Matheuristics: using mathematics for heuristic design

Abstract

Matheuristics are heuristic algorithms based on mathematical tools such as the ones provided by mathematical programming, that are structurally general enough to be applied to different problems with little adaptations to their abstract structure. The result can be metaheuristic hybrids having components derived from the mathematical model of the problems of interest, but the mathematical techniques themselves can define general heuristic solution frameworks. In this paper, we focus our attention on mathematical programming and its contributions to developing effective heuristics. We briefly describe the mathematical tools available and then some matheuristic approaches, reporting some representative examples from the literature. We also take the opportunity to provide some ideas for possible future development.

Matheuristics: survey and synthesis

“…Ever since then, the field of matheuristics has been in rapid expansion. For details, we refer the reader to the surveys (Raidl and Puchinger, 2008;Ball, 2011;Raidl, 2015;Fischetti and Fischetti, 2016;Boschetti and Maniezzo, 2022) and the books (Maniezzo et al, 2010(Maniezzo et al, , 2021.…”

“…The first international matheuristics conference took place in Bertinoro, Italy in 2006 (see Boschetti and Maniezzo, 2022). Ever since then, the field of matheuristics has been in rapid expansion.…”