Structured vs. Unstructured Large Neighborhood Search: A Case Study on Job-Shop Scheduling Problems with Earliness and Tardiness Costs

Abstract

Large Neighborhood Search (LNS) [8] is a local search paradigm based on two main ideas to define and search large neighborhoods. The first key idea of LNS is to define its neighborhoods by fixing a part of an existing solution. The elements of the solution that are fixed are usually explicit or implicit variables of the model. For example, in a scheduling model, one may choose to fix the values of the start times of each activity (explicit variables) or one may add additional constraints that force one activity to be scheduled before another (implicit disjunctive variables). The rest of the variables are released: they are free to change values. The neighborhood is hence defined by all possible extensions of the fixed partial solution. Because a number of variables are released at a time, the neighborhoods defined are usually large, larger than typical local search neighborhoods.