中文摘要：

针对现有交通规划中最优路径算法难以同时集成多种不同类型约束的不足,提出了一种多类型约束下最优路径统一求解的几何代数算法.基于几何基编码的网络表达模型,实现了对节点、边、路径等网络对象及权重和约束条件的统一表达.建立了基于几何邻接矩阵外积的路径延拓、遍历与筛选机制,实现了路径延拓过程中网络拓扑关系和权重结构的同步计算.在此基础上,构建多约束条件下最优路径生成算法.最后,以江苏道路网络为例对算法的正确性进行验证,结果显示,该算法可较好地支撑同时包含数值型、节点型及结构型约束条件下最优路径的计算,可为复杂GIS网络分析提供理论与方法支撑.

英文摘要：

Focused with the leakage of integrating multiple type of constrains in existing optimal path algorithms for traffic planning,this paper proposed a unified geometric algebra algorithm for solving multi type constrained optimal path.The geometric algebra coding and unified expression of networks are firstly proposed,which can integrate the expression of the nodes,edges,paths and the weights.The route extension,emulation and selection are implemented by the outer product applied to the geometric algebra adjacent matrix.The computation of network topology and the path weight are synchronously exported during the route extension.Based on the above,the multi-constrained optimal path algorithm is developed.Experiments based on the data of road networks of Jiangsu Province suggest that this algorithm can well support for finding optimal path with the constrains of numerical values,nodes and route structure types.The works can provide theoretical and methodological support for complex GIS network analysis.