Combining Exact Methods and Heuristics

The combination of exact and heuristic methods is as old as mathematical programming (MP) itself, because usually exact methods cannot work properly without a good bound on the optimal cost, which helps pruning the search space. However, it is only in very recent years that the combination has also gone the other way round, permitting the use of methods originally conceived for exact problem solution also in heuristic frameworks. In this article, we revise the newly identified field of metaheuristics, which refers in particular to algorithms combining metaheuristics with MP techniques and show how current research aims at exploiting MP and metaheuristics synergies.