Tabu search and finite convergence

We establish finite convergence for some tabu search algorithms based on recency memory or frequency memory, distinguishing between symmetric and asymmetric neighborhood structures. These are the first demonstrations of explicit bounds provided by such forms of memory, and their finiteness suggests an important distinction between these ideas and those underlying certain "probabilistic" procedures such as annealing. We also show how an associated Reverse Elimination Memory can be used to create a new type of tree search. Finally, we give designs for more efficient forms of convergent tabu search.