This paper presents a heuristic for solving very large routing problems (thousands of customers and hundreds of vehicles) with side constraints such as time windows. When applied to traditional benchmarks (Solomon's), we obtain high quality results with short resolution time (a few seconds). We also introduce a LDS (Limited Discrepancy Search) variation that produces state-of-the-art results. The heart of this heuristic is a combination of a look-ahead insertion algorithm, an incremental local optimization scheme and a constraint solver for constrained traveling salesman problems. The incrementality means that instead of visiting some large neighborhood after an initial solution has been found, a limited number of moves is examined, after each insertion, on the partial solution. This incremental version is not only faster, it also yields better results than using local optimization once a full solution has been built. We also show how additional constraints can be used in order to guide the insertion process. Because of its use of separate CP (Constraint Programming) modules, this method is flexible and may be used to solve large dispatching problems that include many additional constraints such as setup times (asymmetrical distance) or skill matching.
