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). Solving the Vehicle Routing Problem by an Effective Reactive Bone Route Algorithm, Transportation Research Journal, 1(2), 51-69.Subramanian, A., Drummond, L. M. A., Bentes, C., Ochi, L. S., & Farias, R. (2010). A parallel heuristic for the Vehicle Routing Problem with Simultaneous Pickup and Delivery. Computers & Operations Research, 37(11), 1899-1911. doi:10.1016/j.cor.2009.10.011Syslo, M., Deo, N., Kowalik, J. (1983). Discrete Optimization Algorithms with Pascal Programs, Prentice Hall.Taillard, E. D. (1999). A heuristic column generation method for the heterogeneous fleet VRP, RAIRO Operations Research, 33, 1-14. https://doi.org/10.1051/ro:1999101Tarantilis, C. D., & Kiranoudis, C. T. (2007). A flexible adaptive memory-based algorithm for real-life transportation operations: Two case studies from dairy and construction sector. European Journal of Operational Research, 179(3), 806-822. doi:10.1016/j.ejor.2005.03.059Wang, H.-F., & Chen, Y.-Y. (2012). A genetic algorithm for the simultaneous delivery and pickup problems with time window. Computers & Industrial Engineering, 62(1), 84-95. doi:10.1016/j.cie.2011.08.018Yousefikhoshbakht, M., Didehvar, F., & Rahmati, F. (2013). Solving the heterogeneous fixed fleet open vehicle routing problem by a combined metaheuristic algorithm. International Journal of Production Research, 52(9), 2565-2575. doi:10.1080/00207543.2013.855337Yousefikhoshbakht, M., & Khorram, E. (2012). Solving the vehicle routing problem by a hybrid meta-heuristic algorithm. Journal of Industrial Engineering International, 8(1). doi:10.1186/2251-712x-8-1

Solving the Traveling Salesman Problem Based on The Genetic Reactive Bone Route Algorithm whit Ant Colony System

[EN] The TSP is considered one of the most well-known combinatorial optimization tasks and researchers have paid so much attention to the TSP for many years. In this problem, a salesman starts to move from an arbitrary place called depot and after visits all of the nodes, finally comes back to the depot. The objective is to minimize the total distance traveled by the salesman.  Because this problem is a non-deterministic polynomial (NP-hard) problem in nature, a hybrid meta-heuristic algorithm called REACSGA is used for solving the TSP. In REACSGA, a reactive bone route algorithm that uses the ant colony system (ACS) for generating initial diversified solutions and the genetic algorithm (GA) as an improved procedure are applied. Since the performance of the Metaheuristic algorithms is significantly influenced by their parameters, Taguchi Method is used to set the parameters of the proposed algorithm. The proposed algorithm is tested on several standard instances involving 24 to 318 nodes from the literature. The computational result shows that the results of the proposed algorithm are competitive with other metaheuristic algorithms for solving the TSP in terms of better quality of solution and computational time respectively. In addition, the proposed REACSGA is significantly efficient and finds closely the best known solutions for most of the instances in which thirteen best known solutions are also found.Yousefikhoshbakht, M.; Malekzadeh, N.; Sedighpour, M. (2016). Solving the Traveling Salesman Problem Based on The Genetic Reactive Bone Route Algorithm whit Ant Colony System. International Journal of Production Management and Engineering. 4(2):65-73. doi:10.4995/ijpme.2016.4618.SWORD65734

Solving the Multiple Traveling Salesman Problem by a Novel Meta-heuristic Algorithm

The multiple traveling salesman problem (MTSP) is a generalization of the famous traveling salesman problem (TSP), where more than one salesman is used in the solution. Although the MTSP is a typical kind of computationally complex combinatorial optimization problem, it can be extended to a wide variety of routing problems. This paper presents an efficient and evolutionary optimization algorithm which has been developed through combining Modified Imperialist Competitive Algorithm and Lin-Kernigan Algorithm (MICA) in order to solve the MTSP.  In the proposed algorithm, an absorption function and several local search algorithms as a revolution operator are used. The performance of our algorithm was tested on several MTSP benchmark problems and the results confirmed that the MICA performs well and is quite competitive with other meta-heuristic algorithms

