A Dynamic Model of Tabu Search for the Job-Shop Scheduling Problem

Although tabu search is one of the most effective meta-heuristics for solving the job-shop scheduling problem (JSP), very little is known about why this approach works so well and under what conditions it excels. Our goal is to develop models of tabu search algorithms for the JSP that answer these and other related research questions. We previously demonstrated that the mean distance between random local optima and the nearest optimal solution, denoted lopt-opt, is highly correlated with problem difficulty for a well-known tabu search algorithm for the JSP introduced by Taillard. In this paper, we discuss various shortcomings of the lopt-opt model and develop new models of problem difficulty that correct these deficiencies. We show that Taillard’s algorithm can be modeled with exceptionally high fidelity using a surprisingly simple Markov chain. The Markov model also enables us to characterize the exact conditions under which different initialization methods can be expected to improve performance. Finally, we analyze the relationship between the Markov and lopt-opt models.