On the Convergence of Tabu Search

The Tabu Search (TS) meta-heuristic has proved highly successful for solving combinatorial and nonlinear problems. A key aspect of TS consists of using adaptive forms of memory to forbid the search process to revisit solutions already examined unless the trajectory to reach it is different. In Glover (ORSA Journal on Computing, 1990, 2, 4–32) a special memory design was proposed together with a choice rule for handling the situation where the method was compelled to revisit solutions already encountered. This proposal, which specified the exploration should resume from the earliest solution visited in the past, as accompanied by the conjecture that such a choice has implications for finiteness in the zero-one integer program and optimal set membership examples. Up to now numerous applications of TS in various areas of research are available, however, we are aware of only a few results concerning the convergence of TS. In this paper, we prove that Glover's conjecture is true if the neighborhood employed is strongly connected, yielding a “reversible” path from each solution to every other solution.