On the Effects of Window-Limits on the Distance Profiles of Permutation Neighborhood Operators

Local search algorithms, such as simulated annealing, tabu search, and local hill climbers attempt to optimize a solution to a problem by making locally improving modifications to a candidate solution. They rely on a neighborhood operator to restrict the search to a typically small set of possible successor states. The genetic algorithm mutation operator, likewise, enables the exploration of the local neighborhood of candidate solutions within the genetic algorithm’s population. In this paper, we profile window-limited variations of several commonly employed neighborhood operators for problems in which candidate solutions are represented as permutations. Window-limited neighborhood operators enable tuning the size of the local neighborhood–e.g., to balance cost of search step against likelihood of getting stuck in a local optima. Window limits potentially can even be adjusted dynamically during search–e.g., to give a stagnated search a “kick.” We provide profiles of the distance characteristics of window-limited variations of several of the more common permutation neighborhood operators.