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We consider a family of Rich Vehicle Routing Problems (RVRP) which have theparticularity to combine a heterogeneous fleet with other attributes, such asbackhauls, multiple depots, split deliveries, site dependency, open routes,duration limits, and time windows. To efficiently solve these problems, wepropose a hybrid metaheuristic which combines an iterated local search withvariable neighborhood descent, for solution improvement, and a set partitioningformulation, to exploit the memory of the past search. Moreover, we investigatea class of combined neighborhoods which jointly modify the sequences of visitsand perform either heuristic or optimal reassignments of vehicles to routes. Tothe best of our knowledge, this is the first unified approach for a large classof heterogeneous fleet RVRPs, capable of solving more than 12 problem variants.The efficiency of the algorithm is evaluated on 643 well-known benchmarkinstances, and 71.70\% of the best known solutions are either retrieved orimproved. Moreover, the proposed metaheuristic, which can be considered as amatheuristic, produces high quality solutions with low standard deviation incomparison with previous methods. Finally, we observe that the use of combinedneighborhoods does not lead to significant quality gains. Contrary tointuition, the computational effort seems better spent on more intensive routeoptimization rather than on more intelligent and frequent fleet re-assignments.

A Hybrid Heuristic for a Broad Class of Vehicle Routing Problems with Heterogeneous Fleet