Abstract
The evolution of Mixed-Integer Linear Programming (MIP) solvers has reached a very stable and effective level in which solving real-world problems is possible. However, the computed solution is not always the optimal one also because optimality is often not of primary interest for day-by-day users. We show some structural characteristics of MIP solvers and of computation for MIP problems that reveal the heuristic nature of the solvers. Moreover, we discuss the key components of MIP solvers with special emphasis on the role of heuristic decisions within the solution process. Finally, we present MIP solvers as “open” frameworks whose flexibility can be exploited to devise sophisticated hybrid algorithms.
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