Study On Train Deployment Model And Algorithms During Holidays

There exist many practical issues in areas such as Transportation planning, network design and financial economy, and can be solved by setting up optimization models. With the development of society, many problems are becoming increasingly complicated. It is difficult to work out them substantially only by ordinary mathematical programming methods. This gives rise to mathematical programs with complementary constraints.This paper aims at reducing the problem of imbalance in the flow that causes by a large passenger flow during the holiday season. In this case, it will cause empty driving phenomenon and increase the cost of train deployment. Therefore, we use the minimum costs of train deployment as an objective function in model building. And we use the constraints that round-trip vehicles cannot be all empty and the number of vehicles requiring be deployed as constraint conditions. Among them, the previous constraint is complementary constraint. Thus this problem is complementary constrained optimization problem. And to solve such a problem, the thesis presents optimality condition and interior-point penalty method in the optimal problem of complementarity constraints under certain assumptions. In the next place, the model is solved through the combination with interior-point penalty method for Mathematical Programs with Complementarity Constraints, furthermore, by analyzing the algorithms the thesis analyses proved global convergence and local convergence. Ultimately, we verity the effectiveness of the algorithm of Mathematical Programs with Complementarity Constraints by experimenting and analyzing 24 test issues choosing from test problems of Mathematical Programs with Complementarity Constraints. At the same time, we solve the model by numerical simulation and get the optimum result which is aimed at the least cost.