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Research on the Application of Mixed Integer Programming in Engineering

Author: ZhangMingJia
Tutor: SiJiWen；GongPu
School: Huazhong University of Science and Technology
Course: Engineering Mechanics
Keywords: Mixed Integer Programming Branch and bound method CVaR Risk Measurement Transportation problems
CLC: O221.4
Type: Master's thesis
Year: 2005
Downloads: 521
Quote: 5
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Abstract


Mixed Integer Programming (Mixed Integer Programming, MIP) is related to the integer or discrete variables of a class of mathematical programming problems , such planning issues in practice a wide range of applications , such algorithm is a mathematical programming problem . Since the branch and bound method for solving integer programming problems from the Land and Doig et al , solving mixed integer programming method has been a great development . This paper, mixed integer programming theory and methods engineering actually a combination of doing some useful attempts in modeling and solving mixed integer programming problems , the need for specific problems , improved model or algorithm , a detailed analysis of the process of model building , while introducing some new methods , the problem has a practical significance . Branch and bound method for solving mixed integer programming (Branch-and-Bound algorithm) -based portfolio CVaR metric optimization and transportation problem with interval number of these types of engineering problems to establish a mathematical programming model . On the CVaR metric portfolio optimization model , combined with the Monte Carlo scenario simulation CVaR Models , in the case of a certain scale scenarios , the optimization problem into a convex function , which makes the portfolio contains a large number of assets to optimize it possible . And a model based on the needs of the practical problems it is extended , the introduction of an integer parameter constraints , mathematical programming model is closer to the actual market situation . Transportation problem earlier related to mathematical programming problems due to the practical significance of the problem , the problem itself is an integer programming problem . In this article, we consider the transportation planning problems with the range of the number of parameters to convert the original problem by introducing a new algorithm for two ordinary linear programming problem , using a new algorithm to calculate the simple , high efficiency , and the result is a more intuitive changed only to the interval number represents the way of results . The two engineering problems empirical results show that the model and the methods used are effective , to some extent, improve computational efficiency , making large-scale optimization problems efficient computation can be achieved .

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CLC: > Mathematical sciences and chemical > Mathematics > Operations Research > Planning Theory ( mathematical programming) > Integer Programming
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