur. J. Oper. Res. 94(2), 392–404 (1996)
Brusco, M.J., Jacobs, L.W., Thompson, G.M.: A morphing procedure to supplement a simulated annealing heuristic for cost- and coverage-correlated set-covering problems. Ann. Oper. Res. 86, 611–627 (1999)
Caprara, A., Toth, P., Fischetti, M.: Algorithms for the set covering problem. Ann. Oper. Res. 98, 353–371 (2000)
Caprara, A., Fischetti, M., Toth, P.: A heuristic method for the set covering problem. Oper. Res. 47(5), 730–743 (1999)
Caserta, M.: Tabu search-based metaheuristic algorithm for large-scale set covering
Ceria, S., Nobili, P., Sassano, A.: A Lagrangian-based heuristic for large-scale set covering problems. Math. Program. 81(2), 215–228 (1998)
Chandrasekaran, K., Sishaj, P.S., Padhy, N.P.: Binary real coded firefly algorithm for solving unit commitment problem. Inf. Sci. 249, 67–84 (2013)
Chvatal, V.: A greedy heuristic for the set-covering problem. Math. Oper. Res. 4(3), 233–235 (1979)
Crawford, B., Soto, R., Olivares-Suárez, M., Paredes, F.: A Binary Firefly Algorithm for the Set Covering Problem. In: Silhavy, R., Senkerik, R., Oplatkova, Z.K., Silhavy, P., Prokopova, Z. (eds.) Modern Trends and Techniques in Computer Science. AISC, vol. 285, pp. 65–73. Springer, Heidelberg (2014)
Crawford, B., Castro, C., Monfroy, E., Soto, R., Palma, W., Paredes, F.: Dynamic Selection of Enumeration Strategies for Solving Constraint Satisfaction Problems. Romanian Journal of Information Science and Technology 15(2), 106–128 (2013)
Fisher, M.L., Kedia, P.: Optimal solution of set covering/partitioning problems using dual heuristics. Management Science 36(6) (1990)
Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman & Co., New York (1990)
Lan, G., DePuy, G.W.: On the effectiveness of incorporating randomness and memory into a multi-start metaheuristic with application to the set covering problem. Comput. Ind. Eng. 51(3), 362–374 (2006)
Vasko, F.J., Wolf, F.E.: Optimal selection of ingot sizes via set covering. Oper. Res. 35(3), 346–353 (1987)
Vasko, F.J., Wilson, G.R.: Using a facility location algorithm to solve large set covering problems. Operations Research Letters 3(2), 85–90 (1984)
Yang, X.S.: Nature-Inspired Metaheuristic Algorithms. Luniver Press, UK (2008), Inspired Computing (NaBIC 2009), India, p. 210. IEEE Publications, USA (December 2009)
Yang, X.-S.: Firefly algorithms for multimodal optimization. In: Watanabe, O., Zeugmann, T. (eds.) SAGA 2009. LNCS, vol. 5792, pp. 169–178. Springer, Heidelberg (2009)
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Soto, R., Crawford, B., Vilches, J., Johnson, F., Paredes, F. (2015). Heuristic Feasibility and Preprocessing for a Set Covering Solver Based on Firefly Optimization. In: Silhavy, R., Senkerik, R., Oplatkova, Z., Prokopova, Z., Silhavy, P. (eds) Artificial Intelligence Perspectives and Applications. Advances in Intelligent Systems and Computing, vol 347. Springer, Cham. https://doi.org/10.1007/978-3-319-18476-0_11
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DOI: https://doi.org/10.1007/978-3-319-18476-0_11
Publisher Name: Springer, Cham
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