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

Abstract

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 have previously demonstrated that the mean distance between random local optima and the nearest optimal solution, denoted $\bar d_{lopt - opt}$ , 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 $\bar d_{lopt - opt}$ model and develop new models of problem difficulty that correct these deficiencies. We show that Taillard's algorithm can be modelled with exceptionally high fidelity using a surprisingly simple Markov chain. The Markov model also enables us to characterise the exact conditions under which different initialisation methods can be expected to improve performance. Finally, we analyse the relationship between the Markov and $\bar d_{lopt - opt}$> models.