Contemporary approaches in matheuristics an updated survey

Abstract Matheuristics are problem independent frameworks that use mathematical programming tools to obtain high quality heuristic solutions. They are structurally general enough to be applied to different problems with little adaptation to their abstract structure, so they can be considered as new or hybrid metaheuristics based on components derived from the mathematical model of the problems of interest. In this survey, we emphasize the mathematical tools and describe how they can be used to design heuristics. We focus on mixed-integer linear programming and report representative examples from the literature of how it has been used for effective heuristic optimization. References to contributions to matheuristics deriving from neighboring research areas such as Artificial Intelligence or Quantum Computing are also included. We conclude with some ideas for possible future developments. This paper extends an original version published in 4OR with new sections on CMSA, Incremental Core, AI hybrids and Quantum Heuristics, and includes references to several recent publications.