Solving a Bi-objective Flowshop Scheduling Problem by Pareto-Ant Colony Optimization

  • Joseph M. Pasia
  • Richard F. Hartl
  • Karl F. Doerner
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4150)


In this paper we investigate the performance of pareto ant colony optimization (PACO) in solving a bi-objective permutation flowshop problem. We hybridize this technique by incorporating path relinking (PR) in four different ways. Several test instances are used to test the effectiveness of the different approaches. Computational results show that hybridizing PACO with PR improves the performance of PACO. The hybrid algorithms also show competitive results compared to other state of the art metaheuristics.


Nondominated Solution Total Tardiness Heuristic Information Target Solution Path Relinking 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Lenstra, J., Kan, A., Brucker, P.: Complexity of machine scheduling problems. Annals of Discrete Mathematics 1, 343–362 (1977)CrossRefGoogle Scholar
  2. 2.
    Du, J., Leung, J.: Minimizing total tardiness on one machine is np-hard. Mathematics of operations research 15, 483–495 (1990)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Dorigo, M., Maniezzo, V., Colorni, A.: Ant System: Optimization by a colony of cooperating agents. IEEE Transactions on Systems, Man, and Cybernetics - Part B 26(1), 29–41 (1996)CrossRefGoogle Scholar
  4. 4.
    Dorigo, M., Di Caro, G.: The ant colony optimization meta-heuristic. In: Corne, D., Dorigo, M., Glover, F. (eds.) New Ideas in Optimization, pp. 11–32. McGraw-Hill, New York (1999)Google Scholar
  5. 5.
    Blum, C.: Beam-ACO - hybridizing ant colony optimization with beam search: an application to open shop scheduling. Computers & OR 32, 1565–1591 (2005)CrossRefGoogle Scholar
  6. 6.
    Doerner, K., Gronalt, M., Hartl, R.F., Reimann, M., Strauss, C., Stummer, M.: Savingsants for the vehicle routing problem. In: Cagnoni, S., Gottlieb, J., Hart, E., Middendorf, M., Raidl, G.R. (eds.) EvoIASP 2002, EvoWorkshops 2002, EvoSTIM 2002, EvoCOP 2002, and EvoPlan 2002. LNCS, vol. 2279, pp. 11–20. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  7. 7.
    Merkle, D., Middendorf, M., Schmeck, H.: Ant colony optimization for resource-constrained project scheduling. IEEE Transactions on Evolutionary Computation 6, 333–346 (2002)CrossRefGoogle Scholar
  8. 8.
    Gravel, M., Price, W., Gagné, C.: Scheduling continuous casting of aluminum using a multiple objective ant colony optimization metaheuristic. European Journal of Operational Research 143, 218–229 (2002)MATHCrossRefGoogle Scholar
  9. 9.
    Guntsch, M., Middendorf, M.: Solving multi-criteria optimization problems with population-based aco. In: Fonseca, C.M., Fleming, P.J., Zitzler, E., Deb, K., Thiele, L. (eds.) EMO 2003. LNCS, vol. 2632, pp. 464–478. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  10. 10.
    Doerner, K., Gutjahr, W., Hartl, R., Strauss, C., Stummer, C.: Pareto ant colony optimization: A metaheuristic approach to multiobjective portfolio selection. Annals of Operations Research 131, 79–99 (2004)MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Doerner, K., Gutjahr, W.J., Hartl, R.F., Strauss, C., Stummer, C.: Pareto ant colony optimization in multiobjective project portfolio selection with ILP preprocessing. European Journal of Operational Research 171, 830–841 (2006)MATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Doerner, K., Gutjahr, W.J., Hartl, R.F., Strauss, C., Stummer, C.: Nature-inspired metaheuristics in multiobjective activity crashing (Omega) (to appear)Google Scholar
  13. 13.
    Mariano, C., Morales, E.: A multiple objective ant-q algorithm for the design of water distribution irrigation networks. Technical report, Instituto Mexicano de Tecnolog\({\acute{\mbox i}}\)a del Agua (1999)Google Scholar
  14. 14.
    Shelokar, P., Jayaraman, V., Kulkarni, B.: Ant algorithm for single and multiobjective reliability optimization problems. Quality and Reliability Engineering International 18, 497–514 (2002)CrossRefGoogle Scholar
  15. 15.
    Shelokar, P., Jayaraman, V., Kulkarni, B.: Multiobjective optimization of reactor-regenerator system using ant algorithm. Petroleum Science and Technology 21, 1167–1184 (2003)CrossRefGoogle Scholar
  16. 16.
    García-Martínez, C., Cordón, O., Herrera, F.: An empirical analysis of multiple objective ant colony optimization algorithms for the bi-criteria TSP. In: Dorigo, M., Birattari, M., Blum, C., Gambardella, L.M., Mondada, F., Stützle, T. (eds.) ANTS 2004. LNCS, vol. 3172, pp. 61–72. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  17. 17.
