Neighborhoods Revisited: An Experimental Investigation into the Effectiveness of Variable Neighborhood Descent for Scheduling

Variable neighborhood search (VNS) systematically exploits the idea to alternate between neighborhoods within a local search [4]. Several VNS variants have been described so far and many of them have been applied with success to a variety of combinatorial optimization problems; see [3, 4] for an overview. Yet, even though scheduling is a central problem in production environments, we are not aware of any VNS applications to scheduling problems. In this paper we focus on the application of a particular VNS technique called variable neighborhood descent (VND) to scheduling problems in which a solution can be represented as a single permutation of all jobs. This class of scheduling problems includes single machine problems as well as a variety of multiple machine problems. In this abstract, we present some results of VND when applied to single machine problems minimizing the total tardiness problem, the total weighted tardiness, and the sum of weighted completion times, as well as to the permutation flow shop problem. In addition we investigate whether VND local search performs better than a single neighborhood local search algorithm when it is embedded in a metaheuristic like iterated local search (ILS) [6].