Multi-objective green mixed vehicle routing problem under rough environment

    Joydeep Dutta Affiliation
    ; Partha Sarathi Barma Affiliation
    ; Anupam Mukherjee Affiliation
    ; Samarjit Kar Affiliation
    ; Tanmay De Affiliation
    ; Dragan Pamučar Affiliation
    ; Šarūnas Šukevičius Affiliation
    ; Giedrius Garbinčius Affiliation


This paper proposes a multi-objective Green Vehicle Routing Problem (G-VRP) considering two types of vehicles likely company-owned vehicle and third-party logistics in the imprecise environment. Focusing only on one objective, especially the distance in the VRP is not always right in the sustainability point of view. Here we present a bi-objective model for the G-VRP that can address the issue of the emission of GreenHouse Gases (GHGs). We also consider the demand as a rough variable. This paper uses the Non-Dominated Sorting Genetic Algorithm II (NSGA-II) to solve the proposed model. Finally, it uses Multicriteria Optimization and Compromise Solution (abbreviation in Serbian – VIKOR) method to determine the best alternative from the Pareto front.

First published online 25 February 2021

Keyword : green VRP, multi-objective VRP, evolutionary methods, NSGA-II, VIKOR, sustainability

How to Cite
Dutta, J., Barma, P. S., Mukherjee, A., Kar, S., De, T., Pamučar, D., Šukevičius, Šarūnas, & Garbinčius, G. (2022). Multi-objective green mixed vehicle routing problem under rough environment. Transport, 37(1), 51–63.
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May 24, 2022
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Augerat, P.; Belenguer, J. M.; Benavent, E.; Corberan, A.; Naddef, D.; Rinaldi, G. 1995. Computational Results with a Branch and Cut Code for the Capacitated Vehicle Routing Problem. Technical Report No INPG-RR-949-M. 33 p. Available from Internet:

Barma, P. 2018. ZIP Archive: Rough Data. Available from Internet:

Braekers, K.; Ramaekers, K.; Van Nieuwenhuyse, I. 2016. The vehicle routing problem: state of the art classification and review, Computers & Industrial Engineering 99: 300–313.

Dantzig, G. B.; Ramser, J. H. 1959. The truck dispatching problem, Management Science 6(1): 80–91.

Deb, K.; Pratap, A.; Agarwal, S.; Meyarivan, T. 2002. A fast and elitist multiobjective genetic algorithm: NSGA-II, IEEE Transactions on Evolutionary Computation 6(2): 182–197.

Demir, E.; Bektaş, T.; Laporte, G. 2014. The bi-objective pollutionrouting problem, European Journal of Operational Research 232(3): 464–478.

Ekblom, J. 2019. Air Pollution Caused 400,000 Premature European Deaths in 2016: EU Agency. Reuters. Available from Internet:

EPA. 2019a. Greenhouse Gas Emissions: Global Greenhouse Gas Emissions Data. US Environmental Protection Agency (EPA). Available from Internet:

EPA. 2019b. Greenhouse Gas Emissions: Sources of Greenhouse Gas Emissions. US Environmental Protection Agency (EPA). Available from Internet:

Erdoğan, S.; Miller-Hooks, E. 2012. A green vehicle routing problem, Transportation Research Part E: Logistics and Transportation Review 48(1): 100–114.

Gambardella, L. M.; Taillard, E.; Agazzi, G. 1999. MACSVRPTW: a multiple ant colony system for vehicle routing problems with time windows, in D. Corne, M. Dorigo, F. Glover (Eds.). New Ideas in Optimization, 63–76.

Granada, M.; Toro, E. M.; Gallego, R. 2019. An MIP formulation for the open location‐routing problem considering the topological characteristic of the solution‐paths, Networks: an International Journal 74(4): 374–388.

Granada-Echeverri, M.; Toro, E. M.; Santa, J. J. 2019. A mixed integer linear programming formulation for the vehicle routing problem with backhauls, International Journal of Industrial Engineering Computations 10(2): 295–308.

