Extension of CMSA with a Learning Mechanism: Application to the Far from Most String Problem

One of the problems with exact techniques for solving combinatorial optimization problems is that they tend to run into problems with growing problem instance size. Nevertheless, they might still be very usefully employed, even in the context of large problem instances, as a sub-ordinate method within so-called hybrid metaheuristics. “Construct, Merge, Solve and Adapt” (Cmsa) is a hybrid metaheuristic technique that allows the application of exact methods to large-scale problem instances through intelligent instance reduction. However, Cmsa does not make use of an explicit learning mechanism. In this work, an algorithm called \(\textsc {Learn}\_\textsc {Cmsa}\) $\mathrm{L}\mathrm{E}\mathrm{A}\mathrm{R}\mathrm{N}\_\mathrm{C}\mathrm{M}\mathrm{S}\mathrm{A}$ is presented for the application to the far from most string problem (FFMSP), which is an NP-hard combinatorial optimization problem from the field of string consensus problems. \(\textsc {Learn}\_\textsc {Cmsa}\) $\mathrm{L}\mathrm{E}\mathrm{A}\mathrm{R}\mathrm{N}\_\mathrm{C}\mathrm{M}\mathrm{S}\mathrm{A}$ results from hybridization between Cmsa and a population-based algorithm. By means of this hybridization, explicit learning is introduced to Cmsa. Even though the FFMSP is a well-studied problem, \(\textsc {Learn}\_\textsc {Cmsa}\) $\mathrm{L}\mathrm{E}\mathrm{A}\mathrm{R}\mathrm{N}\_\mathrm{C}\mathrm{M}\mathrm{S}\mathrm{A}$ achieves superior performance when compared to current state-of-the-art solvers.