A Column Generation for the Heterogeneous Fixed Fleet Open Vehicle Routing Problem

[EN] This paper addressed the heterogeneous fixed fleet open vehicle routing problem (HFFOVRP), in which the vehicles are not required to return to the depot after completing a service. In this new problem, the demands of customers are fulfilled by a heterogeneous fixed fleet of vehicles having various capacities, fixed costs and variable costs. This problem is an important variant of the open vehicle routing problem (OVRP) and can cover more practical situations in transportation and logistics. Since this problem belongs to NP-hard Problems, An approach based on column generation (CG) is applied to solve the HFFOVRP. A tight integer programming model is presented and the linear programming relaxation of which is solved by the CG technique. Since there have been no existing benchmarks, this study generated 19 test problems and the results of the proposed CG algorithm is compared to the results of exact algorithm. Computational experience confirms that the proposed algorithm can provide better solutions within a comparatively shorter period of time.Yousefikhoshbakht, M.; Dolatnejad, A. (2017). A Column Generation for the Heterogeneous Fixed Fleet Open Vehicle Routing Problem. International Journal of Production Management and Engineering. 5(2):55-71. doi:10.4995/ijpme.2017.5916SWORD557152Aleman, R. E., & Hill, R. R. (2010). A tabu search with vocabulary building approach for the vehicle routing problem with split demands. International Journal of Metaheuristics, 1(1), 55. doi:10.1504/ijmheur.2010.033123Anbuudayasankar, S. P., Ganesh, K., Lenny Koh, S. C., & Ducq, Y. (2012). Modified savings heuristics and genetic algorithm for bi-objective vehicle routing problem with forced backhauls. Expert Systems with Applications, 39(3), 2296-2305. doi:10.1016/j.eswa.2011.08.009Brandão, J. (2009). A deterministic tabu search algorithm for the fleet size and mix vehicle routing problem. 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The capacitated vehicle routing problem with stochastic demands and time windows. Computers & Operations Research, 38(12), 1775-1783. doi:10.1016/j.cor.2011.02.007Li, X., Leung, S. C. H., & Tian, P. (2012). A multistart adaptive memory-based tabu search algorithm for the heterogeneous fixed fleet open vehicle routing problem. Expert Systems with Applications, 39(1), 365-374. doi:10.1016/j.eswa.2011.07.025Li, X., Tian, P., & Aneja, Y. P. (2010). An adaptive memory programming metaheuristic for the heterogeneous fixed fleet vehicle routing problem. Transportation Research Part E: Logistics and Transportation Review, 46(6), 1111-1127. doi:10.1016/j.tre.2010.02.004Penna, P. H. V., Subramanian, A., & Ochi, L. S. (2011). An Iterated Local Search heuristic for the Heterogeneous Fleet Vehicle Routing Problem. Journal of Heuristics, 19(2), 201-232. doi:10.1007/s10732-011-9186-ySaadati Eskandari, Z., YousefiKhoshbakht, M. (2012). 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BRAIN Journal - An Efficient Combined Meta-Heuristic Algorithm for Solving the Traveling Salesman Problem

<div><i>Abstract</i></div><div><br></div>The traveling salesman problem (TSP) is one of the most important NP-hard Problems and probably the most famous and extensively studied problem in the field of combinatorial optimization. In this problem, a salesman is required to visit each of n given nodes once and only once, starting from any node and returning to the original place of departure. This paper presents an efficient evolutionary optimization algorithm developed through combining imperialist competitive algorithm and lin-kernighan algorithm called (MICALK) in order to solve the TSP. The MICALK is tested on 44 TSP instances involving from 24 to 1655 nodes from the literature so that 26 best known solutions of the benchmark problem are also found by our algorithm. Furthermore, the performance of MICALK is compared with several metaheuristic algorithms, including GA, BA, IBA, ICA, GSAP, ABO, PSO and BCO on 32 instances from TSPLIB. The results indicate that the MICALK performs well and is quite competitive with the above algorithms.<div><br></div><div><b>Find more at:</b></div><div><b>https://www.edusoft.ro/brain/index.php/brain/article/view/631</b><br></div

A Modified Column Generation to Solve the Heterogeneous Fixed Fleet Open Vehicle Routing Problem

In the heterogeneous fixed fleet open vehicle routing problem (HFFOVRP), several different types of vehicles can be used to service the customers. The types of vehicles are different in terms of capacity, fixed cost, and variable cost. In this problem, the vehicles are not required to return to the depot after completing a service and the number of vehicles of each type is fixed and limited. Since this problem belongs to NP-hard problems, in this paper a compound heuristic algorithm called SISEC which includes sweep algorithm, insert, swap, and 2-opt moves, modified elite ant system (EAS), and column generation (CG) is applied to solve the HFFOVRP. We report computational results on 22 problems and solve each problem by using our SISEC. The results which were compared to the results of exact algorithms and the classic CG confirm that the proposed algorithm produces high quality solutions within an acceptable computation time