方法对比
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| 整数规划× | 约束规划× | |
|---|---|---|
| 领域 | 优化 | 优化 |
| 方法族 | Process / pipeline | Process / pipeline |
| 起源年份≠ | 1958 | 2006 |
| 提出者≠ | Ralph Gomory (cutting planes, 1958); land-and-doig branch-and-bound (1960) | Rossi, van Beek & Walsh |
| 类型≠ | Mathematical optimisation — exact combinatorial method | Declarative combinatorial optimization |
| 开创性文献≠ | Wolsey, L.A. (1998). Integer Programming. Wiley. ISBN: 9780471283669 | Rossi, F., van Beek, P., & Walsh, T. (Eds.). (2006). Handbook of Constraint Programming. Elsevier. ISBN: 978-0-444-52726-4 |
| 别名≠ | IP, MIP, mixed-integer programming, mixed-integer linear programming | Constraint Satisfaction Programming, Constraint-Based Optimization, Kısıt Programlama, CSP Optimization |
| 相关≠ | 4 | 3 |
| 摘要≠ | 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. | Constraint Programming (CP) is a declarative optimization paradigm in which a problem is formulated as a set of variables, finite domains, and constraints, and a solver systematically searches for assignments that satisfy all constraints. Formalized comprehensively by Rossi, van Beek, and Walsh in their 2006 Handbook of Constraint Programming, CP unifies propagation-based pruning with intelligent backtracking search to tackle combinatorial problems across scheduling, planning, and configuration domains. |
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