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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 $\epsilon$-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 90C27 Combinatorial optimization 90C29 Multi-objective programming; goal programming 90B10 Network models, deterministic (optimization) 90C57 Polyhedral combinatorics, branch-and-bound, branch-and-cut