Adjusting the order crossover operator for capacitated vehicle routing problems

Abstract

The capacitated vehicle routing problem is a much studied combinatorial optimization problem, reflecting its practical importance within areas such as logistics. The problem is computationally intractable, and heuristics are commonly applied for solving large instances. Among the best heuristics available is a hybrid genetic search that consists of mechanisms from evolutionary algorithms and a range of local search operators. This heuristic applies an order crossover operator that takes as input two existing solutions and produces as output a new solution for the search to explore. An open-source implementation of the heuristic is available, in which the order crossover operator represents 1.4% of the code. This work discusses potential short-comings of the traditional order crossover operator and proposes an adjusted operator. The new operator is evaluated on standard benchmark test instances, and is shown to reduce the gaps to best-known solutions by 4.2%.