A Meta-Heuristic Factory for Vehicle Routing Problems

Abstract

This paper presents a generic technique for improving constraint-based heuristics through the discovery of meta-heuristics. The idea is to represent a family of “push/pull” algorithms, based on inserting and removing tasks in a current solution, with an algebra and let a learning algorithm search for the best possible algebraic term (which represents a hybrid algorithm), for a given set of problems and an optimization criterion. This paper describes an application of this idea using vehicle routing with time windows (VRPTW) as the domain example, although this approach can be applied to many other problems which can be seen as the assignment of tasks to resources (generalized assignments). We suppose that a domain-dependent (constraint-based) algorithm has been built, which is able to insert and remove tasks and handle the domain-specific constraints. Our goal is to improve such an algorithm with techniques like LDS (Limited Discrepancy Search), LNS (Large Neighborhood Search), ejection trees or chains, which can be described in a generic manner using the insertion and deletion operations. We show that the automatic tuning of the best hybrid combination of such techniques yields a better solution than hand-tuning, with considerably less effort. The contribution of the paper is thus twofold: we demonstrate a combination of meta-heuristics that yields new best-known results on the Solomon benchmarks, and we provide with a method to automatically adjust this combination to handle problems with different sizes, complexity and optimization objectives.