Matheuristics: Optimization, Simulation and Control

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Matheuristics are heuristic algorithms made by the interoperation of metaheuristics and mathematic programming (MP) techniques. An essential feature is the exploitation in some part of the algorithms of features derived from the mathematical model of the problems of interest, thus the definition “model-based metaheuristics” appearing in the title of some events of the conference series dedicated to matheuristics [1]. The topic has attracted the interest of a community of researchers, and this led to the publication of dedicated volumes and journal special issues, [13], [14], besides to dedicated tracks and sessions on wider scope conferences.

The increasing maturity of the area permits to outline some trends and possibilities offered by matheuristic approaches. A word of caution is needed before delving into the subject, because obviously the use of MP for solving optimization problems, albeit in a heuristic way, is much older and much more widespread than matheuristics. However, this is not the case for metaheuristics, and also the very idea of designing MP methods specifically for heuristic solution has innovative traits, when opposed to exact methods which turn into heuristics when enough computational resources are not available.