Variable Neighborhood Decomposition Search

The recent Variable Neighborhood Search (VNS) metaheuristic combines local search with systematic changes of neighborhood in the descent and escape from local optimum phases. When solving large instances of various problems, its efficiency may be enhanced through decomposition. The resulting two level VNS, called Variable Neighborhood Decomposition Search (VNDS), is presented and illustrated on the p-median problem. Results on 1400, 3038 and 5934 node instances from the TSP library show VNDS improves notably upon VNS in less computing time, and gives much better results than Fast Interchange (FI), in the same time that FI takes for a single descent. Moreover, Reduced VNS (RVNS), which does not use a descent phase, gives results similar to those of FI in much less computing time.