Hybridization Based on Large Neighborhood Search

Abstract

The type of algorithm addressed in this chapter is based on the following general idea. Given a valid solution to the tackled problem instance—henceforth called the incumbent solution—first, destroy selected parts of it, resulting in a partial solution. Then apply some other, possibly exact, technique to find the best valid solution on the basis of the given partial solution, that is, the best valid solution that contains the given partial solution. Thus, the destroy-step defines a large neighborhood, from which a best (or nearly best) solution is determined not by naive enumeration but by the application of a more effective alternative technique. In our examples here, we mainly consider a MIP solver for this purpose, which is applied to a MIP model for the original problem in which the variables corresponding to the given partial solution get respective fixed values preassigned. The motivating aspect for this concept is the same as that described in the context of hybrid algorithms based on instance reduction in Chapter 3: Even though it might be unfeasible to apply a MIP solver to the original problem instance, the solver might be particularly effective in solving the reduced ILP model in which a part of the variables has fixed values.