Soft Computing

, Volume 21, Issue 17, pp 5159–5178 | Cite as

A bi-criteria evolutionary algorithm for a constrained multi-depot vehicle routing problem

  • Vikas Agrawal
  • Constance Lightner
  • Carin Lightner-Laws
  • Neal Wagner
Methodologies and Application


Most research about the vehicle routing problem (VRP) does not collectively address many of the constraints that real-world transportation companies have regarding route assignments. Consequently, our primary objective is to explore solutions for real-world VRPs with a heterogeneous fleet of vehicles, multi-depot subcontractors (drivers), and pickup/delivery time window and location constraints. We use a nested bi-criteria genetic algorithm (GA) to minimize the total time to complete all jobs with the fewest number of route drivers. Our model will explore the issue of weighting the objectives (total time vs. number of drivers) and provide Pareto front solutions that can be used to make decisions on a case-by-case basis. Three different real-world data sets were used to compare the results of our GA vs. transportation field experts’ job assignments. For the three data sets, all 21 Pareto efficient solutions yielded improved overall job completion times. In 57 % (12/21) of the cases, the Pareto efficient solutions also utilized fewer drivers than the field experts’ job allocation strategies.


Vehicle routing problem Bi-criteria genetic algorithm Pareto front Multi-depot transportation problem  Hard and soft time windows 


Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Vikas Agrawal
    • 1
  • Constance Lightner
    • 2
  • Carin Lightner-Laws
    • 3
  • Neal Wagner
    • 4
  1. 1.Jacksonville UniversityJacksonvilleUSA
  2. 2.Fayetteville State UniversityFayettevilleUSA
  3. 3.Clayton State UniversityMorrowUSA
  4. 4.MIT Lincoln LaboratoryLexingtonUSA

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