A Green Competitive Vehicle Routing Problem under Uncertainty Solved by an Improved Differential Evolution Algorithm

Document Type : Original Article

Authors

1 Department of Industrial Engineering, Tehran Central Branch, Islmic Azad University, Tehran, Iran

2 School of Industrial Engineering, College of Engineering, University of Tehran, Tehran, Iran

3 Arts et Métiers ParisTech, LCFC, Metz, France

4 Department of Industrial Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran

5 Department of Industrial and Systems Engineering, Isfahan University of Technology, Isfahan, Iran

Abstract

Regarding the development of distribution systems in the recent decades, fuel consumption of trucks has increased noticeably, which has a huge impact on greenhouse gas emissions. For this reason, the reduction of fuel consumption has been one of the most important research areas in the last decades. The aim of this paper is to propose a robust mathematical model for a variant of a vehicle routing problem (VRP) to optimize sales of distributers, in which the time of distributor service to customers is uncertain. To solve the model precisely, the improved differential evolution (IDE) algorithm is used and obtained results were compared with the result of a particle swarm optimization (PSO) algorithm. The results indicate that the IDE algorithm is able to obtain better solutions in solving large-sized problems; however, the computational time is worse than PSO.

Keywords


 
6. REFERENCES

1. Fallah, M., Mohajeri, A. and Barzegar-Mohammadi, M., “A New
Mat hematical Model To Optimize A Green Gas Network: A Case
St udy”, International Journal of Engineering-Transactions A:
Basics, Vol. 30, No. 7, (2017), 1029–1037.
2. Sbihi, A. and Eglese, R.W., “Combinatorial optimization and
green logist ics”, Annals of Operations Research, Vol. 175, No.
1, (2010), 159–175.  
3. Norouzi, N., Sadegh-Amalnick, M. and Tavakkoli-Moghaddam,
R., “Modified particle swarm optimization in a t ime-dependent
vehicle rout ing problem: minimizing fuel consumption”,
Optimization Letters, Vol. 11, No. 1, (2017), 121–134.
4. Xiao, Y., Zhao, Q., Kaku, I. and Xu, Y., “Development of a fuel
consumption opt imization model for t he capacit ated vehicle
rout ing problem”, Computers & Operations Research, Vol. 39,
No. 7, (2012), 1419–1431.
5. Arab, R., Ghaderi, S.F. and Tavakkoli-Moghaddam, R., “Solving
a New Mult i-objective Inventory-Routing Problem by a Nondominat
ed Sorting Genetic Algorithm”, International Journal of
Engineering - Transactions A: Basics, Vol. 31, No. 4, (2018),
588–596.  
6. Tavakkoli-Moghaddam, R., Gazanfari, M., Alinaghian, M.,
Salamat bakhsh, A. and Norouzi, N., “A new mathematical model
for a competitive vehicle routing problem wit h t ime windows
solved by simulat ed annealing”, Journal of manufacturing
systems, Vol. 30, No. 2, (2011), 83–92.  
7. Norouzi, N., Tavakkoli-Moghaddam, R., Ghazanfari, M.,
Alinaghian, M. and Salamatbakhsh, A., “A new mult i-objective
competitive open vehicle routing problem solved by particle
swarm opt imization”, Networks and Spatial Economics, Vol. 12,
No. 4, (2012), 609–633.  
8. Salamat bakhsh-Varjovi, A., Tavakkoli-Moghaddam, R.,
Alinaghian, M. and Najafi, E., “Robust  Periodic Vehicle Routing
Problem wit h T ime Windows under Uncertainty: An Efficient
Algorit hm”, KSCE Journal of Civil Engineering, Vol. 22, No.
11, (2018), 4626–4634.  
9. Erera, A.L., Morales, J.C. and Savelsbergh, M., “The vehicle
rout ing problem wit h st ochastic demand and duration
const raints”, Transportation Science, Vol. 44, No. 4, (2010),
474–492.  

 
10. Qi, M., Qin, K., Zhao, Y. and Liu, J., “A st udy of t he vehicle
scheduling problem for vict im t ransportation”, International
Journal of Management Science and Engineering
Management, Vol. 8, No. 4, (2013), 276–282.  
11. Goodson, J.C., Ohlmann, J.W. and Thomas, B.W., “Cyclic-order
neighborhoods wit h application t o t he vehicle routing problem
wit h st ochastic demand”, European Journal of Operational
Research, Vol. 217, No. 2, (2012), 312–323.  
12. Mulvey, J.M., Vanderbei, R.J. and Zenios, S.A., “Robust
opt imization of large-scale systems”, Operations Research, Vol.
43, No. 2, (1995), 264–281.
13. Hamidieh, A., Arshadikhamseh, A. and Fazli-Khalaf, M., “A
Robust  Reliable Closed Loop Supply Chain Net work Design
under Uncert ainty: A Case St udy in Equipment  T raining
Cent ers”, International Journal of Engineering-Transactions
A: Basics, Vol. 31, No. 4, (2017), 648–658.  
14. Lenst ra, J.K. and Kan, A.R., “Complexity of vehicle rout ing and
scheduling problems”, Networks, Vol. 11, No. 2, (1981), 221–
227.
15. Jia, H., Li, Y., Dong, B. and Ya, H., “An improved t abu search
approach t o vehicle rout ing problem”, Procedia-Social and
Behavioral Sciences, Vol. 96, (2013), 1208–1217.  
16. Fazel Zarandi, M.H., Hemmati, A., Davari, S. and Turksen, I.B.,
“A simulat ed annealing algorithm for routing problems with
fuzzy const rains”, Journal of Intelligent & Fuzzy Systems, Vol.
26, No. 6, (2014), 2649–2660.  
17. Goksal, F.P., Karaoglan, I. and Altiparmak, F., “A hybrid discrete
part icle swarm opt imization for vehicle rout ing problem with
simult aneous pickup and delivery”, Computers & Industrial
Engineering, Vol. 65, No. 1, (2013), 39–53.  
18. St orn, R. and Price, K., “Differential evolution–a simple and
efficient  heurist ic for global opt imization over cont inuous
spaces”, Journal of global optimization, Vol. 11, No. 4, (1997),
341–359.  
19. Qin, A.K. and Sugant han, P.N., “Self-adapt ive differential
evolut ion algorithm for numerical optimization”, In 2005 IEEE
congress on evolut ionary computation, Vol. 2, IEEE, (2005),
1785–1791.  
20. Cordeau, J.F., Gendreau, M. and Laport e, G., “A t abu search
heurist ic for periodic and mult i‐depot vehicle routing problems”,
Networks: An International Journal, Vol. 30, No. 2, (1997),
105–119.