Skip to main content
SpringerLink
Log in

Heuristics and memetic algorithm for the two-dimensional loading capacitated vehicle routing problem with time windows

  • Original Paper
  • Published:
Central European Journal of Operations Research Aims and scope Submit manuscript

Abstract

This work deals with a new combinatorial optimization problem, the two-dimensional loading capacitated vehicle routing problem with time windows which is a realistic extension of the well known vehicle routing problem. The studied problem consists in determining vehicle trips to deliver rectangular objects to a set of customers with known time windows, using a homogeneous fleet of vehicles, while ensuring a feasible loading of each vehicle used. Since it includes NP-hard routing and packing sub-problems, six heuristics are firstly designed to quickly compute good solutions for realistic instances. They are obtained by combining algorithms for the vehicle routing problem with time windows with heuristics for packing rectangles. Then, a Memetic algorithm is developed to improve the heuristic solutions. The quality and the efficiency of the proposed heuristics and metaheuristic are evaluated by adding time windows to a set of 144 instances with 15–255 customers and 15–786 items, designed by Iori et al. (Transport Sci 41:253–264, 2007) for the case without time windows.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Alvarez-Valdes R, Parreno F, Tamarit JM (2005) A GRASP algorithm for constrained two-dimensional non guillotine cutting problems. J Oper Res Soc 414–425

  • Alvarenga GB, Mateus GR, Tomi G (2007) A genetic and set partitioning two-phase approch for the vehicle routing problem with time windows. Comput Oper Res 34: 1561–1584

    Article  Google Scholar 

  • Alvarez-Valdes R, Parreno F, Tamarit JM (2007) A tabu search algorithm for two-dimensional non guillotine cutting problems. Eur J Oper Res 183: 1167–1182

    Article  Google Scholar 

  • Alvarez-Valdes R, Parreno F, Tamarit JM (2008) Reactive GRASP for the strip-packing problem. Comput Oper Res 35(4): 1065–1083

    Article  Google Scholar 

  • Belov G, Scheithauer G, Mukhacheva EA (2008) One-dimensional heuristics adapted for two-dimensional rectangular strip packing. J Oper Res Soc 59(6): 823–832

    Article  Google Scholar 

  • Ben Messaoud S (2004) Caractérisation, modélisation et algorithmes pour des problèmes de découpe guillotine. PhD thesis, University of Technology of Troyes, France (in French)

  • Berger J, Barkaoui M, Bräysy O (2003) A route-directed hybrid genetic approach for the vehicle routing problem with time windows. Inf Syst Oper Res 41: 179–194

    Google Scholar 

  • Blanton JL, Wainwright RL (1993) Multiple vehicle routing with time and capacity constraints using genetic algorithms. In: Proceedings of the fifth international conference on genetic algorithms. Morgan Kaufmann, San Francisco, pp 452–459

  • Bortfeldt A (2006) A genetic algorithm for the two-dimensional strip packing problem with rectangular pieces. Eur J Oper Res 172(3): 814–837

    Article  Google Scholar 

  • Boschetti MA, Mingozzi A (2003) The two-dimensional finite bin packing problem Part I: new lower bounds for the oriented case. 4OR 1: 27–42

    Google Scholar 

  • Boschetti MA, Mingozzi A (2003) The two-dimensional finite bin packing problem, Part II: new lower and upper bounds. 4OR 1: 137–147

    Google Scholar 

  • Bräysy O, Gendreau M (2005) Vehicle routing problem with time windows, part i: heuristics. INFORMS J Comput 39: 119–139

    Google Scholar 

  • Bräysy O, Gendreau M (2005) Vehicle routing problem with time windows, part ii: metaheuristics. INFORMS J Comput 39: 119–139

    Google Scholar 

  • Burke EK, Kendall G, Whitwell G (2004) A new placement heuristic for the orthogonal stock-cutting problem. Oper Res 54(4): 655–671

    Article  Google Scholar 

  • Burke EK, Kendall G, Whitwell G (2009) A simulated annealing enhancement of the best-fit heuristic for the orthogonal stock cutting problem. INFORMS J Comput 21(3): 505–516

    Article  Google Scholar 

  • Chazelle B (1983) The bottom left bin packing heuristic: an efficient algorithm. IEEE Trans Comput, 697–707

  • Christofides N, Whitlock C (1977) An algorithm for two-dimensional cutting problems. Oper Res 25: 30–40

    Article  Google Scholar 

  • Clautiaux F (2005) Bornes inférieures et méthodes exactes pour le problème de bin-packing en deux dimensions avec orientations fixes. PhD Thesis, Université de Technologie de Compiègne

  • Conover WJ (1999) Practical nonparametric statistics. Wiley, New York

    Google Scholar 

  • Fekete S, Schepers J (2001) New classes of fast lower bounds for bin packing problems. Math Program 91: 11–31

    Google Scholar 

  • Fekete S, Schepers J (2004) A general framework for bounds for higher-dimensional orthogonal packing problems. Math Methods Oper Res 60: 311–329

    Article  Google Scholar 

  • Fekete S, Schepers J, Vander Veen J (2007) Exact solution of the two dimensional finite bin packing problem. Oper Res 55(3): 569–587

    Article  Google Scholar 

  • Fuellerer G, Doerner KF, Hartl FH, Iori M (2009) Ant colony optimization for the two-dimensional loading vehicle routing problem. Comput Oper Res 36: 655–673

    Article  Google Scholar 

  • Gendreau M, Iori M, Laporte G, Martello S (2007) A tabu search heuristic for the vehicle routing problem with two-dimensional loading constraints. Networks 51: 4–18

    Article  Google Scholar 

  • Hashimoto H, Yagiura M, Imahori S, Ibaraki T (2010) Recent progress of local search in handling the time window constraints of the vehicle routing problem. 4OR 8(3): 221–238

