Local search

Abstract

Local search methods start from any feasible solution and visit other (feasible or infeasible) solutions, until a feasible solution that cannot be further improved is found. Local improvements are evaluated with respect to neighboring solutions that can be obtained by slight modifications applied to a solution being visited. We introduce in this chapter the concept of solution representation, which is instrumental in the design and implementation of local search methods. We also define neighborhoods of combinatorial optimization problems and moves between neighboring solutions. We illustrate the definition of a neighborhood by a number of examples for different problems. Local search methods are introduced and different implementation issues are discussed, such as neighborhood search strategies, quick cost updates, and candidate list strategies