Geometric Algebra-based Multi-criteria Constrained Maximal Flow Analysis

Network analysis is a fundamental basis for community resources scheduling applications.Discussed in this paper is a multi-criteria-constrained maximal flow problem with route capacity changing over time.Geometric algebra unit based coding is used to obtain a geometric algebra expression for a network diagram.Network connectivity and path search are implemented based on this geometric product.Using independent computation the inner linkage between Boolean operations in geometric algebra computation are exploited,multi- criteria are integrated based on a constrained matrix.A multi-criteria-constrained maximal flow analysis algorithm with changing route capacity is proposed.The algorithm was implemented and validated by maximum flow analysis dealing with pollutant dispersion cases.The results show that,under the constraints imposed by a materials scheduling analysis,the geometric algebra based network algorithm can effectively support multi-dimensional community networks.The algorithm also supports rapid computing and updating of the weight of external constraints as well as changes in the conditions of maximum flow problems.