Model reduction based global optimization for large-scale steady state
nonlinear systems
Abstract
Many engineering processes can be accurately modeled using partial
differential equations (PDEs), but high dimensionality and non-convexity
of the resulting systems pose limitations on their efficient
optimization. In this work, a model reduction methodology combining
principal component analysis (PCA) and artificial neural networks (ANNs)
is employed to construct a reduced surrogate model, which is then
utilized by advanced deterministic global optimization algorithms to
compute global optimal solutions with theoretical guarantees. However,
the optimization framework is still time-consuming due to the high
non-convexity of the activation functions inside the reduced ANN
structure. To further enhance the capability of our optimization
framework, two alternative strategies have been proposed. The first one
is a piecewise-affine reformulation while the second one is based on
deep rectifier neural networks with ReLU activation function. The
performances of the two improved frameworks is demonstrated through two
illustrative case studies.