Very Large-Scale Neighborhood Search: Overview and Case Studies on Coloring Problems

Two key issues in local search algorithms are the definition of a neighborhood and the way to examine it. In this chapter we consider techniques for examining very large neighborhoods, in particular, ways for exactly searching them. We first illustrate such techniques using three paradigmatic examples. In the largest part of the chapter, we focus on the development and experimental study of very largescale neighborhood search algorithms for two coloring problems. The first example concerns the well-known (vertex) graph coloring problem. Despite initial promising results on the use of very large-scale neighborhoods, our final conclusion was negative: the usage of the proposed very large-scale neighborhoods did not help to improve the performance of effective stochastic local search algorithms. The second example, the graph set T-coloring problem, yielded more positive results. In this case, a very large-scale neighborhood that was specially tailored for this problem and that can be efficiently searched, resulted to be an essential component of a new state-of-the-art algorithm for various instance classes.