手法を比較

	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	シミュヘリスティクス：確率的最適化のためのシミュレーションとメタヒューリスティクスの統合
分野	最適化	最適化
系統	Process / pipeline	Process / pipeline
提唱年	2009	2015
提唱者	Maniezzo, Stützle & Voß	Juan et al.
種類	Hybrid optimization framework	Hybrid simulation-optimization framework
原典	Maniezzo, V., Stützle, T., & Voß, S. (Eds.). (2009). Matheuristics: Hybridizing Metaheuristics and Mathematical Programming. Springer. ISBN: 978-1-4419-1305-0	Juan, A. A., et al. (2015). A review of simheuristics: Extending metaheuristics to deal with stochastic combinatorial optimization problems. Operations Research Perspectives, 2, 62–72.
別名	Hybrid Metaheuristics, MIP-based Heuristics, Math-Programming Hybrids, Matematiksel Sezgisel Yöntemler	Simulation-based Metaheuristics, Stochastic Metaheuristics with Simulation, Hybrid Simulation-Optimization, Simülistik Sezgiseller
関連	3	3
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.	Simheuristics is a hybrid algorithmic framework that integrates Monte Carlo or discrete-event simulation into metaheuristic search procedures to solve stochastic combinatorial optimization problems. Introduced by Juan et al. in 2015, it addresses settings where objective function evaluations involve random variables, providing near-optimal solutions with probabilistic quality guarantees. The approach is especially suited for real-world logistics, transportation, and scheduling problems where uncertainty is inherent and classical deterministic solvers fail to capture variability.