An Efficient Solution for the VRP by Using a Hybrid Elite Ant System

The vehicle routing problem (VRP) is a well-known NP-Hard problemin operation research which has drawn enormous interest from many researchers duringthe last decades because of its vital role in planning of distribution systems andlogistics. This article presents a modified version of the elite ant system (EAS) algorithmcalled HEAS for solving the VRP. The new version mixed with insert and swapalgorithms utilizes an effective criterion for escaping from the local optimum points.In contrast to the classical EAS, the proposed algorithm uses only a global updatingwhich will increase pheromone on the edges of the best (i.e. the shortest) route andwill at the same time decrease the amount of pheromone on the edges of the worst(i.e. the longest) route. The proposed algorithm was tested using fourteen instancesavailable from the literature and their results were compared with other well-knownmeta-heuristic algorithms. Results show that the suggested approach is quite effectiveas it provides solutions which are competitive with the best known algorithms in theliterature

A Combined Metaheuristic Algorithm for the Vehicle Routing Problem and its Open Version

Abstract: The Open Vehicle Routing Problem (OVRP) is one of the most important extensions of the vehicle routing problem (VRP) that has many applications in industrial and service. In the VRP, a set of customers with a specified demand of goods are given and a depot where a fleet of identical capacitated vehicles is located. We are also given the ‘‘traveling costs’’ between the depot and all the customers, and between each pair of customers. In the OVRP against to VRP, vehicles are not required to return to the depot after completing service. Because VRP and OVRP belong to NP-hard Problems, an efficient hybrid elite ant system called EACO is proposed for solving them in the paper. In this algorithm, a modified tabu search (TS), a new state transition rule and a modified pheromone updating rule are used for more improving solutions. These modifications lead that the proposed algorithm does not trapped at the local optimum and discovers different parts of the solution space. Computational results on fourteen standard benchmark instances for VRP and OVRP show that EACO finds the best known solutions for most of the instances and is comparable in terms of solutions quality to the best performing published metaheuristics in the literature

A Mixed Integer Programming Formulation for the Heterogeneous Fixed Fleet Open Vehicle Routing Problem

The heterogeneous fixed fleet open vehicle routing problem (HFFOVRP) is one of the most significant extension problems of the open vehicle routing problem (OVRP). The HFFOVRP is the problem of designing collection routes to a number of predefined nodes by a fixed fleet number of vehicles with various capacities and related costs. In this problem, the vehicle doesn’t return to the depot after serving the last customer. Because of its numerous applications in industrial and service problems, a new model of the HFFOVRP based on mixed integer programming is proposed in this paper. Furthermore, due to its NP-hard nature, an ant colony system (ACS) algorithm was proposed. Since there were no existing benchmarks, this study generated some test problems. From the comparison with the results of exact algorithm, the proposed algorithm showed that it can provide better solutions within a comparatively shorter period of time

Solving the Traveling Salesman Problem: A Modified Metaheuristic Algorithm

The traveling salesman problem (TSP) is one of the most important issues in combinatorial optimization problems that are used in many engineering sciences and has attracted the attention of many scientists and researchers. In this issue, a salesman starts to move from a desired node called warehouse and returns to the starting place after meeting n customers provided that each customer is only met once. The aim of this issue is to determine a cycle with a minimum cost for this salesman. One of the major weaknesses of the PSO algorithm in the classical version is that it gets stuck in local optimizations. Therefore, in the proposed algorithm, called MPSO, the best solution in the current iteration is also used in the movement step. In addition, a variety of local search algorithms are provided that are used when better answers are generated than before. Also, a new method for moving the particle towards the best particle is presented, which, in addition to probably increasing the quality of the new answer, prevents the premature convergence of the algorithm due to consideration of the concept of random. The results evaluated with the results of several metaheuristic algorithms in the literature show the efficiency of the MPSO algorithm because it has been able to achieve excellent solutions in most of these instances