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An enhanced ant colony optimization (EACO) applied to capacitated vehicle routing problem

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Abstract

In this paper, an enhanced ant colony optimization (EACO) is proposed for capacitated vehicle routing problem. The capacitated vehicle routing problem is to service customers with known demands by a homogeneous fleet of fixed capacity vehicles starting from a depot. It plays a major role in the field of logistics and belongs to NP-hard problems. Therefore, it is difficult to solve the capacitated vehicle routing problem directly when solutions increase exponentially with the number of serviced customers.

The framework of this paper is to develop an enhanced ant colony optimization for the capacitated vehicle routing problem. It takes the advantages of simulated annealing and ant colony optimization for solving the capacitated vehicle routing problem. In the proposed algorithm, simulated annealing provides a good initial solution for ant colony optimization. Furthermore, an information gain based ant colony optimization is used to ameliorate the search performance. Computational results show that the proposed algorithm is superior to original ant colony optimization and simulated annealing separately reported on fourteen small-scale instances and twenty large-scale instances.

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References

  1. Beasley JE (1983) Route first-cluster second methods for vehicle P *(θ) routing. Omega 11:403–408

    Article  Google Scholar 

  2. Christofides N, Mingozzi A, Toth P (1979) The vehicle routing Problem. In: Christofides N, Mingozzi A, Toth P, Sandi C (eds) Combinatorial optimization. Wiley, Chichester, pp 325–338

    Google Scholar 

  3. Hanshar FT, Ombuki-Berman BM (2007) Dynamic vehicle routing using genetic algorithms. Appl Intell 27:89–99

    Article  Google Scholar 

  4. Gillett BE, Miller LR (1974) A heuristic algorithm for the vehicle dispatch problem. Oper Res 22:340–349

    Article  MATH  Google Scholar 

  5. Haimovich M, Kan AHGR (1985) Bounds and heuristics for capacitated routing problems. Math Oper Res 10:527–542

    Article  MATH  MathSciNet  Google Scholar 

  6. Ho SC, Gendreau M (2006) Path relinking for the vehicle routing problem. J Heuristics 12:55–72

    Article  MATH  Google Scholar 

  7. Laporte G, Semet F (2001) The vehicle routing problem. In: Toth P, Vigo D (eds) SIAM monographs on discrete mathematics and application. SIAM, Philadelphia, pp 109–125

    Google Scholar 

  8. Prins C (2004) A simple and effective evolutionary algorithm for the vehicle routing problem. Comput Oper Res 31:1985–2002

    Article  MATH  MathSciNet  Google Scholar 

  9. Van Laarhoven PJM, Arts EHL (1992) Simulated annealing: theory and applications. Kluwer Academic, Dordrecht

    Google Scholar 

  10. Bäck T, Hammel U, Schwefel H-P (1997) Evolutionary computation: Comments on the History and current state. IEEE Trans Evol Comput 1(1):3–17

    Article  Google Scholar 

  11. Dorigo M, Stützle T (2004) Ant colony optimization. MIT Press, Cambridge

    MATH  Google Scholar 

  12. Lee Z-J, Lee C-Y (2005) A hybrid search algorithm with heuristics for resource allocation problem. Inf Sci 173:155–167

    Article  Google Scholar 

  13. Lee Z-J, Lee C-Y, Su S-F (2002) An immunity based ant colony optimization algorithm for solving weapon-target assignment problem. Appl Soft Comput 2:39–47

    Article  Google Scholar 

  14. Lee Z-J, Su S-F, Lee C-Y (2003) Efficiently solving general weapon-target assignment problem by genetic algorithms with greedy eugenics. IEEE Trans Syst Man Cybern Part B 33:113–121

    Article  Google Scholar 

  15. Lee Z-J, Lin S-W, Su S-FP, Lin C-Y (2008) A hybrid watermarking technique applied to digital images. Appl Soft Comput 8:798–808

    Article  Google Scholar 

  16. Lee C-Y, Su S-F, Lee Z-J (2007) Incorporation of genetic algorithms and Hopfield neural networks with ant colony optimization. Eng Intell Syst 1:25–32

