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Biased random-key genetic algorithms for combinatorial optimization

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Abstract

Random-key genetic algorithms were introduced by Bean (ORSA J. Comput. 6:154–160, 1994) for solving sequencing problems in combinatorial optimization. Since then, they have been extended to handle a wide class of combinatorial optimization problems. This paper presents a tutorial on the implementation and use of biased random-key genetic algorithms for solving combinatorial optimization problems. Biased random-key genetic algorithms are a variant of random-key genetic algorithms, where one of the parents used for mating is biased to be of higher fitness than the other parent. After introducing the basics of biased random-key genetic algorithms, the paper discusses in some detail implementation issues, illustrating the ease in which sequential and parallel heuristics based on biased random-key genetic algorithms can be developed. A survey of applications that have recently appeared in the literature is also given.

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References

  • Aarts, E.H.L., Van Laarhoven, P.J.M., Lenstra, J.K., Ulder, N.L.J.: A computational study of local search algorithms for job shop scheduling. INFORMS J. Comput. 6, 118–125 (1994)

    Article  MATH  Google Scholar 

  • Aiex, R.M., Binato, S., Resende, M.G.C.: Parallel GRASP with path-relinking for job shop scheduling. Parallel Comput. 29, 393–430 (2003)

    Article  MathSciNet  Google Scholar 

  • Alvarez-Valdes, R., Parreño, F., Tamarit, J.M.: A GRASP algorithm for constrained two-dimensional non-guillotine cutting problems. J. Oper. Res. Soc. 56, 414–425 (2005)

    Article  MATH  Google Scholar 

  • Alvarez-Valdes, R., Parreño, F., Tamarit, J.M.: A tabu search algorithm for a two-dimensional non-guillotine cutting problem. Eur. J. Oper. Res. 183, 1167–1182 (2007)

    Article  MATH  Google Scholar 

  • Andrade, D.V., Buriol, L.S., Resende, M.G.C., Thorup, M.: Survivable composite-link IP network design with OSPF routing. In: Proceedings of The Eighth INFORMS Telecommunications Conference (2006)

  • Baar, T., Brucker, P., Knust, S.: Tabu-search algorithms and lower bounds for the resource-constrained project scheduling problem. In: Voss, S., Martello, S., Osman, I., Roucairol, C. (eds.) Meta-Heurisitics: Advances and Trends in Local Search Paradigms for Optimization, pp. 1–8. Kluwer, Dordrecht (1998)

    Google Scholar 

  • Bean, J.C.: Genetic algorithms and random keys for sequencing and optimization. ORSA J. Comput. 6, 154–160 (1994)

    MATH  Google Scholar 

  • Beasley, J.E.: An exact two-dimensional non-guillotine cutting tree search procedure. Oper. Res., 49–64 (1985)

  • Beasley, J.E.: A population heuristic for constrained two-dimensional non-guillotine cutting. Eur. J. Oper. Res. 156, 601–627 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  • Binato, S., Hery, W.J., Loewenstern, D.M., Resende, M.G.C.: A GRASP for job shop scheduling. In: Ribeiro, C.C., Hansen, P. (eds.) Essays and Surveys in Metaheuristics. Kluwer Academic, Dordrecht (2002)

    Google Scholar 

  • Bouleimen, K., Lecocq, H.: A new efficient simulated annealing algorithm for the resource-constrained project scheduling problem and its multiple mode version. Eur. J. Oper. Res. 149, 268–281 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  • Breslau, L., Diakonikolas, I., Duffield, N., Gu, Y., Hajiaghayi, M., Johnson, D.S., Karloff, H., Resende, M.G.C., Sen, S.: Node placement for path disjoint monitoring. Technical report, AT&T Labs Research, Shannon Laboratory, Florham Park, NJ 07932, USA (2009)

  • Buriol, L.S., Resende, M.G.C., Ribeiro, C.C., Thorup, M.: A hybrid genetic algorithm for the weight setting problem in OSPF/IS-IS routing. Networks 46, 36–56 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  • Buriol, L.S., Resende, M.G.C., Thorup, M.: Survivable IP network design with OSPF routing. Networks 49, 51–64 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  • Buriol, L.S., Hirsch, M.J., Pardalos, P.M., Querido, T., Resende, M.G.C., Ritt, M.: A hybrid genetic algorithm for road congestion minimization. In: Proceedings of the XLI Symposium of the Brazilian Operational Research Society (XLI SBPO), Porto Seguro, Brazil (2009)

