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| 数理ヒューリスティクス：数理計画法とメタヒューリスティクスのハイブリダイゼーション× | 整数計画法× | |
|---|---|---|
| 分野 | 最適化 | 最適化 |
| 系統 | Process / pipeline | Process / pipeline |
| 提唱年≠ | 2009 | 1958 |
| 提唱者≠ | Maniezzo, Stützle & Voß | Ralph Gomory (cutting planes, 1958); land-and-doig branch-and-bound (1960) |
| 種類≠ | Hybrid optimization framework | Mathematical optimisation — exact combinatorial method |
| 原典≠ | Maniezzo, V., Stützle, T., & Voß, S. (Eds.). (2009). Matheuristics: Hybridizing Metaheuristics and Mathematical Programming. Springer. ISBN: 978-1-4419-1305-0 | Wolsey, L.A. (1998). Integer Programming. Wiley. ISBN: 9780471283669 |
| 別名≠ | Hybrid Metaheuristics, MIP-based Heuristics, Math-Programming Hybrids, Matematiksel Sezgisel Yöntemler | IP, MIP, mixed-integer programming, mixed-integer linear programming |
| 関連≠ | 3 | 4 |
| 概要≠ | Matheuristics is a class of hybrid optimization methods that tightly couple exact mathematical programming components—such as mixed-integer programming (MIP) solvers—with metaheuristic search procedures. Formally introduced and named by Maniezzo, Stützle, and Voß in 2009, the framework leverages the global-search capability of metaheuristics and the structural exploitation of mathematical programming to tackle large-scale combinatorial optimization problems that neither approach can solve effectively alone. | Integer programming (IP), also called mixed-integer programming (MIP) when only some variables are restricted to whole numbers, is a branch of mathematical optimisation in which some or all decision variables must take integer or binary values. Building on linear programming, it was formalised through Ralph Gomory's cutting-plane method (1958) and the Land-and-Doig branch-and-bound algorithm (1960), and it has since become the standard exact framework for scheduling, assignment, routing, and resource-allocation problems. |
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