    Google Scholar 

  17. Hung K-S, Su S-F, Lee Z-J (2007) Improving ant colony optimization algorithms for solving traveling salesman problems. J Adv Comput Intell Intell Inform 11(4):433–442. JACIII

    Google Scholar 

  18. Robusté F, Daganzo CF, Souleyrette RR II (1990) Implementing vehicle routing models. Transp Res 24B:263–286

    Article  Google Scholar 

  19. Alfa AS, Heragu SS, Chen M (1991) A 3-opt based simulated annealing algorithm for vehicle routing problem. Comput Ind Eng 21:635–639

    Article  Google Scholar 

  20. Osman IH (1993) Metastrategy simulated annealing and tabu search algorithms for the vehicle routing problem. Ann Oper Res 41:421–451

    Article  MATH  Google Scholar 

  21. Bullnheimer B, Hartl RF, Strauss C (1999) An improved ant system algorithm for the vehicle routing problem. Ann Oper Res 89:319–328

    Article  MATH  MathSciNet  Google Scholar 

  22. Bell JE, McMullen PR (2004) Ant colony optimization techniques for the vehicle routing. Adv Eng Inform 18:41–48

    Article  Google Scholar 

  23. Manfrin M (2004) Ant colony optimization for the vehicle routing problem. DEA defense at ULB, September 3, Brussels, Belgium

  24. Mazzeo S, Loiseau I (2004) An ant colony algorithm for the capacitated vehicle routing. Electron Notes Discrete Math 18:181–186

    Article  MathSciNet  Google Scholar 

  25. Lin W-D, Cai T-X (2006) Ant colony optimization for VRP and mail delivery problems. In: 2006 IEEE international conference on industrial informatics, pp 1143–1148

  26. Zeng L, Ong HL, Ng KM (2005) An assignment-based local search method for solving vehicle routing problems. Asia-Pac J Oper Res 22:85–104

    Article  MATH  MathSciNet  Google Scholar 

  27. Lin S-W, Ying K-C, Lee Z-J, His F-H (2006) Applying simulated annealing approach for capacitated vehicle routing problems. In: Proceeding of 2006 IEEE international conference on systems, man, and cybernetics, pp 639–644

  28. Dorigo M, Caro GD (1999) Ant colony optimization: A new meta-heuristic. In: Proceedings of the 1999 congress on evolutionary computation, vol 2, pp 1470–1477

  29. Metropolis N, Rosenbluth AW, Rosenbluth MN, Teller AH, Teller E (1953) Equations of state calculations by fast computing machines. J Chem Phys 21:1087–1092

    Article  Google Scholar 

  30. Kirkpatrick S, Gelatt CD, Vecchi JMP (1983) Optimization by simulated annealing. Science 220:671–680

    Article  MathSciNet  Google Scholar 

  31. Toth P, Vigo D (2003) The granular tabu search and its application to the vehicle-routing problem. INFORMS J Comput 15:333–346

    Article  MathSciNet  Google Scholar 

  32. Lee C-Y, Su S-F, Lee Z-J (2007) Incorporation of genetic algorithms and Hopfield neural networks with ant colony optimization. Eng Intell Syst 1:25–32

    Google Scholar 

  33. Reimann M, Doerner K, Richard FH (2004) D-Ants: Savings based ants divide and conquer the vehicle routing problem. Comput Oper Res 31:563–591

    Article  MATH  Google Scholar 

  34. Pisinger D, Ropke S (2007) A general heuristic for vehicle routing problems. Comput Oper Res 34:2403–2435

    Article  MATH  MathSciNet  Google Scholar 

  35. Gendreau MP, Hertz A, Laporte G (1994) A tabu search heuristic for the vehicle routing problem. Manage Sci 40:1276–1290

    Article  MATH  Google Scholar 

Download references

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Lee, CY., Lee, ZJ., Lin, SW. et al. An enhanced ant colony optimization (EACO) applied to capacitated vehicle routing problem. Appl Intell 32, 88–95 (2010). https://doi.org/10.1007/s10489-008-0136-9

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