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A hybrid heuristic for the set covering problem

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Abstract

In this paper, we present a hybrid approach combining an artificial bee colony (ABC) algorithm with a local search to solve the non-unicost Set Covering Problem (SCP). Given a 0–1 matrix where each column is associated with a non-negative cost. A 1 at the jth column of ith row of this matrix indicates that row i is covered by column j, whereas, a 0 indicates that it is not. The objective of the SCP is to find a subset of columns with minimum cost such that each row of the matrix is covered by at least one column. The ABC algorithm is a recent metaheuristic technique based on the intelligent foraging behavior of honey bee swarm. Computational results show that our ABC algorithm is competitive in terms of solution quality with other metaheuristic approaches for the SCP problem.

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References

  • Aickelin U (2002) An indirect genetic algorithm for set covering problems. J Oper Res Soc 53:1118–1126

    Article  Google Scholar 

  • Balas E, Carrera M (1996) A dynamic subgradient-based branch-and-bound procedure for set covering. Oper Res 44:875–890

    Article  Google Scholar 

  • Basturk B, Karaboga D (2006) An artificial bee colony (ABC) algorithm for numeric function optimization. In: Proceeding of the IEEE swarm intelligence symposium, Indianapolis, 12–14 May

  • Beasley JE (1987) An algorithm for set covering problem. Eur J Oper Res 31:85–93

    Article  Google Scholar 

  • Beasley JE (1990) A Lagrangian heuristic for set covering problems. Naval Res Logist 37:151–164

    Article  Google Scholar 

  • Beasley JE, Chu PC (1996) A genetic algorithm for the set covering problem. Eur J Oper Res 94:392–404

    Article  Google Scholar 

  • Beasley JE, JØrnsten K (1992) Enhancing an algorithm for set covering problems. Eur J Oper Res 58:293–300

    Article  Google Scholar 

  • Boros E, Hammer PL, Ibaraki T, Kogan A (1997) Logical analysis of numerical data. Math Program 79(1–3):163–190

    Google Scholar 

  • Brusco MJ, Jacobs LW, Thompson GM (1999) A morphing procedure to supplement a simulated annealing heuristic for cost- and coverage-correlated set-covering problems. Ann Oper Res 86:611–627

    Article  Google Scholar 

  • Caprara A, Fischetti M, Toth P (1999) A heuristic method for the set covering problem. Oper Res 47(5):730–743

    Article  Google Scholar 

  • Caprara A, Toth P, Fischetti M (2000) Algorithms for the set covering problem. Ann Oper Res 98:353–371

    Article  Google Scholar 

  • Caserata M (2007) Tabu search-based metaheuristic algorithm for large-scale set covering problems. In: Doerner KF et al (eds) Metaheuristics: progress in complex systems optimization. Springer, Berlin, pp 43–63

    Google Scholar 

  • Ceria S, Nobili P, Sassano A (1998a) A Lagrangian-based heuristic for large-scale set covering problems. Math Program 81(2):215–228

    Article  Google Scholar 

  • Ceria S, Nobili P, Sassano A (1998b) Set covering problem. Annotated bibliographies in combinatorial optimization. Wiley, New York, pp 415–428

    Google Scholar 

  • Fisher ML, Kedia P (1990) Optimal solution of set covering/partitioning problems using dual heuristics. Manag Sci 36:674–688

    Article  Google Scholar 

  • Fisher ML, Rosenwein MB (1989) An interactive optimization system for bulk-cargo ship scheduling. Naval Res Logist 36:27–42

    Article  Google Scholar 

  • Foster BA, Ryan DM (1976) An integer programming approach to the vehicle scheduling problem. Oper Res Q 27:367–384

    Article  Google Scholar 

  • Garey MR, Johnson DS (1979) Computers and intractability: a guide to the theory of NP-completeness. Freeman, San Francisco

    Google Scholar 

  • Haouari M, Chaouachi JS (2002) A probabilistic greedy search algorithm for combinatorial optimization with application to the set covering problem. J Oper Res Soc 53:792–799

    Article  Google Scholar 

  • Karaboga D (2005) An idea based on honey bee swarm for numerical optimization. Technical Report TR06. Computer Engineering Department, Erciyes University, Turkey

    Google Scholar 

  • Karaboga D, Akay B (2009) A survey: algorithms simulating bee swarm intelligence. Artif Intell Rev 31:61–85

    Article  Google Scholar 

  • Karaboga D, Basturk B (2007a) A powerful and efficient algorithm for numeric function optimization: artificial bee colony (ABC) algorithm. J Glob Optim 39:459–471

    Article  Google Scholar 

  • Karaboga D, Basturk B (2007b) Artificial bee colony (ABC) optimization algorithm for solving constrained optimization problems. Lecture notes in Artificial Intelligence, vol 4529. Springer, Berlin, pp 789–798

    Google Scholar 

  • Karaboga D, Basturk B (2008) On the performance of artificial bee colony (ABC) algorithm. Appl Soft Comput 8:687–697

    Article  Google Scholar 

  • Lan G, Depuy GW, Whitehouse GE (2007) An effective and simple heuristic for the set covering problem. Eur J Oper Res 176:1387–1403

    Article  Google Scholar 

  • Lessing L, Dumitrescu I, Stützle T (2004) A comparison between ACO algorithms for the set covering problem. In: Proceedings of ANTS 2004, Lecture Notes in Computer Science, vol 3172, pp 1–12

  • Ren Z, Feng Z, Ke L, Chang H (2008) A fast and efficient ant colony optimization approach for the set covering problem. In: Proceedings of the 2008 IEEE congress on evolutionary computation (CEC 2008). IEEE Press, pp 1839–1844

  • Ren ZG, Feng ZR, Ke LJ, Zhang ZJ (2010) New ideas for applying ant colony optimization to the set covering problem. Comput Ind Eng 58:774–784

    Article  Google Scholar 

  • Singh A (2009) An artificial bee colony (ABC) algorithm for the leaf-constrained minimum spanning tree problem. Appl Soft Comput 9(2):625–631

    Article  Google Scholar 

  • Smith BM (1988) Impacs–a bus crew scheduling system using integer programming. Math Program 42(1–3):181–187

    Article  Google Scholar 

  • Toregas C, Swain R, Revelle C, Bergman L (1971) The location of emergency service facilities. Oper Res 19:1363–1373

    Article  Google Scholar 

  • Utemani S, Yagiura M (2007) Relaxation heuristics for the set covering problem. J Oper Res Soc Jpn 50:350–375

    Google Scholar 

  • Vasko FJ, Wolf FE, Stott KL (1989) A set covering approach to metallurgical grade assignment. Eur J Oper Res 38:27–34

    Article  Google Scholar 

  • Yagiura M, Kishida M, Ibaraki T (2006) A 3-flip neighborhood local search for the set covering problem. Eur J Oper Res 172:472–499

    Article  Google Scholar 

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Acknowledgments

We thank two anonymous reviewers for their valuable comments and suggestions that helped in improving the content of this paper.

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  1. Department of Computer and Information Sciences, University of Hyderabad, Hyderabad, 500046, Andhra Pradesh, India

    Shyam Sundar & Alok Singh

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  1. Shyam Sundar
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  2. Alok Singh
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Correspondence to Alok Singh.

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Sundar, S., Singh, A. A hybrid heuristic for the set covering problem. Oper Res Int J 12, 345–365 (2012). https://doi.org/10.1007/s12351-010-0086-y

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