  • Chandrasekharan, M.P., Rajagopalan, R.: ZODIAC—an algorithm for concurrent formation of part-families and machine-cells. Int. J. Prod. Res. 25, 835–850 (1987)

    Article  MATH  Google Scholar 

  • Cheng, C.H., Gupta, Y.P., Lee, W.H., Wong, K.F.: A TSP-based heuristic for forming machine groups and part families. Int. J. Prod. Res. 36, 1325–1337 (1998)

    Article  MATH  Google Scholar 

  • Christofides, N., Whitlock, C.: An algorithm for two-dimensional cutting problems. Operations Research, 30–44 (1977)

  • Debels, D., Vanhoucke, M.: A decomposition-based heuristic for the resource-constrained project scheduling problem. Technical report, Ghent University, Faculty of Economics and Business Administration, Belgium (2005)

  • Debels, D., De Reyck, B., Leus, R., Vanhoucke, M.: A hybrid scatter search/electromagnetism meta-heuristic for project scheduling. Eur. J. Oper. Res. 169, 638–653 (2006)

    Article  MATH  Google Scholar 

  • Della Croce, F., Tadei, R., Volta, G.: A genetic algorithm for the job shop problem. Comput. Oper. Res. 22, 15–24 (1995)

    Article  MATH  Google Scholar 

  • Dimopoulos, C., Mort, N.: A hierarchical clustering methodology based on genetic programming for the solution of simple cell-formation problems. Int. J. Prod. Res. 39, 1–19 (2001)

    Article  MATH  Google Scholar 

  • Dorndorf, U., Pesch, E.: Evolution based learning in a job shop scheduling environment. Comput. Oper. Res. 22, 25–40 (1995)

    Article  MATH  Google Scholar 

  • Ericsson, M., Resende, M.G.C., Pardalos, P.M.: A genetic algorithm for the weight setting problem in OSPF routing. J. Comb. Optim. 6, 299–333 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  • Fekete, S., Schepers, J.: A new exact algorithm for general orthogonal d-dimensional knapsack problems. In: Algorithms, ESA’97, pp. 144–156. Springer, Berlin (1997)

    Google Scholar 

  • Fekete, S.P., Schepers, J.: A combinatorial characterization of higher-dimensional orthogonal packing. Mathematics of Operations Research, 353–368 (2004)

  • Feo, T.A., Resende, M.G.C.: A probabilistic heuristic for a computationally difficult set covering problem. Oper. Res. Lett. 8, 67–71 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  • Feo, T.A., Resende, M.G.C.: Greedy randomized adaptive search procedures. J. Glob. Optim. 6, 109–133 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  • Fisher, H., Thompson, G.L.: Probabilistic learning combinations of local job-shop scheduling rules. In: Muth, J.F., Thompson, G.L. (eds.) Industrial Scheduling, pp. 225–251. Prentice-Hall, Englewood Cliffs (1963)

    Google Scholar 

  • Fleszar, K., Hindi, K.S.: Solving the resource-constrained project scheduling problem by a variable neighbourhood search. Eur. J. Oper. Res. 155, 402–413 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  • Fontes, D., Hadjiconstantinou, E., Christofides, N.: Upper bounds for single source uncapacitated minimum concave-cost network flow problems. Networks 41, 221–228 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  • Fontes, D.B.M.M., Gonçalves, J.F.: Heuristic solutions for general concave minimum cost network flow problems. Networks 50, 67–76 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  • Fontes, D.B.M.M., Hadjiconstantinou, E., Christofides, N.: A dynamic programming approach for solving single-source uncapacitated concave minimum cost network flow problems. Eur. J. Oper. Res. 174, 1205–1219 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  • Fortz, B., Thorup, M.: Increasing internet capacity using local search. Comput. Optim. Appl. 29, 13–48 (2004). Preliminary short version of this paper published as “Internet Traffic Engineering by Optimizing OSPF weights,” in Proc. IEEE INFOCOM 2000, The Conference on Computer Communications

    Article  MathSciNet  MATH  Google Scholar 

  • Glover, F., Kochenberger, G. (eds.) Handbook of Metaheuristics. Kluwer Academic, Dordrecht (2003)

    MATH  Google Scholar 

  • Goldberg, D.E.: Genetic Algorithms in Search, Optimization, and Machine Learning. Addison-Wesley, Reading (1989)

    MATH  Google Scholar 

  • Gonçalves, J.F.: A hybrid genetic algorithm-heuristic for a two-dimensional orthogonal packing problem. Eur. J. Oper. Res. 183, 1212–1229 (2007)

