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Zbl 1245.90010
Reiter, Peter; Gutjahr, Walter J.
Exact hybrid algorithms for solving a bi-objective vehicle routing problem.
(English)
[J] CEJOR, Cent. Eur. J. Oper. Res. 20, No. 1, 19-43 (2012). ISSN 1435-246X; ISSN 1613-9178/e

Summary: 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 $\varepsilon$-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.
MSC 2000:
*90B06 Transportation, logistics
90C27 Combinatorial programming
90C29 Multi-objective programming, etc.
90B10 Flows in networks
90C57 Polyhedral combinatorics, branch-and-bound, branch-and-cut

Keywords: capacitated vehicle routing problem; distance constraints; multiobjective combinatorial optimization; branch-and-cut; {\tt TSPLIB}

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