Huang, J.; Jin, L.; Zhang, C. 2017. Mathematical modeling and a hybrid NSGA-II algorithm for process planning problem considering machining cost and carbon emission, Sustainability 9(10): 1769.

Jabir, E.; Panicker, V. V.; Sridharan, R. 2015. Multi-objective optimization model for a green vehicle routing problem, Procedia – Social and Behavioral Sciences 189: 33–39.

Jozefowiez, N.; Semet, F.; Talbi, E.-G. 2009. An evolutionary algorithm for the vehicle routing problem with route balancing, European Journal of Operational Research 195(3): 761–769.

Jozefowiez, N.; Semet, F.; Talbi, E.-G. 2008. Multi-objective vehicle routing problems, European Journal of Operational Research 189(2): 293–309.

Kancharla, S. R.; Ramadurai, G. 2018. Incorporating driving cycle based fuel consumption estimation in green vehicle routing problems, Sustainable Cities and Society 40: 214–221.

Knowles, J.; Corne, D. 1999. The Pareto archived evolution strategy: a new baseline algorithm for Pareto multiobjective optimisation, in Proceedings of the 1999 Congress on Evolutionary Computation – CEC99, 6–9 July 1999, Washington, DC, US, 98–105.

Kundu, P.; Kar, M. B.; Kar, S.; Pal, T.; Maiti, M. 2017. A solid transportation model with product blending and parameters as rough variables, Soft Computing 21(9): 2297–2306.

Lawler, E. L.; Lenstra, J. K.; Kan, A. H. G. R.; Shmoys, D. B. 1985. The Traveling Salesman Problem: a Guided Tour of Combinatorial Optimization. Wiley. 476 p.

Lin, C.; Choy, K. L.; Ho, G. T. S.; Chung, S. H.; Lam, H. Y. 2014. Survey of green vehicle routing problem: past and future trends, Expert Systems with Applications 41(4): 1118–1138.

Liu, R.; Jiang, Z. 2012. The close–open mixed vehicle routing problem, European Journal of Operational Research 220(2): 349–360.

Mardani, A.; Zavadskas, E. K.; Govindan, K.; Senin, A. A.; Jusoh, A. 2016. VIKOR technique: a systematic review of the state of the art literature on methodologies and applications, Sustainability 8(1): 37.

Matl, P.; Hartl, R. F.; Vidal, T. 2018. Workload equity in vehicle routing problems: a survey and analysis, Transportation Science 52(2): 239–260.

Matl, P.; Hartl, R. F.; Vidal, T. 2019a. Leveraging single‐objective heuristics to solve bi‐objective problems: heuristic box splitting and its application to vehicle routing, Networks: an International Journal 73(4): 382–400.

Matl, P.; Hartl, R. F.; Vidal, T. 2019b. Workload equity in vehicle routing: the impact of alternative workload resources, Computers & Operations Research 110: 116–129.

Mohammed, M. A.; Abd Ghani, M. K.; Hamed, R. I.; Mostafa, S. A.; Ibrahim, D. A.; Jameel, H. K.; Alallah, A. H. 2017. Solving vehicle routing problem by using improved k-nearest neighbor algorithm for best solution, Journal of Computational Science 21: 232–240.

Molina, J. C.; Eguia, I.; Racero, J.; Guerrero, F. 2014. Multi-objective vehicle routing problem with cost and emission functions, Procedia – Social and Behavioral Sciences 160: 254–263.

Montoya, A.; Gueret, C.; Mendoza, J. E.; Villegas, J. G. 2016. A multi-space sampling heuristic for the green vehicle routing problem, Transportation Research Part C: Emerging Technologies 70: 113–128.

Murata, T.; Itai, R. 2007. Local search in two-fold EMO algorithm to enhance solution similarity for multi-objective vehicle routing problems, Lecture Notes in Computer Science 4403: 201–215.