    Article  MATH  Google Scholar 

  • Gonçalves, J.F., Almeida, J.: A hybrid genetic algorithm for assembly line balancing. J. Heuristics 8, 629–642 (2002)

    Article  Google Scholar 

  • Gonçalves, J.F., Beirão, N.C.: Um algoritmo genético baseado em chaves aleatórias para sequenciamento de operações. Rev. Desenvolv. Investig. Oper. 19, 123–137 (1999)

    Google Scholar 

  • Gonçalves, J.F., Resende, M.G.C.: An evolutionary algorithm for manufacturing cell formation. Comput. Ind. Eng. 47, 247–273 (2004)

    Article  Google Scholar 

  • Gonçalves, J.F., Resende, M.G.C.: A parallel multi-population genetic algorithm for a constrained two-dimensional orthogonal packing problem. J. Comb. Optim. (2010). doi:10.1007/s10878-009-9282-1

  • Gonçalves, J.F., Mendes, J.J.M., Resende, M.G.C.: A hybrid genetic algorithm for the job shop scheduling problem. Eur. J. Oper. Res. 167, 77–95 (2005)

    Article  MATH  Google Scholar 

  • Gonçalves, J.F., Mendes, J.J.M., Resende, M.G.C.: A genetic algorithm for the resource constrained multi-project scheduling problem. Eur. J. Oper. Res. 189, 1171–1190 (2008)

    Article  MATH  Google Scholar 

  • Gonçalves, J.F., Resende, M.G.C., Mendes, J.J.M.: A biased random-key genetic algorithm with forward-backward improvement for the resource constrained project scheduling problem. Technical report, AT&T Labs Research J. Heuristics (2009a, to appear)

  • Gonçalves, J.F., Resende, M.G.C., Silva, R.M.A.: Biased versus unbiased random key genetic algorithms: a experimental analysis. Technical report, AT&T Labs Research (2009b)

  • Hadjiconstantinou, E., Christofides, N.: An exact algorithm for general, orthogonal, two-dimensional knapsack problems. Eur. J. Oper. Res. 83, 39–56 (1995)

    Article  MATH  Google Scholar 

  • Hadjiconstantinou, E., Iori, M.: A hybrid genetic algorithm for the two-dimensional knapsack problem. Eur. J. Oper. Res. 183, 1150–1166 (2007a)

    Article  MathSciNet  MATH  Google Scholar 

  • Hadjiconstantinou, E., Iori, M.: A hybrid genetic algorithm for the two-dimensional single large object placement problem. Eur. J. Oper. Res. 183, 1150–1166 (2007b)

    Article  MathSciNet  MATH  Google Scholar 

  • Hart, J.P., Shogan, A.W.: Semi-greedy heuristics: an empirical study. Oper. Res. Lett. 6, 107–114 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  • Hartmann, S.: A self-adapting genetic algorithm for project scheduling under resource constraints. Nav. Res. Logist. 49, 433–448 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  • Hartmann, S.: A competitive genetic algorithm for resource-constrained project scheduling. Nav. Res. Logist. 45, 279–302 (1998)

    Article  MathSciNet  Google Scholar 

  • Hifi, M.: Exact algorithms for the guillotine strip cutting/packing problem. Comput. Oper. Res. 25, 925–940 (1998)

    Article  MATH  Google Scholar 

  • Hoffmann, T.R.: Assembly line balancing: a set of challenging problems. Int. J. Prod. Res. 28, 1807–1815 (1990)

    Article  Google Scholar 

  • Hoffmann, T.R.: EUREKA: a hybrid system for assembly line balancing. Manag. Sci. 38, 39–47 (1992)

    Article  MATH  Google Scholar 

  • Holland, J.H.: Adaptation in Natural and Artificial Systems. MIT Press, Cambridge (1975)

    Google Scholar 

  • Hopper, E., Turton, B.C.H.: An empirical investigation of meta-heuristic and heuristic algorithms for a 2D packing problem. Eur. J. Oper. Res. 128, 34–57 (2001)

    Article  MATH  Google Scholar 

  • Jakobs, S.: On genetic algorithms for the packing of polygons. Eur. J. Oper. Res. 88, 165–181 (1996)

    Article  MATH  Google Scholar 

  • Kochetov, Y., Stolyar, A.: Evolutionary local search with variable neighborhood for the resource constrained project scheduling problem. In: Proceedings of the 3rd International Workshop of Computer Science and Information Technologies (2003)

