Heuristics for vehicle routing problems: Sequence or set optimization?

TL;DR

This paper explores a structural decomposition approach for the CVRP, combining assignment and sequencing decisions, introducing intermediate search techniques, and achieving new best solutions for small instances.

Contribution

It introduces an intermediate search space and novel speed-up techniques for CVRP, improving solution accuracy and efficiency over classic methods.

Findings

Significant solution improvements for small CVRP instances.

Effective combination of assignment and sequencing optimization.

New best solutions for instances with as few as 256 customers.

Abstract

We investigate a structural decomposition for the capacitated vehicle routing problem (CVRP) based on vehicle-to-customer "assignment" and visits "sequencing" decision variables. We show that an heuristic search focused on assignment decisions with a systematic optimal choice of sequences (using Concorde TSP solver) during each move evaluation is promising but requires a prohibitive computational effort. We therefore introduce an intermediate search space, based on the dynamic programming procedure of Balas & Simonetti, which finds a good compromise between intensification and computational efficiency. A variety of speed-up techniques are proposed for a fast exploration: neighborhood reductions, dynamic move filters, memory structures, and concatenation techniques. Finally, a tunneling strategy is designed to reshape the search space as the algorithm progresses. The combination of these techniques within a classical local search, as well as in the unified hybrid genetic search (UHGS) leads to significant improvements of solution accuracy. New best solutions are found for surprisingly small instances with as few as 256 customers. These solutions had not been attained up to now with classic neighborhoods. Overall, this research permits to better evaluate the respective impact of sequence and assignment optimization, proposes new ways of combining the optimization of these two decision sets, and opens promising research perspectives for the CVRP and its variants.