Bounds for probabilistic integer programming problems

Darinka Dentcheva; Andras Prekopa; Andrzej Ruszcynski

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Bounds for probabilistic integer programming problems

机译：概率整数编程问题的界线

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摘要

We consider stochastic integer programming problems with probabilistic constraints. The concept of p-efficient points of a probability distribution is used to derive various equivalent problem formulations. Next we introduce new methods for constructing lower and upper bounds for probabilistically constrained integer programs. We also show how limited information about the distribution can be used to construct such bounds. The concepts and methods are illustrated on an example of a vehicle routing problem.

机译：我们考虑具有概率约束的随机整数规划问题。概率分布的p有效点的概念用于导出各种等效问题公式。接下来，我们介绍为概率约束整数程序构造上下限的新方法。我们还展示了有关分布的有限信息如何用于构造此类边界。在车辆路径问题的示例上说明了概念和方法。

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《Discrete Applied Mathematics》 |2002年第3期|共11页
作者
Darinka Dentcheva; Andras Prekopa; Andrzej Ruszcynski;
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原文格式 PDF
正文语种 eng
中图分类离散数学;
关键词
stochastic programming; integer programming; probabilistic constraints; column generation;

机译：随机规划;整数规划;概率约束;列生成;

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专利

1. Bounds for probabilistic integer programming problems [J] . Darinka Dentcheva, Andras Prekopa, Andrzej Ruszcynski Discrete Applied Mathematics . 2002,第1a3期

机译：概率整数编程问题的界线
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3. Lagrangian decomposition and mixed-integer quadratic programming reformulations for probabilistically constrained quadratic programs [J] . Zheng X., Sun X., Li D., European Journal of Operational Research . 2012,第1期

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4. Computing policies and performance bounds for deterministic dynamic programs using mixed integer programming [C] . Cogill Randy, Hindi Haitham 2011 American Control Conference . 2011

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6. A novel method for inference of acyclic chemical compounds with bounded branch-height based on artificial neural networks and integer programming [O] . Naveed Ahmed Azam, Jianshen Zhu, Yanming Sun, 2021

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7. A branch and bound algorithm for integer and mixed-integer linear programs. [O] . Missal Joseph Bannan 1969

机译：整数和混合整数线性程序的分支定界算法。

Bounds for probabilistic integer programming problems

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