    Gambardella, L., Taillard, E., Agazzi, G.: MACS-VRPTW: A multiple ant colony system for vehicle routing problems with time windows. In: Corne, D., Dorigo, M., Glover, F. (eds.) New Ideas in Optimization, pp. 63–76. McGraw-Hill, New York (1999)Google Scholar
  18. 18.
    Iredi, S., Merkle, D., Middendorf, M.: Bi-criterion optimization with multi colony ant algorithms. In: Zitzler, E., Deb, K., Thiele, L., Coello Coello, C.A., Corne, D.W. (eds.) EMO 2001. LNCS, vol. 1993, pp. 359–372. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  19. 19.
    Stützle, T.: An ant approach to the flow shop problem. In: Proceedings of EUFIT 1998, Aachen, pp. 1560–1564 (1998)Google Scholar
  20. 20.
    Dorigo, M., Gambardella, L.: Ant colonies for the traveling salesman problem. Biosystems 43(2), 73–81 (1997)CrossRefGoogle Scholar
  21. 21.
    Merkle, D., Middendorf, M.: An ant algorithm with a new pheromone evaluation rule for total tardiness problems. In: Oates, M.J., Lanzi, P.L., Li, Y., Cagnoni, S., Corne, D.W., Fogarty, T.C., Poli, R., Smith, G.D. (eds.) EvoIASP 2000, EvoWorkshops 2000, EvoFlight 2000, EvoSCONDI 2000, EvoSTIM 2000, EvoTEL 2000, and EvoROB/EvoRobot 2000. LNCS, vol. 1803, pp. 287–296. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  22. 22.
    Rajendran, C., Ziegler, H.: Ant-colony algorithms for permutation flowshop scheduling to minimize makespan/total flowtime of jobs. European Journal of Operational Research 155, 426–438 (2004)MATHCrossRefMathSciNetGoogle Scholar
  23. 23.
    Liu, J., Reeves, C.: Constructive and composite heuristic solutions to the p∥ ∑ C i scheduling problem. European Journal of Operational Research 132, 439–452 (2001)MATHCrossRefMathSciNetGoogle Scholar
  24. 24.
    Basseur, M., Seynhaeve, F., Talbi, E.: Path relinking in pareto multi-objective genetic algorithms. In: Coello Coello, C.A., Hernández Aguirre, A., Zitzler, E. (eds.) EMO 2005. LNCS, vol. 3410, pp. 120–134. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  25. 25.
    Taillard, E.: Benchmarks for basic scheduling problems. European Journal of Operational Research 64, 278–285 (1993)MATHCrossRefGoogle Scholar
  26. 26.
    Talbi, E. G., Rahoual, M., Mabed, M., Dhaenens, C.: A hybrid evolutionary approach for multicriteria optimization problems: Application to the flow shop. In: Zitzler, E., Deb, K., Thiele, L., Coello Coello, C.A., Corne, D.W. (eds.) EMO 2001. LNCS, vol. 1993, pp. 416–428. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  27. 27.
    Basseur, M., Seynhaeve, F., Talbi, E.: Design on multi-objective evolutionary algorithms to flow-shop scheduling problem. In: Congress on Evolutionary Computation, Piscataway, vol. 2. IEEE Service Center (2002)Google Scholar
  28. 28.
    Basseur, M., Seynhaeve, F., Talbi, E.: Adaptive mechanisms for multi-objective evolutionary algorithms. In: IMACS multiconference, Computational Engineering in Systems Applications (CESA 2003), Piscataway. IEEE Service Center (2003) S3-R-00-222Google Scholar
  29. 29.
    Geiger, M.: MOOPPS - An optimization system for multiobjective production scheduling. In: The Sixth Metaheuristic International Conference (MIC 2005), Vienna, Austria (2005)Google Scholar
  30. 30.
    Geiger, M.J.: Personal CommunicationGoogle Scholar
  31. 31.
    Zitzler, E., Thiele, L., Laumanns, M., Fonseca, C., Fonseca, V.: Performance assessment of multiobjective optimizers: An analysis and review. IEEE Trans. Evolutionary Computation 7, 117–132 (2003)CrossRefGoogle Scholar
  32. 32.
    Czyzack, P., Jaszkiewicz, A.: Pareto simulated annealing - a metaheuristic technique for multiple-objective combinatorial optimization. Journal of Multi-Criteria Decision Analysis 7, 34–47 (1998)CrossRefGoogle Scholar
  33. 33.
    Zitzler, E., Thiele, L.: Multiobjective optimization using evolutionary algorithms - A comparative case study. In: Eiben, A.E., Bäck, T., Schoenauer, M., Schwefel, H.-P. (eds.) PPSN 1998. LNCS, vol. 1498, pp. 292–301. Springer, Heidelberg (1998)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Joseph M. Pasia
    • 1
    • 2
  • Richard F. Hartl
    • 2
  • Karl F. Doerner
    • 2
  1. 1.Department of MathematicsUniversity of the Philippines-DilimanQuezon CityPhilippines
  2. 2.Department of Management ScienceUniversity of ViennaViennaAustria

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