  • Kolisch, R.: Project Scheduling Under Resource Constraints: Efficient Heuristics for Several Problem Classes. Physica-Verlag, Heidelburg (1995)

    Google Scholar 

  • Kolisch, R.: Serial and parallel resource-constrained project scheduling methods revisited: theory and computation. Eur. J. Oper. Res. 90, 320–333 (1996a)

    Article  MATH  Google Scholar 

  • Kolisch, R.: Efficient priority rules for the resource-constrained project scheduling problem. J. Oper. Manag. 14, 179–192 (1996b)

    Article  Google Scholar 

  • Kolisch, R., Drexl, A.: Adaptative search for solving hard project scheduling problems. Nav. Res. Logist. 43, 23–40 (1996)

    Article  MATH  Google Scholar 

  • Kolisch, R., Sprecher, A., Drexl, A.: Characterization and generation of a general class of resource-constrained project scheduling problems. Manag. Sci. 41, 1693–1703 (1995)

    Article  MATH  Google Scholar 

  • Lai, K.K., Chan, W.M.: An evolutionary algorithm for the rectangular cutting stock problem. Int. J. Ind. Eng. 4, 130–139 (1997)

    Google Scholar 

  • Lawrence, S.: Resource constrained project scheduling: an experimental investigation of heuristic scheduling techniques. Technical report, Graduate School of Industrial Administration, Carnegie Mellon University, Pittsburgh, PA (1984)

  • Leon, V.J., Ramamoorthy, B.: Strength and adaptability of problem-space based neighborhoods for resource constrained scheduling. OR Spektrum 17, 173–182 (1995)

    Article  MATH  Google Scholar 

  • Leung, T.W., Chan, C.K., Troutt, M.D.: Application of a mixed simulated annealing-genetic algorithm heuristic for the two-dimensional orthogonal packing problem. Eur. J. Oper. Res. 145, 530–542 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  • Li, G.: Single machine earliness and tardiness scheduling. Eur. J. Oper. Res. 96, 546–558 (1997)

    Article  MATH  Google Scholar 

  • Mendes, J.J.M., Gonçalves, J.F., Resende, M.G.C.: A random key based genetic algorithm for the resource constrained project scheduling problem. Comput. Oper. Res. 36, 92–109 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  • Möhring, R.H., Schulz, A.S., Stork, F., Uetz, M.: Solving project scheduling problems by minimum cut computations. Manag. Sci. 49, 330–350 (2003)

    Article  Google Scholar 

  • Nonobe, K., Ibaraki, T.: Formulation and tabu search algorithm for the resource constrained project scheduling problem. In: Ribeiro, C.C., Hansen, P. (eds.) Essays and Surveys in Metaheuristics, pp. 557–588. Kluwer Academic, Dordrecht (2002)

    Google Scholar 

  • Noronha, T.F., Ribeiro, C.C.: Routing and wavelength assign by partition coloring. Eur. J. Oper. Res. 171, 797–810 (2006)

    Article  MATH  Google Scholar 

  • Noronha, T.F., Resende, M.G.C., Ribeiro, C.C.: A biased random-key genetic algorithm for routing and wavelength assignment. Technical report, AT&T Labs Research, Florham Park, NJ 07932 (2010)

  • Nowicki, E., Smutnicki, C.: A fast taboo search algorithm for the job shop problem. Manag. Sci. 42, 797–813 (1996)

    Article  MATH  Google Scholar 

  • Oliveira, J.F.: Private communication (2004)

  • Onwubolu, G.C., Mutingi, M.: A genetic algorithm approach to cellular manufacturing systems. Comput. Ind. Eng. 39, 125–144 (2001)

    Article  Google Scholar 

  • Palpant, M., Artigues, C., Michelon, P.: LSSPER: solving the resource-constrained project scheduling problem with large neighbourhood search. Ann. Oper. Res. 131, 237–257 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  • Pardalos, P.M., Resende, M.G.C. (eds.) Handbook of Applied Optimization. Oxford University Press, Oxford (2002)

    MATH  Google Scholar 

  • Reis, R., Ritt, M., Buriol, L.S., Resende, M.G.C.: A biased random-key genetic algorithm for OSPF and DEFT routing to minimize network congestion. Technical report, AT&T Labs Research, Florham Park, NJ 07932. Int. Trans. Oper. Res. (2011, to appear)

