Exponential extrapolation memory for tabu search

Tabu search is a well-established metaheuristic framework for solving hard combinatorial optimization problems. At its core, the method uses different forms of memory to guide a local search through the solution space so as to identify high-quality local optima while avoiding getting stuck in the vicinity of any particular local optimum. This paper examines characteristics of moves that can be exploited to make good decisions about steps that lead away from recently visited local optima and towards a new local optimum. Our approach uses a new type of adaptive memory based on a construction called exponential extrapolation. The memory operates by means of threshold inequalities that ensure selected moves will not lead to a specified number of most recently encountered local optima. Computational experiments on a set of one hundred different benchmark instances for the binary integer programming problem suggest that exponential extrapolation is a useful type of memory to incorporate into a tabu search.