    Article  Google Scholar 

  • Iori M, Martello S (2010) Routing problems with loading constraints. TOP 18: 4–27

    Article  Google Scholar 

  • Iori M, Salazar-Gonzalez JJ, Vigo D (2007) An exact approach for the vehicle routing problem with two-dimensional loading constraints. Transport Sci 41: 253–264

    Article  Google Scholar 

  • Khebbache S, Prins C, Yalaoui A (2008) Iterated local search algorithm for the constrained two-dimensional non-guillotine cutting stock problem. J Ind Syst Eng 2: 164–179

    Google Scholar 

  • Kindervater GAP, Savelsbergh MWP (1997) Vehicle routing: handling edge exchanges. In: Aarts EHL, Lenstra JK (eds) Local search in combinatorial optimization. Wiley, Chichester, pp 337–360

    Google Scholar 

  • Kontoravdis G, Bard J (1995) A GRASP for the vehicle routing problem with time windows. ORSA J Comput 7: 10–23

    Article  Google Scholar 

  • Labadi N, Prins C, Reghioui M (2008) A memetic algorithm for the vehicle routing problem with time windows. RAIRO Oper Res 42: 415–431

    Article  Google Scholar 

  • Lodi A, Martello S, Vigo D (1999) Heuristic and metaheuristic approaches for a class of two-dimensional bin packing problems. INFORMS J Comput 11: 345–357

    Article  Google Scholar 

  • Martello S, Vigo D (1998) Exact solution of the two-dimensional finite bin packing problem. Manage Sci 44: 388–399

    Article  Google Scholar 

  • Moscato P (1999) Memetic algorithms: a short introduction. In: Come D, Dorigo M, Glover F (eds) New ideas in optimization. McGraw-Hill, New York, pp 219–234

    Google Scholar 

  • Moura A (2008) A multi-objective genetic algorithm for the vehicle routing with time windows and loading problem. In: Bortfeldt A, Homberger J, Kopfer H, Pankratz G, Stangmeier R (eds) Intelligent decision support. Gabler, Wiesbaden, pp 187–201

    Chapter  Google Scholar 

  • Moura A, Oliveira JF (2008) An integrated approach to the routing and loading problems. OR Spectrum, doi:10.1007/s00291-008-0129-4

  • Pisinger D, Sigurd MM (2007) Using decomposition techniques and constraint programming for solving the two-dimensional bin packing problem. INFORMS J Comput 19: 36–51

    Article  Google Scholar 

  • Pisinger D, Sigurd M (2007) Using decomposition techniques and constraint programming for solving the two-dimensional bin-packing problem. INFORMS J Comput 19(1): 36–51

    Article  Google Scholar 

  • Potvin JY, Bengio S (1996) The vehicle routing with time windows Part II genetic search Informs. J Comput 8: 165–172

    Google Scholar 

  • Potvin JY, Rousseau JM (1995) An exchange heuristic for routing problems with time windows. J Oper Res Soc 46: 1433–1446

    Google Scholar 

  • Prins C (2004) A simple and effective evolutionary algorithm for the vehicle routing problem. Comput Oper Res 31: 1985–2002

    Article  Google Scholar 

  • Reinelt G (1991) TSPLIB-A travelling salesman problem library. ORSA J Comput 3: 376–384

    Article  Google Scholar 

  • Rochat Y, Taillard ED (1995) Probabilistic diversification algorithm for the vehicle routing problem. J Heuristics, 147–167

  • Russell RA (1995) Hybrid heuristics for the vehicle routing problem with time windows. Transport Sci 29: 156–166

    Article  Google Scholar 

  • Solomon MM (1987) Algorithms for the vehicle routing and scheduling problem with time window constraints. Oper Res 35: 254–265

    Article  Google Scholar 

  • Tan KC, Lee LH, Ou K (2001) Hybrid genetic algorithms in solving ehicle routing problems with time window constraints. Asia-Pacific J Oper Res 18: 121–130

    Google Scholar 

  • Tarantilis CD, Zachariadis E, Kiranoudis CT (2009) A hybrid metaheuristic algorithm for the integrated vehicle routing and three dimensional container-loading problem. IEEE Trans Intell Transport Syst 10(2): 255–271

    Article  Google Scholar 

  • Toth P, Vigo D (2002) An overview of vehicle routing problems. In: Toth P, Vigo D (eds) The vehicle routing problem, SIAM monographs on discrete mathematics and applications. Philadelphia, PA, pp 1–24

    Chapter  Google Scholar 

  • Zachariadis E, Tarantilis CD, Kiranoudis CT (2009) A guided tabu search for the vehicle routing problem with two-dimensional loading constraints. Eur J Oper Res 195: 729–743

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. MGSI/IUT de Montreuil, 140, rue de la Nouvelle France, 93100, Montreuil, France

    Selma Khebbache-Hadji

  2. ICD-LOSI, University of Technology of Troyes, BP 2060, 10010, Troyes Cedex, France

    Christian Prins & Alice Yalaoui

  3. ENSA de Tétouan (ELI) Mhannech II, BP 2121, Tétouan, Morocco

    Mohamed Reghioui

Authors
  1. Selma Khebbache-Hadji
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Christian Prins
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Alice Yalaoui
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Mohamed Reghioui
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Selma Khebbache-Hadji.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Khebbache-Hadji, S., Prins, C., Yalaoui, A. et al. Heuristics and memetic algorithm for the two-dimensional loading capacitated vehicle routing problem with time windows. Cent Eur J Oper Res 21, 307–336 (2013). https://doi.org/10.1007/s10100-011-0204-9

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10100-011-0204-9

Keywords

Search

Navigation