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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4638))

Abstract

In this paper we propose the application of Pareto ant colony optimization (PACO) in solving a bi-objective capacitated vehicle routing problem with route balancing (CVRPRB). The objectives of the problem are minimization of the tour length and balancing the routes. We propose PACO as our response to the deficiency of the Pareto-based local search (P-LS) approach, which we also developed to solve CVRPRB. The deficiency of P-LS is the lack of information flow among its pools of solutions. PACO is a natural choice in addressing this deficiency since PACO and P-LS are similar in structure. It resolves the absence of information flow through its pheromone values. Several test instances are used to demonstrate the contribution and importance of information flow among the pools of solutions. Computational results show that PACO improves P-LS in most instances with respect to different performance metrics.

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References

  1. Dantzig, G., Ramsey, J.: The truck dispatching problem. Management Science 6, 80–91 (1959)

    Article  MATH  MathSciNet  Google Scholar 

  2. Lenstra, J., Kan, A.: Complexity of vehicle routing and scheduling problem. Networks 11, 221–227 (1981)

    Article  Google Scholar 

  3. Pasia, J.M., Doerner, K.F., F., H.R., Reimann, M.: A population-based local search for solving a bi-objective vehicle routing problem. In: Cotta, C., van Hemert, J. (eds.) Evolutionary Computation in Combinatorial Optimisation - EvoCOP 2007. LNCS, vol. 4446, pp. 166–175. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  4. 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)

    Article  MATH  MathSciNet  Google Scholar 

  5. 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)

    Article  Google Scholar 

  6. Clarke, G., Wright, J.: Scheduling of vehicles from a central depot to a number of delivery points. Operations Research 12, 568–581 (1964)

    Google Scholar 

  7. 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)

    Chapter  Google Scholar 

  8. Jozefowiez, N., Semet, F., Talbi, E.: Parallel and hybrid models for multi-objective optimization: Application to the vehicle routing problem. In: Guervós, J.J.M., Adamidis, P.A., Beyer, H.-G., Fernández-Villacañas, J.-L., Schwefel, H.-P. (eds.) Parallel Problem Solving from Nature - PPSN VII. LNCS, vol. 2439, pp. 271–280. Springer, Heidelberg (2002)

    Google Scholar 

  9. Christofides, N., Mingozzi, A., Toth, P.: The vehicle routing problem. In: Christofides, N., Mingozzi, A., Toth, P., Sandi, C. (eds.) Combinatorial Optimization, John Wiley and Sons, Chichester (1979)

    Google Scholar 

  10. Knowles, J., Thiele, L., Zitzler, E.: A tutorial on the performance assessment of stochastic multiobjective optimizers. Technical Report TIK-Report No. 214, Computer Engineering and Networks Laboratory, ETH Zurich, Switzerland (2006)

    Google Scholar 

  11. Zitzler, E., Thiele, L.: Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach. IEEE Trans. Evolutionary Computation 3(4), 257–271 (1999)

    Article  Google Scholar 

  12. Hansen, M., Jaszkiewicz, A.: Evaluating the quality of approximations to the non-dominated set. Technical Report Technical Report IMM-REP-1998-7, Technical University of Denmark (1998)

    Google Scholar 

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Thomas Stützle Mauro Birattari Holger H. Hoos

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© 2007 Springer-Verlag Berlin Heidelberg

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Pasia, J.M., Doerner, K.F., Hartl, R.F., Reimann, M. (2007). Solving a Bi-objective Vehicle Routing Problem by Pareto-Ant Colony Optimization. In: Stützle, T., Birattari, M., H. Hoos, H. (eds) Engineering Stochastic Local Search Algorithms. Designing, Implementing and Analyzing Effective Heuristics. SLS 2007. Lecture Notes in Computer Science, vol 4638. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74446-7_15

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  • DOI: https://doi.org/10.1007/978-3-540-74446-7_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-74445-0

  • Online ISBN: 978-3-540-74446-7

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