Abstract
The ant system (AS) is a metaheuristic approach originally developed for solving the traveling salesman problem. AS has been successfully applied to various hard combinatorial optimization problems and different variants have been proposed in the literature. In this paper, we introduce a time-based pheromone approach for AS (TbAS). Due to this nature TbAS is applicable to routing problems involving time-windows. The novelty in TbAS is the multi-layer pheromone network structure which implicitly utilizes the service time information associated with the customers as a heuristic information. To investigate the performance of TbAS, we use the well-known vehicle routing problem with time-windows as our testbed and we conduct an extensive computational study using the Solomon (Algorithms for the vehicle routing and scheduling problems with time window constraints 35:254–265, 1987) instances. Our results reveal that the proposed time-based pheromone approach is effective in obtaining good quality solutions.
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References
Alvarenga G.B., Mateus G.R., Tomi G.: A genetic and set partitioning two-phase approach for the vehicle routing problem with time windows. Comput. Oper. Res. 34, 1561–1584 (2007)
Badeau P., Guertin F., Gendreau M., Potvin J., Taillard E.: A parallel tabu search heuristic for the vehicle routing problem with time windows. Transp. Res. C-Emer 5, 109–122 (1997)
Bräysy O., Gendreau M.: Vehicle routing problem with time windows, Part I: route construction and local search algorithms. Transp. Sci. 39, 104–118 (2005)
Bräysy O., Gendreau M.: Vehicle routing problem with time windows, Part II: metaheuristics. Transp. Sci. 39, 119–139 (2005)
Bullnheimer B., Hartl R.F., Strauss C.: A new rank-based version of the ant system: a computational study. Cent. Eur. J. Oper. Res. Econ. 7, 25–38 (1999)
Bullnheimer B., Hartl R.F., Strauss C.: An improved ant system algorithm for the vehicle routing problem. Ann. Oper. Res. 89, 319–328 (1999)
Cordeau J-F., Laporte G., Mercier A.: A unified tabu search heuristic for vehicle routing problems with time windows. J. Oper. Res. Society 52, 928–936 (2001)
Dorigo M.: Ant colony optimization. Scholarpedia 2(3), 1461 (2010)
Dorigo M., Gambardella L.M.: Ant colony system: a cooperative learning approach to the traveling salesman problem. IEEE Trans. Evol. Comput. 1, 53–66 (1997)
Dorigo M., Maniezzo V., Colorni A.: The ant system: optimization by a colony of cooperating agents. IEEE Trans. Syst. Man Cybern. Part B 26, 29–41 (1996)
Dorigo M., Stützle T.: Ant Coloy Optimization. The MIT Press, London (2004)
Eglese R., Maden W., Slater A.: A road timetableTM to aid vehicle routing and scheduling. Comput. Oper. Res. 33, 3508–3519 (2006)
Ellabib I., Basir O.A., Calamai P.: An experimental study of a simple ant c. ANTS2002: Lect. Notes Comput. Sci. 2463, 53–64 (2002)
Fleischmann B., Gietz M., Gnutzmann S.: Time-varying travel times in vehicle routing. Transp. Sci. 38, 160–173 (2004)
Floudas C.A., Pardalos P.M.: Encyclopedia of Optimization. Springer, New York (2009)
Gambardella L.M., 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, London (1999)
Garcia-Najera A., Bullinaria J.A.: An improved multi-objective evolutionary algorithm for the vehicle routing problem with time windows. Comput. Oper. Res. 38, 287–300 (2011)
Jung, S., Moon, B-R.: A hybrid genetic algorithm for the vehicle routing problem with time windows. In: Proceedings of the 2002 Genetic and Evolutionary Computation Conference (GECCO 2002), pp. 1309–1316. Morgan Kaufmann Publishers, San Francisco (2002)
Koskosidis Y.A., Powell W.B., Solomon M.M.: An optimization-based heuristic for vehicle routing and scheduling with soft time window constraints. Transp. Sci. 26, 69–85 (1992)
Muter İ., Birbil Ş.İ., Şahin G.: Combination of metaheuristic and exact algorithms for solving set covering-type optimization problems. INFORMS J. Comput. 22, 603–619 (2010)
Oliveira H.C.B., Vasconcelos G.C.: A hybrid search method for the vehicle routing problem with time windows. Ann. Oper. Res. 180(1), 125–144 (2008)
Ombuki B., Ross B.J., Hanshar F.: Multi-objective genetic algorithms for vehicle routing problem with time windows. Appl. Intell. 24, 17–30 (2006)
Pardalos P.M., Resende M.G.C.: Handbook of Applied Optimization. Oxford University Press, New York (2002)
Pisinger D., Ropke S.: A general heuristic for vehicle routing problems. Comput. Oper. Res. 34, 2403–2435 (2007)
Rochat Y., Taillard E.D.: Probabilistic diversification and intensification in local search for vehicle routing. J. Heuristics 1, 147–167 (1995)
Rousseau, L.M., Gendreau, M., Pesant, G.: Using constraint-based operators with variable neighborhood search to solve the vehicle routing problem with time windows. In: Proceedings of the 1999 Workshop on Integration of AI and OR techniques in Constraint Programming for Combinatorial Optimization Problems (CP-AI-OR’99), pp. 43–58. Ferrara (1999)
Savelsbergh M.W.P.: The vehicle routing problem with time windows: minimizing route duration. ORSA J. Comput. 4, 146–154 (1992)
Shaw, P.: Using constraint programming and local search methods to solve vehicle routing problems. In: Maher, M., Puget, J.F. (eds.) Principles and Practice of Constraint Programming (CP’98). Lect. Notes Comput. Sci. Springer, Berlin, pp. 417–431 (1998)
Solomon M.M.: Algorithms for the vehicle routing and scheduling problems with time window constraints. Oper. Res. 35, 254–265 (1987)
Stützle, T., Hoos, H.H.: The MAX-MIN ant system and local search for the traveling salesman problem. In: Bäck, T., Michalewicz, Z., Yao, X. (eds.) Proceedings of the 1997 IEEE International Conference on Evolutionary Computation (ICEC’97), pp. 309–314. IEEE Press, Piscataway (1997)
Tan K.C., Lee L.H., Zhu Q.L., Ou K.: Heuristic methods for vehicle routing problem with time windows. Artif. Intell. Eng. 15, 281–295 (2001)
Toth P., Vigo D.: The vehicle routing problem. SIAM Monographs on Discrete Mathematics and Applications, Philadelphia (2002)
Zufferey, N.: Optimization by ant algorithms: possible roles for an individual ant. Optim. Lett. (2011). doi:10.1007/s11590-011-0327-x
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Yildirim, U.M., Çatay, B. A time-based pheromone approach for the ant system. Optim Lett 6, 1081–1099 (2012). https://doi.org/10.1007/s11590-012-0451-2
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DOI: https://doi.org/10.1007/s11590-012-0451-2