Abstract
Electric vehicles are becoming popular in transport systems due to subsidies provided by the governments and the reduction of environmental issues. A bilevel optimization problem rises when the interests of governments (minimizing the infrastructure costs) and transportation companies (minimizing the routing costs) are considered. Also, both electric vehicles and internal combustion vehicles can be used, increasing the complexity of the problem. This work proposes a Variable Neighborhood Descent combined with an Ant Colony Optimization with local search and a Route Selection Procedure for solving a bilevel optimization problem. Variable Neighborhood Descent is applied at the upper level in the Station Allocation Problem while Ant Colony Optimization with local search and Route Selection Procedure are applied to the lower level in the Vehicle Routing Problem. Computational experiments were performed using two different sets of instances and the results obtained indicate that the proposal achieved good results at both levels when compared with other approaches from the literature, with low construction and routing cost and always keeping the proportion of electric vehicles higher than requested.
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The instance sets used can be found at https://neo.lcc.uma.es/vrp/vrp-instances/capacitated-vrp-instances/ and https://mavrovouniotis.github.io/EVRPcompetition2020/
References
Balinski ML, Quandt RE (1964) On an integer program for a delivery problem. Oper Res 12 (2):300–304
Castillo O, Lizárraga E, Soria J, Melin P, Valdez F (2015) New approach using ant colony optimization with ant set partition for fuzzy control design applied to the ball and beam system. Inf Sci 294:203–215. Innovative Applications of Artificial Neural Networks in Engineering
Desaulniers G, Errico F, Irnich S, Schneider M (2016) Exact algorithms for electric vehicle-routing problems with time windows. Oper Res 64:1–18
Dorigo M, Gambardella LM (1997) Ant colony system: a cooperative learning approach to the traveling salesman problem. IEEE Trans Evol Comput 1(1):53–66
Duarte A, Sánchez-Oro J, Mladenović N, Todosijević R (2018) Variable Neighborhood Descent. Springer International Publishing, Cham, pp 341–367
Erdoğan S, Miller-Hooks E (2012) A green vehicle routing problem. Transp Res Part E: Logist Transp Rev 48(1):100–114. Select Papers from the 19th International Symposium on Transportation and Traffic Theory
Faust OS, Mehli CG, Hanne T, Dornberger R (2020) A genetic algorithm for optimizing parameters for ant colony optimization solving capacitated vehicle routing problems. In: Proceedings of the 2020 4th International Conference on Intelligent Systems, Metaheuristics & Swarm Intelligence, ISMSI ’20. Association for Computing Machinery, New York, pp 52–58
Gambardella LM, Dorigo M (1995) Ant-q: a reinforcement learning approach to the traveling salesman problem. In: Prieditis A, Russell S (eds) Machine Learning Proceedings 1995. Morgan Kaufmann, San Francisco, pp 252–260
Gong Y, Zhang J, Liu O, Huang R, Chung HS, Shi Y (2012) Optimizing the vehicle routing problem with time windows: A discrete particle swarm optimization approach. IEEE Trans Syst Man Cybern Part C (Appl Rev) 42(2):254–267
Guo F, Yang J, Lu J (2018) The battery charging station location problem: Impact of users’ range anxiety and distance convenience. Transp Res Part E: Logist Transp Rev 114:1–18
Gurobi Optimization L (2020) Gurobi optimizer reference manual. http://www.gurobi.com
He F, Yin Y, Zhou J (2015) Deploying public charging stations for electric vehicles on urban road networks. Transp Res Part C: Emerging Technol 60:227–240
He J, Yang H, Tang TQ, Huang HJ (2018) An optimal charging station location model with the consideration of electric vehicle’s driving range. Transp Res Part C: Emerging Technol 86:641–654
Hiermann G, Hartl RF, Puchinger J, Vidal T (2019) Routing a mix of conventional, plug-in hybrid, and electric vehicles. Europ J Oper Res 272(1):235–248
In J, Bell JE (2015) Alternative fuel infrastructure and customer location impacts on fleet mix and vehicle routing. Transp J 54(4):409–437
Jia YH, Mei Y, Zhang M (2021) A bilevel ant colony optimization algorithm for capacitated electric vehicle routing problem. IEEE Trans Cybern:1–14
Jung J, Chow JY, Jayakrishnan R, Park JY (2014) Stochastic dynamic itinerary interception refueling location problem with queue delay for electric taxi charging stations. Transp Res Part C: Emerging Technol 40:123–142
Kruskal WH, Wallis WA (1952) Use of ranks in one-criterion variance analysis. J Am Stat Assoc 47(260):583–621
Lee YG, Kim HS, Kho SY, Lee C (2014) Ue-based location model of rapid charging stations for evs with batteries that have different states-of-charge. In: Proceedings of the annual meeting on transportation research board, pp 12–16
