Deterministic global optimization of process flowsheets in a reduced space using McCormick relaxations
Deterministic global optimization of process flowsheets in a reduced space using McCormick relaxations
复制标题
使用 McCormick 松弛在缩小的空间内确定性全局优化工艺流程
DOI：
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发表时间：
2017
影响因子：
1.8
通讯作者：
A. Mitsos
中科院分区：
文献类型：
--
作者：
D. Bongartz;A. Mitsos
流程表优化的确定性全局方法几乎仅依赖于方程式的公式，在该公式中，所有模型变量均由优化器控制，所有模型方程都被视为平等约束，这导致了很大的优化问题。一种可能的替代方法是一个缩小的空间公式，类似于局部流动表优化中采用的顺序模块化路径方法。这种方法利用了模型方程的结构，以减少问题大小。优化器仅在模型变量的一小部分中运行，并且只有很少的平等约束，而大多数则隐藏在外部定义的函数中，从中可以查询目标函数的函数值和放松，并且可以查询其约束。通过自动传播麦考密克放松，可以提供紧密的放松及其对这些外部功能的亚级别。增加复杂性的三个蒸汽功率周期用作案例研究来评估不同的配方。与局部优化或依赖间隔方法的先前顺序方法不同，使用McCormick弛豫的缩小空间公式的解决方案可与常规方程式公式相比，可以在计算时间的急剧减少。尽管实现的分支和结合求解器的简单性并不能完全利用外部功能返回的紧密放松，但使用亚级别依赖于单个点的进一步仿射放松，但在某些情况下，它可以解决降低的空间配方与最先进的求解器男爵相比，没有任何范围的速度要快得多，可以解决面向方程式的公式。
Deterministic global methods for flowsheet optimization have almost exclusively relied on an equation-oriented formulation where all model variables are controlled by the optimizer and all model equations are considered as equality constraints, which results in very large optimization problems. A possible alternative is a reduced-space formulation similar to the sequential modular infeasible path method employed in local flowsheet optimization. This approach exploits the structure of the model equations to achieve a reduction in problem size. The optimizer only operates on a small subset of the model variables and handles only few equality constraints, while the majority is hidden in externally defined functions from which function values and relaxations for the objective function and constraints can be queried. Tight relaxations and their subgradients for these external functions can be provided through the automatic propagation of McCormick relaxations. Three steam power cycles of increasing complexity are used as case studies to evaluate the different formulations. Unlike in local optimization or in previous sequential approaches relying on interval methods, the solution of the reduced-space formulation using McCormick relaxations enables dramatic reductions in computational time compared to the conventional equation-oriented formulation. Despite the simplicity of the implemented branch-and-bound solver that does not fully exploit the tight relaxations returned by the external functions but relies on further affine relaxation at a single point using the subgradients, in some cases it can solve the reduced-space formulation significantly faster without any range reduction than the state-of-the-art solver BARON can solve the equation-oriented formulation.
影响因子：
1.8
作者：
A. Tsoukalas;A. Mitsos
通讯作者：
A. Tsoukalas;A. Mitsos