Abstract
In this work we present a greedy randomized adaptive search procedure (GRASP)-based strategy for the set covering problem. The goal of this problem is to find a subset of columns from a zero-one matrix in order to cover all the rows with the minimal possible cost. The GRASP is a technique that through a sequential and finite number of steps constructs a solution using a set of simple randomized rules. Additionally, we also propose an iterated local search and reward/penalty procedures in order to improve the solutions found by the GRASP. Our approach has been tested using the well-known 65 non-unicost SCP benchmark instances from OR-library showing promising results.
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References
Balas E, Carrera MC (1996) A dynamic subgradient-based branch-and-bound procedure for set covering. Oper Res 44(6):875–890
Bartholdi JJ III (1981) A guaranteed-accuracy round-off algorithm for cyclic scheduling and set covering. Oper Res 29(3):501–510
Bautista J, Pereira J (2007) A grasp algorithm to solve the unicost set covering problem. Comput Oper Res 34(10):3162–3173
Beasley JE (1987) An algorithm for set covering problem. Eur J Oper Res 31(1):85–93
Beasley JE, Chu PC (1996) A genetic algorithm for the set covering problem. Eur J Oper Res 94(2):392–404
Bramel J, Simchi-Levi D (1997) On the effectiveness of set covering formulations for the vehicle routing problem with time windows. Oper Res 45(2):295–301
Brusco M, Jacobs L, Thompson G (1999) A morphing procedure to supplement a simulated annealing heuristic for cost- and coverage-correlated set-covering problems. Ann Oper Res 86:611–627
Chvatal V (1979) A greedy heuristic for the set-covering problem. Math Oper Res 4(3):233–235
Crawford B, Soto R, Cuesta R, Paredes F (2014) Application of the artificial bee colony algorithm for solving the set covering problem. Sci World J 2014:1–8
Crawford B, Soto R, Peña C, Palma W, Johnson F, Paredes F (2015) Solving the set covering problem with a shuffled frog leaping algorithm. In: Asian conference on intelligent information and database systems. Springer, pp 41–50
Crawford B, Soto R, Riquelme-Leiva M, Peña C, Torres-Rojas C, Johnson F, Paredes F (2015) Modified binary firefly algorithms with different transfer functions for solving set covering problems. In: Software engineering in intelligent systems. Springer, pp 307–315
Crawford B, Soto R, Córdova J, Olguín E (2016) A nature inspired intelligent water drop algorithm and its application for solving the set covering problem. In: Artificial intelligence perspectives in intelligent systems. Springer, pp 437–447
Fisher ML, Kedia P (1990) Optimal solution of set covering/partitioning problems using dual heuristics. Manage Sci 36(6):674–688
García J, Crawford B, Soto R, García P (2017) A multi dynamic binary black hole algorithm applied to set covering problem. In: International conference on harmony search algorithm. Springer, pp 42–51
García J, Crawford B, Soto R, Astorga G (2019) A clustering algorithm applied to the binarization of swarm intelligence continuous metaheuristics. Swarm Evol Comput 44:646–664
Garey MR, Johnson DS (1979) Computers and intractability: a guide to the theory of NP-completeness. Freeman, San Francisco
Lan G, DePuy GW (2006) 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
Lan G, DePuy GW, Whitehouse GE (2007) An effective and simple heuristic for the set covering problem. Eur J Oper Res 176(3):1387–1403
Lu Y, Vasko FJ (2015) An or practitioner’s solution approach for the set covering problem. Int J Appl Metaheuristic Comput (IJAMC) 6(4):1–13
Munagala K, Babu S, Motwani R, Widom J, Thomas E (2005) The pipelined set cover problem. In: ICDT, vol 5. Springer, pp 83–98
Nemenyi P (1963) Distribution-free multiple comparisons. Unpublished Ph.D. dissertation, Princeton University, New Jersey, 73 pp
Pessoa LS, Resende MG, Ribeiro CC (2013) A hybrid lagrangean heuristic with grasp and path-relinking for set k-covering. Comput Oper Res 40(12):3132–3146
Resende MG (1998) Computing approximate solutions of the maximum covering problem with grasp. J Heuristics 4(2):161–177
Resende MG, Ribeiro CC (2010) Greedy randomized adaptive search procedures: advances, hybridizations, and applications. In: Handbook of metaheuristics. Springer, pp 283–319
Resende MG, Martí R, Gallego M, Duarte A (2010) Grasp and path relinking for the max–min diversity problem. Comput Oper Res 37(3):498–508
Solar M, Parada V, Urrutia R (2002) A parallel genetic algorithm to solve the set-covering problem. Comput Oper Res 29(9):1221–1235
Soto R, Crawford B, Olivares R, Barraza J, Figueroa I, Johnson F, Paredes F, Olguín E (2017) Solving the non-unicost set covering problem by using cuckoo search and black hole optimization. Nat Comput 16(2):213–229
Umetani S (2017) Exploiting variable associations to configure efficient local search algorithms in large-scale binary integer programs. Eur J Oper Res 263(1):72–81
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This work is supported by the Fondecyt Project 1160224.
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Reyes, V., Araya, I. A GRASP-based scheme for the set covering problem. Oper Res Int J 21, 2391–2408 (2021). https://doi.org/10.1007/s12351-019-00514-z
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DOI: https://doi.org/10.1007/s12351-019-00514-z