基于正弦型光滑打磨函数对0-1规划问题的连续化求解方法

发布时间：2018-03-05 09:33

  本文选题：阶跃函数　切入点：-规划问题　出处：《运筹学学报》2017年03期 　论文类型：期刊论文

【摘要】：传统的求解0-1规划问题方法大多属于直接离散的解法.现提出一个包含严格转换和近似逼近三个步骤的连续化解法:(1)借助阶跃函数把0-1离散变量转化为[0,1]区间上的连续变量;(2)对目标函数采用逼近折中阶跃函数近光滑打磨函数,约束条件采用线性打磨函数逼近折中阶跃函数,把0-1规划问题由离散问题转化为连续优化模型;(3)利用高阶光滑的解法求解优化模型.该方法打破了特定求解方法仅适用于特定类型0-1规划问题惯例,使求解0-1规划问题的方法更加一般化.在具体求解时,采用正弦型光滑打磨函数来逼近折中阶跃函数,计算效果很好.
[Abstract]:Most of the traditional methods for solving 0-1 programming problems are direct discrete solutions. This paper presents a continuous solution method, which consists of three steps of strict transformation and approximate approximation, to transform 0-1 discrete variables into [01] interval by means of step function. The objective function is approximated to the eclectic step function by using the near smooth polishing function. The linear grinding function is used to approximate the eclectic step function. The 0-1 programming problem is transformed from a discrete problem to a continuous optimization model. By using a high order smooth solution, the method breaks the convention that a specific solution method is only suitable for a given type of 0-1 programming problem. The method of solving 0-1 programming problem is generalized and the sinusoidal smooth grinding function is used to approximate the eclectic step function.
【作者单位】： 北京工业大学机械工程与电子技术学院;内蒙古大学数学科学学院;内蒙古师范大学数学科学学院;
【基金】：国家自然科学基金(No.11672103) 内蒙古自治区自然科学基金(No.2014MS0119) 内蒙古自治区高等学校科学研究项目(No.NJSY16030) 内蒙古师范大学科研基金(Nos.2016ZRYB001,2016ZRYB002)
【分类号】：O221.4
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