Iterated Local Search or ILS for short, is a stochastic global search optimization algorithm.
It is related to or an extension of stochastic hill climbing and stochastic hill climbing with random starts.
Stochastic hill climbing is a local search algorithm that involves making random modifications to an existing solution and accepting the modification only if it results in better results than the current working solution.
Local search algorithms in general can get stuck in local optima. One approach to address this problem is to restart the search from a new randomly selected starting point. The restart procedure can be performed many times and may be triggered after a fixed number of function evaluations or if no further improvement is seen for a given number of algorithm iterations. This algorithm is called stochastic hill climbing with random restarts. Iterated local search is similar to stochastic hill climbing with random restarts, except rather than selecting a random starting point for each restart, a point is selected based on a modified version of the best point found so far during the broader search.
The perturbation of the best solution so far is like a large jump in the search space to a new region, whereas the perturbations made by the stochastic hill climbing algorithm are much smaller, confined to a specific region of the search space. This allows the search to be performed at two levels. The hill climbing algorithm is the local search for getting the most out of a specific candidate solution or region of the search space, and the restart approach allows different regions of the search space to be explored.
In this way, the algorithm Iterated Local Search explores multiple local optima in the search space, increasing the likelihood of locating the global optima.
The Iterated Local Search was proposed for combinatorial optimization problems, such as the traveling salesman problem (TSP), although it can be applied to continuous function optimization by using different step sizes in the search space: smaller steps for the hill climbing and larger steps for the random restart.