Creating very large scale neighborhoods out of smaller ones by compounding moves

This paper discusses neighborhood search algorithms where the size of the neighborhood is “verylarge” with respect to the size of the input data. We concentrate on such a very large scale neigh-borhood (VLSN) search technique based on compounding independent moves (CIM) such as 2-opts,swaps, and insertions. We present a systematic way of creating and searching CIM neighborhoodsfor routing problems with side constraints. For such problems, the exact search of the CIM neigh-borhood becomes NP-hard. We introduce a multi-label shortest path algorithm for searching theseneighborhoods heuristically. Results of a computational study on the vehicle routing problem withcapacity and distance restrictions shows that CIM algorithms are very competitive approaches forsolving vehicle routing problems. Overall, the solutions generated by the CIM algorithm have thebest performance among the current solution methodologies in terms of percentage deviation fromthe best-known solutions for large-scale capacitated VRP instances.