matheuristic

A matheuristic is a metaheuristic optimization algorithm that incorporates mathematical programming techniques. It is a hybrid approach, combining the problem-solving power of metaheuristics with the rigor of mathematical optimization. Metaheuristics, such as genetic algorithms or simulated annealing, are general-purpose optimization strategies designed to find good solutions to complex problems, often without guarantees of optimality. Mathematical programming, on the other hand, deals with formulating optimization problems as mathematical models and solving them using techniques like linear programming or integer programming, which can provide optimal solutions but may struggle with very large or complex instances.

Matheuristics leverage mathematical programming as a subroutine or component within a metaheuristic framework. For instance, a metaheuristic might be used to explore the search space and identify promising regions, and then a mathematical programming solver could be employed to find a high-quality or optimal solution within that region. Alternatively, mathematical programming might be used to generate initial solutions or to repair infeasible solutions encountered by the metaheuristic. This synergy allows matheuristics to tackle problems that are too large or too complex for pure mathematical programming methods, while also achieving better solution quality than standalone metaheuristics. They are particularly effective for combinatorial optimization problems arising in areas like logistics, scheduling, and network design.