Optimization Algorithms For Some Problems Of Minimum And Maximum In Transportation Network

For a given transportation network, the research on Maximum Flow Problem (MFP)and Minimum Cost Flow Problem (MCFP) is an eternal research subject, in this paper wedesign an algorithm for minimum cost maximum flow and implement it in the VisualC++6.0environment. The full text is divided into four chapters:In chapter one, as an introduction, we study the transportation network, and give areview about the history of Minimum Cost Maximum Flow Problem（MCMFP）as wellas the main algorithm research results in these areas.In chapter two, we mainly discuss the transportation network N=(V, s, t; A; C; B),formulate MCMFP by a bi-level programming model, design an algorithm andcorresponding numerical algorithm to find the optimal solution of the model, and presentthe numerical algorithm’s core code which can run accurately in Visual C++6.0environment.In chapter three, we exemplify the above algorithm by four different transportationnetworks where to find minimum cost maximum flow, and employ the program derivedfrom compiling the core code of the second chapter in Visual C++6.0environment tosolve the four examples，and execute the derived prgram to verify the feasibility of thealgorithm and its advantages in the aspect of computing.In chapter four, we mainly discuss the optimization algorithm for CapacitatedTransportation Problem with Bounds on Rim Conditions (CTPBRC) in order to find itsbest solution minimizing transportation duration and cost simultaneously in network withlower&upper arc capacities N=(V, s, t; A; C, C; B).