Murata, T.; Itai, R. 2005. Multi-objective vehicle routing problems using two-fold EMO algorithms to enhance solution similarity on non-dominated solutions, Lecture Notes in Computer Science 3410: 885–896.

NEO. 2013. Capacitated VRP Instances. Networking and Emerging Optimization (NEO), Malaga, Spain. Available from Internet:

Ombuki, B.; Ross, B. J.; Hanshar, F. 2006. Multi-objective genetic algorithms for vehicle routing problem with time windows, Applied Intelligence 24(1): 17–30.

Pacheco, J.; Marti, R. 2006. Tabu search for a multi-objective routing problem, Journal of the Operational Research Society 57(1): 29–37.

Poonthalir, G.; Nadarajan, R. 2018. A fuel efficient green vehicle routing problem with varying speed constraint (F-GVRP), Expert Systems with Applications 100: 131–144.

Qian, J.; Eglese, R. 2014. Finding least fuel emission paths in a network with time‐varying speeds, Networks: an International Journal 63(1): 96–106.

Qian, J.; Eglese, R. 2016. Fuel emissions optimization in vehicle routing problems with time-varying speeds, European Journal of Operational Research 248(3): 840–848.

Ralphs, T. 2003. Vehicle Routing Data Sets. Lehigh University, Bethlehem, PA, US. Available from Internet:

Ribeiro, R.; Lourenco, H. R. D. 2001. A Multi-Objective Model for a Multi-Period Distribution Management Problem. Social Science Research Network (SSRN). 22 p.

Schrijver, A. 2002. On the history of combinatorial optimization (till 1960), Handbooks in Operations Research and Management Science 12: 1–68.

Siu, W. S. H.; Chan, C.-K.; Chan, H. C. B. 2012. Green cargo routing using genetic algorithms, in International MultiConference of Engineers and Computer Scientists, IMECS 2012, 14–16 March 2012, Kowloon, Hong Kong, 1: 170–175.

Tan, K. C.; Chew, Y. H.; Lee, L. H. 2006. A hybrid multiobjective evolutionary algorithm for solving vehicle routing problem with time windows, Computational Optimization and Applications 34(1): 115–151.

Toro, E. M.; Franco, J. F.; Granada-Echeverri, M.; Guimaraes, F. G. 2017a. A multi-objective model for the green capacitated location-routing problem considering environmental impact, Computers & Industrial Engineering 110: 114–125.

Toro, E. M.; Franco, J. F.; Granada-Echeverri, M.; Guimaraes, F. G.; Rendon, R. A. G. 2017b. Green open location-routing problem considering economic and environmental costs, International Journal of Industrial Engineering Computations 8(2): 203–216.

Turkson, R. F.; Yan, F.; Ali, M. K. A.; Liu, B.; Hu, J. 2016. Modeling and multi-objective optimization of engine performance and hydrocarbon emissions via the use of a computer aided engineering code and the NSGA-II genetic algorithm, Sustainability 8(1): 72.

VRP-REP. 2018. Datasets. Vehicle Routing Problem Repository (VRP-REP). Available from Internet:

Wen, L.; Eglese, R. 2016. Minimizing CO2e emissions by setting a road toll, Transportation Research Part D: Transport and Environment 44: 1–13.

Xiao, Y.; Zhao, Q.; Kaku, I.; Xu, Y. 2012. Development of a fuel consumption optimization model for the capacitated vehicle routing problem, Computers & Operations Research 39(7): 1419–1431.

Zhou, J.; Wang, C.; Zhu, J. 2016. Multi-objective optimization of a spring diaphragm clutch on an automobile based on the non-dominated sorting genetic algorithm (NSGA-II), Mathematical and Computational Applications 21(4): 47.

Zitzler, E.; Laumanns, M.; Thiele, L. 2001. SPEA2: Improving the Strength Pareto Evolutionary Algorithm. TIK-Report 103. Computer Engineering and Networks Laboratory (TIK), Swiss Federal Institute of Technology (ETH) Zurich, Switzerland. 21 p.