Research On The Application Of Belief Propagation Algorithm For Network Flow

With the rapid development of artificial intelligence,network flow models are widely used in various fields of engineering construction and scientific production,and many problems in life can be converted into network flow problems.Network flow problem is an important research branch in operations research,and it is a kind of combinatorial optimization problem.Among them,maximum flow,minimum cost and maximum flow are the most widely involved types of problems.Under the condition of P?NP,there is no polynomial time algorithm to solve this problem.At present,there have been a lot of research results on network flow problems.However,with the development of the big data era,the scale of actual problems continues to expand,posing new challenges to the original network flow algorithm,and also provides a source of power for the further development of the network flow algorithm.The Belief Propagation algorithm uses the calculation method of parallel transmission of information between nodes,which makes it have a good effect in solving partial combinatorial optimization problems.The belief propagation algorithm is an information iterative algorithm based on the graph model.When the algorithm converges,the marginal probability distribution of the variable can be obtained,so that the value of some variables can be fixed with high probability to solve the problem.This article explores the use of belief propagation algorithms to solve maximum flow and minimum cost maximum flow problems.Specifically,the main innovations are as follows:(1)According to the proposed graph model conversion algorithm,the maximum flow problem is converted into a factor graph model,the maximum flow problem constraint conditions,linear equations are used to improve the description function and iterative function in the BP algorithm,and a solution to the maximum flow problem is designed.Belief propagation algorithm;(2)On the basis of studying the maximum flow problem,further study the minimum cost and maximum flow problem.After the graph model conversion algorithm,the maximum flow value of the network is solved first,and the maximum flow threshold is set.According to constraint conditions and linear equations,the description function and iterative function are improved,and the optimal feasible flow path is selected through probability.A belief propagation algorithm for solving the network minimum cost and maximum flow problem is given.