线性约束优化问题的相容解优化法及其应用Compatible Solutions Optimization Method for Linear Constrained Optimization Problem and Its Application
丘文千,丘凌
QIU Wenqian,QIU Ling
摘要(Abstract)：
给出一种求解线性约束优化问题的数值方法,利用广义逆矩阵方法求取与线性约束条件等价的线性不定方程组的相容解集合,并利用粒子群优化算法直接在相容解集合中寻优,称之为相容解优化法或相容解直接优化法,可用于求解线性规划问题,也可用于求解具有线性约束的非线性规划问题。该方法具有算法简捷、数值稳定性好等特点,对于具有线性约束的非线性规划问题,比一般的非线性规划方法更快捷有效。结合相容解优化法在直流偏磁限流电阻优化计算的应用实例,验证了方法的有效性和实用性。
The paper presents a numerical method for solving linear constrained optimization problems, called compatible solutions optimization method or compatible solutions direct optimization method, which uses the generalized inverse matrix method to calculate the compatible solutions set of the linear indefinite equations which are equivalent to the linear constraints to find the optimal solution directly from the compatible solutions set by particle swarm optimization algorithm. The method can be used to solve the linear programming problem and nonlinear programming problems with linear constraints. The method is characterized by its simple algorithm and numerical stability, so it is faster and more efficient than any other methods in solving nonlinear programming problems with linear constraints. In accordance with the application of compatible solutions optimization method in optimized calculation of DC bias current-limiting resistor, the paper verifies that the method is effective and practicable.
关键词(KeyWords)：
最优化方法;广义逆矩阵;粒子群优化方法;限制短路电流;抑制直流偏磁
optimal method;generalized inverse matrix;particle swarm optimization;short circuit current limiting;inhibition of DC bias
基金项目(Foundation):
作者(Author):
丘文千,丘凌
QIU Wenqian,QIU Ling
DOI: 10.19585/j.zjdl.2015.12.008
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