  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.
