基于演化计算的线性规划原对偶内点法中的初始点选取算法  

Initial Point Selection in Primal-Dual Interior Point Method for Linear Programming Based on Evolutionary Algorithm

作　　者：贾伟 雍龙泉[1,2] 李娜 JIA Wei;YONG Longquan;LI Na(School of Mathematics and Computer Science,Shaanxi University of Technology,Hanzhong,723001,China;Shaanxi Key Laboratory of Industrial Automation,Hanzhong,723001,China)

机构地区：[1]陕西理工大学数学与计算机科学学院,汉中723001 [2]陕西省工业自动化重点实验室,汉中723001

出　　处：《南京航空航天大学学报》2020年第2期334-340,共7页Journal of Nanjing University of Aeronautics & Astronautics

基　　金：国家自然科学基金(11401357)资助项目;陕西省教育厅科研基金(17JK0146)资助项目;陕西理工大学科研基金(SLGKY16-15)资助项目。

摘　　要：采用原对偶内点法求解线性规划问题,对初始点要求严格。根据初始可行内点的准则,定义了相应的达成度函数,并由达成度函数定义了适应值函数,从而提出了基于演化计算的线性规划原对偶内点法中的初始点选取算法。该算法基于和声搜索演化算法实现,经数值实验测试,结果表明,对所选取测试的典型线性规划问题,算法都能求得大部分问题的初始可行内点。The primal-dual interior point method requires strict initial feasible points in solving linear programming problems. The degree function is given based on the criterion of the initial feasible point in the primal-dual interior point method,and the fitness function in the evolutionary algorithm is designated by the degree function. The initial feasible point selection of the primal-dual interior point method for linear programming based on the evolutionary computation is proposed. It is taken by the harmony search.Numerical experiments show that the algorithm can find an initial feasible point of most given problems,thus validating the effectiveness of the algorithm.

关 键 词：线性规划 原对偶内点法 初始点选取 演化计算 和声搜索 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程] O221[自动化与计算机技术—控制科学与工程]