  • Schirmer, A., Riesenberg, S.: Case-based reasoning and parameterized random sampling for project scheduling. Technical report, University of Kiel, Germany (1998)

  • Scholl, A.: Data of assembly line balancing problems. Technical Report 16/1993, Schriften zur Quantitativen Betriebswirtschaftslehre, TU Darmstadt (1993)

  • Scholl, A., Voß, S.: Simple assembly line balancing—Heuristic approaches. J. Heuristics 2, 217–244 (1997)

    Article  Google Scholar 

  • Skorin-Kapov, N.: Routing and wavelength assignment in optical networks using bin packing based algorithms. Eur. J. Oper. Res. 177, 1167–1179 (2007)

    Article  MATH  Google Scholar 

  • Spears, W.M., DeJong, K.A.: On the virtues of parameterized uniform crossover. In: Proceedings of the Fourth International Conference on Genetic Algorithms, pp. 230–236 (1991)

  • Srinivasan, G.: A clustering algorithm for machine cell formation in group technology using minimum spanning trees. Int. J. Prod. Res. 32, 2149–2158 (1994)

    Article  MATH  Google Scholar 

  • Srinivasan, G., Narendran, T.T.: GRAFICS—a nonhierarchical clustering algorithm for group technology. Int. J. Prod. Res. 29, 463–478 (1991)

    Article  Google Scholar 

  • Storer, R.H., Wu, S.D., Park, I.: Genetic algorithms in problem space for sequencing problems. In: Proceedings of a Joint US-German Conference on Operations Research in Production Planning and Control, pp. 584–597 (1992)

  • Talbot, F.B., Patterson, J.H., Gehrlein, W.V.: A comparative evaluation of heuristic line balancing techniques. Manag. Sci. 32, 430–454 (1986)

    Article  Google Scholar 

  • Tormos, P., Lova, A.: Integrating heuristics for resource constrained project scheduling: one step forward. Technical report, Department of Statistics and Operations Research, Universidad Politecnica de Valencia (2003)

  • Valente, J.M.S.: Heuristics for the single machine scheduling problem with early and quadratic tardy penalties. Eur. J. Ind. Eng. 1, 431–448 (2007)

    Article  Google Scholar 

  • Valente, J.M.S.: Beam search heuristics for the single machine scheduling problem with linear earliness and quadratic tardiness costs. Asia-Pac. J. Oper. Res. 26, 319–339 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  • Valente, J.M.S., Gonçalves, J.F.: A genetic algorithm approach for the single machine scheduling problem with linear earliness and quadratic tardiness penalties. Comput. Oper. Res. 35, 3696–3713 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  • Valente, J.M.S., Gonçalves, J.F., Alves, R.A.F.S.: A hybrid genetic algorithm for the early/tardy scheduling problem. Asia-Pac. J. Oper. Res. 23, 393–405 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  • Valls, V., Ballestin, J., Quintanilla, M.S.: A hybrid genetic algorithm for the RCPSP. Technical report, Department of Statistics and Operations Research, University of Valencia (2003)

  • Valls, V., Ballestin, F., Quintanilla, M.S.: A population-based approach to the resource-constrained project scheduling problem. Ann. Oper. Res. 131, 305–324 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  • Valls, V., Ballestin, F., Quintanilla, M.S.: Justification and RCPSP: a technique that pays. Eur. J. Oper. Res. 165, 375–386 (2005)

    Article  MATH  Google Scholar 

  • Wang, L., Zheng, D.Z.: An effective hybrid optimization strategy for job-shop scheduling problems. Comput. Oper. Res. 28, 585–596 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  • Wang, P.Y.: Two algorithms for constrained two-dimensional cutting stock problems. Oper. Res., 573–586 (1983)

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Authors and Affiliations

  1. LIAAD, Faculdade de Economia do Porto, Universidade do Porto, Porto, Portugal

    José Fernando Gonçalves

  2. Algorithms & Optimization Research Department, AT&T Labs Research, Florham Park, NJ, USA

    Mauricio G. C. Resende

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  1. José Fernando Gonçalves
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  2. Mauricio G. C. Resende
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Correspondence to Mauricio G. C. Resende.

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This research was partially supported by Fundação para a Ciência e Tecnologia (FCT) project PTDC/GES/72244/2006. AT&T Labs Research Technical Report.

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Gonçalves, J.F., Resende, M.G.C. Biased random-key genetic algorithms for combinatorial optimization. J Heuristics 17, 487–525 (2011). https://doi.org/10.1007/s10732-010-9143-1

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