Leite MR, Bernandino HS, Gonçalves L. B., Soares S (2019) Optimization in Multilevel Green Transportation Problems with Electrical Vehicles, chap. 9. Wiley, pp 203–228
Li Y, Zhang P, Wu Y (2018) Public recharging infrastructure location strategy for promoting electric vehicles: a bi-level programming approach. J Cleaner Prod 172:2720–2734
Liu X, Guo RY, Zhang CY (2017) Bi-level programming model of locating public charging stations for electric vehicles. In: International conference of transportation professionals, Shanghai, pp 3465–3474
Macrina G, Pugliese LDP, Guerriero F, Laporte G (2019) The green mixed fleet vehicle routing problem with partial battery recharging and time windows. Comput Oper Res 101:183–199
Mavrovouniotis M, Ellinas G, KIOS MP (2018) Ant colony optimization for the electric vehicle routing problem. In: 2018 IEEE Symposium series on computational intelligence (SSCI), pp 1234–1241
Mavrovouniotis M, Menelaou C, Timotheou S, Panayiotou C, Ellinas G, Polycarpou M (2020) Benchmark set for the ieee wcci-2020 competition on evolutionary computation for the electric vehicle routing problem. Tech. rep., University of Cyprus, Department of Electrical and Computer Engineering, Nicosia
Olivas F, Valdez F, Castillo O, Gonzalez CI, Martinez G, Melin P (2017) Ant colony optimization with dynamic parameter adaptation based on interval type-2 fuzzy logic systems. Appl Soft Comput 53:74–87
Othman WAFW, Wahab AAA, Alhady SSN, Wong HN (2018) Solving Vehicle Routing Problem using Ant Colony Optimisation (ACO) Algorithm. Int J Res Eng 5(9):500–507
Pellonperä T (2014) Ant colony optimization and the vehicle routing problem. Master’s thesis, Tampere University
Reinelt G (1994) The traveling salesman. Springer, Berlin
Solomon MM (1987) Algorithms for the vehicle routing and scheduling problems with time window constraints. Oper Res 35(2):254–265
Sttzle T, Hoos HH (1996) Improving the ant system: A detailed report on the max-min ant system. Tech. rep., Technical University of Darmstadt, Darmstadt
Stützle T, Hoos HH (1997) Max-min ant system and local search for the traveling salesman problem. In: Proceedings of 1997 IEEE International Conference on Evolutionary Computation (ICEC ’97), vol 16, pp 309–314
Xiong Y, Gan J, An B, Miao C, Bazzan ALC (2018) Optimal electric vehicle fast charging station placement based on game theoretical framework. IEEE Trans Intell Transp Syst 19(8):2493–2504
Xu H, Pu P, Duan F (2018) Dynamic vehicle routing problems with enhanced ant colony optimization. Discret Dyn Nat Soc 2018:1295485
Yang J, Sun H (2015) Battery swap station location-routing problem with capacitated electric vehicles. Comput Oper Res 55(C):217–232
Yu VF, Jodiawan P, Gunawan A, Widjaja AT (2019) A mathematical programming model for the green mixed fleet vehicle routing problem with realistic energy consumption and partial recharges. In: 2019 IEEE International conference on industrial engineering and engineering management (IEEM), pp 1339–1343
Yu VF, Redi AP, Hidayat YA, Wibowo OJ (2017) A simulated annealing heuristic for the hybrid vehicle routing problem. Appl Soft Comput 53:119–132
Zang H, Fu Y, Chen M, Shen H, Miao L, Zhang S, Wei Z, Sun G (2018) Bi-level planning model of charging stations considering the coupling relationship between charging stations and travel route. Appl Sci 8(7):1130
Zhang G, Yang H, Dong J (2015) Electric vehicle charging stations layout research based on bi-level programming. In: 2015 5Th international conference on electric utility deregulation and restructuring and power technologies (DRPT), pp 609–614
Zheng H, He X, Li Y, Peeta S (2017) Traffic equilibrium and charging facility locations for electric vehicles. Netw Spatial Econ 17(2):435–457
Zhikharevich V, Matsiuk N, Ostapov S (2016) Solving the routing problem by ant colony optimization algorithms. Int J Comput 15:84–91
Acknowledgments
This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES) - Finance Code 001. The authors also thank FAPEMIG (APQ-00337-18) and CNPq (312682/2018-2).
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This work was supported by Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES), Fundação de Amparo à Pesquisa do Estado de Minas Gerais(FAPEMIG) and Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPQ).
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Leite, M.R., Bernardino, H.S. & Gonçalves, L.B. A variable neighborhood descent with ant colony optimization to solve a bilevel problem with station location and vehicle routing. Appl Intell 52, 7070–7090 (2022). https://doi.org/10.1007/s10489-021-02748-x
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DOI: https://doi.org/10.1007/s10489-021-02748-x