方法对比
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| 整数规划× | 最小成本路径 / 成本距离分析× | |
|---|---|---|
| 领域≠ | 优化 | 空间分析 |
| 方法族 | Process / pipeline | Process / pipeline |
| 起源年份≠ | 1958 | 1994 |
| 提出者≠ | Ralph Gomory (cutting planes, 1958); land-and-doig branch-and-bound (1960) | Edsger Dijkstra (shortest path); GIS cost-surface adaptation |
| 类型≠ | Mathematical optimisation — exact combinatorial method | Raster cost-surface routing |
| 开创性文献≠ | Wolsey, L.A. (1998). Integer Programming. Wiley. ISBN: 9780471283669 | Dijkstra, E. W. (1959). A note on two problems in connexion with graphs. Numerische Mathematik, 1(1), 269–271. DOI ↗ |
| 别名≠ | IP, MIP, mixed-integer programming, mixed-integer linear programming | cost-distance analysis, accumulated cost surface, least-cost corridor, en düşük maliyetli yol |
| 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. | Least-cost path analysis finds the route between two locations that minimizes accumulated travel cost across a landscape, rather than minimizing straight-line distance. By encoding terrain, slope, land cover, and other frictions into a cost surface and accumulating cost outward from a source, it identifies optimal corridors for roads, pipelines, trails, power lines, and wildlife movement — a core raster-GIS technique built on Dijkstra's shortest-path logic. |
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