Is my understanding, Matheuristics is the interoperation of Meta-heuristics and Mathematical programming. What is the advantage and disadvantage of Matheuristics?
Matheuristics are optimization algorithms made by the interoperation of metaheuristics and mathematical 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.
Metaheuristics and exact algorithms are complementary optimization strategies in terms of the quality of solutions and the search time used to find them. Thus, combining both fields seems to be a very promising new research area. Some of the key research lines are:
- Using MP techniques to improve local search. For example, using branch and bound methods to reduce large neighborhoods around promising solutions.
- The hybridization of (meta)heuristics and exact techniques from MP. For example, using mathematical models to solve sub-problem as part of a given metaheuristic, or for improving some heuristic operators.
- The use of Lagrangean relaxation and/or Bender decomposition to guide the search of subordinate heuristics.
- The use of mathematical models as theoretical background for the design of new metaheuristics.
Perhaps some of these papers can help you get a better idea:
Conference Paper Matheuristics: Optimization, Simulation and Control
Article Matheuristics for Traffic Counter Location
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