方法对比

	数学启发式算法：数学规划与元启发式算法的混合	超启发式算法	整数规划	模拟启发式算法：结合仿真与元启发式算法求解随机优化问题
领域	优化	优化	优化	优化
方法族	Process / pipeline	Process / pipeline	Process / pipeline	Process / pipeline
起源年份	2009	2013	1958	2015
提出者	Maniezzo, Stützle & Voß	Burke et al.	Ralph Gomory (cutting planes, 1958); land-and-doig branch-and-bound (1960)	Juan et al.
类型	Hybrid optimization framework	High-level search methodology	Mathematical optimisation — exact combinatorial method	Hybrid simulation-optimization framework
开创性文献	Maniezzo, V., Stützle, T., & Voß, S. (Eds.). (2009). Matheuristics: Hybridizing Metaheuristics and Mathematical Programming. Springer. ISBN: 978-1-4419-1305-0	Burke, E. K., et al. (2013). Hyper-heuristics: A survey of the state of the art. Journal of the Operational Research Society, 64(12), 1695–1724.	Wolsey, L.A. (1998). Integer Programming. Wiley. ISBN: 9780471283669	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.
别名	Hybrid Metaheuristics, MIP-based Heuristics, Math-Programming Hybrids, Matematiksel Sezgisel Yöntemler	Heuristic of Heuristics, Algorithm Selection Hyper-Heuristic, Selection Hyper-Heuristic, Hiyer-Sezgisel	IP, MIP, mixed-integer programming, mixed-integer linear programming	Simulation-based Metaheuristics, Stochastic Metaheuristics with Simulation, Hybrid Simulation-Optimization, Simülistik Sezgiseller
相关	3	3	4	3
摘要	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.	Hyper-heuristics are high-level methodologies that search over a space of heuristics rather than directly over the space of solutions. Introduced systematically by Burke et al. (2013) in their landmark survey, hyper-heuristics operate by selecting or generating low-level heuristics to solve hard combinatorial optimisation and search problems, aiming to automate the design of optimisation algorithms across diverse problem domains without requiring deep problem-specific knowledge.	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.	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.