Central European Journal of Operations Research

, Volume 20, Issue 1, pp 19–43

Exact hybrid algorithms for solving a bi-objective vehicle routing problem

Original Paper

DOI: 10.1007/s10100-010-0158-3

Cite this article as:
Reiter, P. & Gutjahr, W.J. Cent Eur J Oper Res (2012) 20: 19. doi:10.1007/s10100-010-0158-3


The paper investigates a capacitated vehicle routing problem with two objectives: (1) minimization of total travel cost and (2) minimization of the length of the longest route. We present algorithmic variants for the exact determination of the Pareto-optimal solutions of this bi-objective problem. Our approach is based on the adaptive ε-constraint method. For solving the resulting single-objective subproblems, we apply a branch-and-cut technique, using (among others) a novel implementation of Held-Karp-type bounds. Incumbent solutions are generated by means of a single-objective genetic algorithm and, alternatively, by the multi-objective NSGA-II algorithm. Experimental results for a benchmark of 54 test instances from the TSPLIB are reported.


Capacitated vehicle routing problemDistance constraintsMultiobjective combinatorial optimizationBranch-and-cutGenetic algorithmsNSGA-II

Supplementary material

10100_2010_158_MOESM1_ESM.pdf (60 kb)
ESM 1 (PDF 60 kb)

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Department of Statistics and Decision Support SystemsUniversity of ViennaViennaAustria