A Beginner’s Introduction to Iterated Local Search

The importance of high performance algorithms for tackling NP-hard optimization problems cannot be understated, and in many practical cases the most successful methods are metaheuristics. When designing a metaheuristic, it is preferable that it be simple, both conceptually and in practice. Naturally, it also must be effective, and if possible, general purpose. Iterated local search (ILS) is such a metaheuristic; its essence can be given in a nut-shell: one iteratively builds a sequence of solutions generated by an embedded heuristic, leading to far better solutions than if one were to use repeated random trials of that heuristic. This simple idea [4] has a long history, and its rediscovery by many authors has lead to many different names for ILS like iterated descent [3], large-step Markov chains [14], iterated Lin-Kernighan [7], chained local optimization [13], or combinations of these [1] ... Readers interested in these historical developments should consult the review [8]. For us, there are two main points that make an algorithm an ILS: (i) there is a single chain that is followed; (ii) the search for better solutions occurs in a reduced space defined by the output of an embedded heuristic. In practice, local search has been the most frequently used embedded heuristic, but in fact any optimizer can be used, be-it deterministic or not.