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Optimizing Partially Defined Black-Box Functions Under Unknown Constraints via Sequential Model Based Optimization: An Application to Pump Scheduling Optimization in Water Distribution Networks

机译:通过基于顺序模型的优化,在未知约束下优化部分定义的黑箱函数:在供水管网泵调度优化中的应用

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This paper proposes a Sequential Model Based Optimization framework for solving optimization problems characterized by a black-box, multi-extremal, expensive and partially defined objective function, under unknown constraints. This is a typical setting for simulation-optimization problems, where the objective function cannot be computed for some configurations of the decision/control variables due to the violation of some (unknown) constraint. The framework is organized in two consecutive phases, the first uses a Support Vector Machine classifier to approximate the boundary of the unknown feasible region within the search space, the second uses Bayesian Optimization to find a globally optimal (feasible) solution. A relevant difference with traditional Bayesian Optimization is that the optimization process is performed on the estimated feasibility region, only, instead of the entire search space. Some results on three 2D test functions and a real case study for the Pump Scheduling Optimization in Water Distribution Networks are reported. The proposed framework proved to be more effective and efficient than Bayesian Optimization approaches using a penalty for function evaluations outside the feasible region.
机译:本文提出了一种基于序列模型的优化框架,用于解决在未知约束下以黑匣子,多极值,昂贵和部分定义的目标函数为特征的优化问题。这是模拟优化问题的典型设置,在这种情况下,由于违反某些(未知)约束,因此无法为决策/控制变量的某些配置计算目标函数。该框架分为两个连续的阶段,第一个阶段使用支持向量机分类器来近似搜索空间内未知可行区域的边界,第二个阶段使用贝叶斯优化来找到全局最优(可行)解决方案。与传统贝叶斯优化的一个重要区别是,优化过程仅在估计的可行性区域上执行,而不是在整个搜索空间上执行。报告了三个二维测试功能的一些结果以及水分配网络中泵调度优化的实际案例研究。事实证明,所提出的框架比贝叶斯优化方法更有效,更有效,贝叶斯优化方法在可行区域之外对功能进行了惩罚。

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