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一类带有MaxEMin评判的补偿型随机规划算法

张艳丽1  马新顺1,*   

  1. 1. 华北电力大学数理系, 河北保定 071003
  • 收稿日期:2016-04-19 出版日期:2016-12-15 发布日期:2016-12-15
  • 通讯作者: 马新顺 maxs@sina.com
  • 基金资助:

    国家自然科学基金(No. 51576066)

A class recourse  stochastic programs algorithm with MaxEMin evaluation

ZHANG Yanli1  MA Xinshun1,*   

  1. 1. Department of Mathematics and Physics, North China Electric Power University, Baoding 071003, Hebei, China
  • Received:2016-04-19 Online:2016-12-15 Published:2016-12-15

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摘要：

补偿型随机规划一般假定随机变量的概率分布具有完备信息, 但实际情况往往只能获得部分信息. 针对离散概率具有一类线性部分信息条件而建立了带有MaxEMin评判的两阶段随机规划模型, 借助二次规划和对偶分解方法得到了可行性切割和最优切割, 给出了基于L-型的求解算法, 并证明了算法的收敛性. 通过数值实验表明了算法的有效性.

关键词: 随机规划, 不完备概率分布, 补偿函数, 二次规划, L-型算法

Abstract:

The recourse-based stochastic programming generally assumes that the probability distribution of the random variables has complete information, but the actual situation is that we often get only part of the information. In this paper, we establish a two-stage stochastic programming model with MaxEMin evaluation under linear partial information of discrete probability distribution. We use quadratic programming and the dual decomposition method to get the feasible and optimal cuttings, then give an algorithm based on the L-shaped method. Finally, a numerical example shows the effectiveness of the proposed algorithm.

Key words: stochastic programming, incomplete probability distribution, recourse function, quadratic programming, L-shaped algorithm