Sequential search and its application to vehicle-routing problems

Local search is the most frequently used heuristic technique for solving combinatorial optimization problems. It is also the basis for modern metaheuristics, like, e.g., Tabu Search, and Variable Neighborhood Search. The paper introduces sequential search as a generic technique for the efficient exploration of local-search neighborhoods. One of its key concepts is the systematic decomposition of moves, which allows pruning within local search based on associated partial gains. The application of theoretical concepts to several well-known neighborhoods of the vehicle-routing problem (VRP) is demonstrated. Computational tests show substantial speedup factors, e.g., up to 10 000 for the 3-opt* neighborhood. This underlines the superiority of sequential search over straightforward techniques in the VRP context.