随机约束规划：一种基于场景的方法
Stochastic Constraint Programming: A Scenario-Based Approach
摘要：
为了模拟涉及不确定性和概率的组合决策问题，我们引入了基于场景的随机约束规划。随机约束程序既包含我们可以设置的决策变量，也包含遵循离散概率分布的随机变量。我们提供了一个语义的随机约束程序的基础上的场景树。使用这种语义，我们可以将随机约束程序编译成常规（非随机）约束程序。这使我们能够充分利用现有的约束求解器。我们已经在随机OPL中实现了这个框架，用于在不确定性下进行决策，OPL是一种基于OPL约束建模语言的语言[Hentenryck等人，1999年]。为了说明这一框架的潜力，我们在投资组合多样化，农业规划和生产/库存管理等领域的各种问题。
英文摘要：
To model combinatorial decision problems involving uncertainty and probability, we introduce scenario based stochastic constraint programming. Stochastic constraint programs contain both decision variables, which we can set, and stochastic variables, which follow a discrete probability distribution. We provide a semantics for stochastic constraint programs based on scenario trees. Using this semantics, we can compile stochastic constraint programs down into conventional (non-stochastic) constraint programs. This allows us to exploit the full power of existing constraint solvers. We have implemented this framework for decision making under uncertainty in stochastic OPL, a language which is based on the OPL constraint modelling language [Hentenryck et al., 1999]. To illustrate the potential of this framework, we model a wide range of problems in areas as diverse as portfolio diversification, agricultural planning and production/inventory management.
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