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**Exact hybrid algorithms for solving a bi-objective vehicle routing problem.**
*(English)*
Zbl 1245.90010

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:

90B06 | Transportation, logistics and supply chain management |

90C27 | Combinatorial optimization |

90C29 | Multi-objective and goal programming |

90B10 | Deterministic network models in operations research |

90C57 | Polyhedral combinatorics, branch-and-bound, branch-and-cut |

### Keywords:

capacitated vehicle routing problem; distance constraints; multiobjective combinatorial optimization; branch-and-cut; TSPLIB
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\textit{P. Reiter} and \textit{W. J. Gutjahr}, CEJOR, Cent. Eur. J. Oper. Res. 20, No. 1, 19--43 (2012; Zbl 1245.90010)

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