Real-time optimization meets Bayesian optimization and derivative-free optimization: A tale of modifier adaptation

Conventional real‐time optimization (RTO) requires detailed process models, which may be challenging or expensive to obtain. Model‐free RTO methods are an attractive alternative to circumvent the challenge of developing accurate models. Most model‐free RTO methods are based on estimating the steady‐state cost gradient with respect to the decision variables and driving the estimated gradient to zero using integral action. However, accurate gradient estimation requires clear time scale separation from the plant dynamics, such that the dynamic plant can be assumed to be a static map. For processes with long settling times, this can lead to prohibitively slow convergence to the optimum. To avoid the need to estimate the cost gradients from the measurement, this article uses Bayesian optimization, which is a zeroth order black‐box optimization framework. In particular, this article uses a safe Bayesian optimization based on interior point methods to ensure that the setpoints computed by the model‐free steady‐state RTO layer are guaranteed to be feasible with high probability (i.e., the safety‐critical constraints will not be violated at steady‐state). The proposed method can thus be seen as a model‐free variant of the conventional two‐step steady‐state RTO framework (with steady‐state detection), which is demonstrated on a benchmark Williams‐Otto reactor example.

Section: Discussionmentioning

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Section: Proposed Methodsmentioning

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Section: Algorithm 1 Model-free Rto Using Safe Bayesian Optimizationmentioning

confidence: 99%

Section: Unmeasured Disturbancesmentioning

confidence: 99%

Section: Unmeasured Disturbancesmentioning

confidence: 99%

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Model‐free real‐time optimization of process systems using safe Bayesian optimization

Krishnamoorthy

Doyle²

2023

Data‐driven coordination of subproblems in enterprise‐wide optimization under organizational considerations

Berg¹,

Petsagkourakis²,

Shah³

et al. 2023

Self Cite

While decomposition techniques in mathematical programming are usually designed for numerical efficiency, coordination problems within enterprise-wide optimization are often limited by organizational rather than numerical considerations. We propose a "data-driven" coordination framework which manages to recover the same optimum as the equivalent centralized formulation while allowing coordinating agents to retain autonomy, privacy, and flexibility over their own objectives, constraints, and variables. This approach updates the coordinated, or shared, variables based on derivative-free optimization (DFO) using only coordinated variables to agent-level optimal subproblem evaluation "data." We compare the performance of our framework using different DFO solvers (CUATRO, Py-BOBYQA, DIRECT-L, GPyOpt) against conventional distributed optimization (ADMM) on three case studies: collaborative learning, facility location, and multiobjective blending. We show that in low-dimensional and nonconvex subproblems, the exploration-exploitation trade-offs of DFO solvers can be leveraged to converge faster and to a better solution than in distributed optimization.

A globally convergent composite‐step trust‐region framework for real‐time optimization

Zhang,

Li,

Wang

et al. 2023

Inaccurate models limit the performance of model‐based real‐time optimization (RTO) and even cause system instability. Therefore, a RTO framework that guarantees global convergence in the presence of plant‐model mismatch is desired. In this regard, the trust‐region framework is intuitive and simple to implement for unconstrained problems. Constrained RTO problems are converted to unconstrained ones by the penalty function, and global convergence is guaranteed if the penalty coefficient is large enough. However, a sufficiently large penalty coefficient is hard to determine and may lead to numerical difficulties. This paper addresses this issue and proposes a novel composite‐step trust‐region framework for constrained RTO problems that handles inequality constraints directly. The trial step is decomposed into a normal step that improves feasibility and a tangential step that reduces the cost function. A rigorous proof of its global convergence property is given.