Investigação de abordagens evolutivas e otimização Bayesiana restrita no problema de otimização em tempo-real

Abstract

Real-time optimization (RTO) is a technique capable of iteratively leading an industrial process (plant) to its optimal economic operation, using for this an approximate mathematical model combined with the solution of a non-linear optimization problem. In order to deal with model-plant mismatch, different approaches are available in the literature, among which the Modifier Adaptation (MA) stands out. It applies first-order corrections to the cost and constraints functions in order to achieve plant optimality upon convergence. However, the calculation of these corrections depends on plant gradient information, which is difficult to obtain. Promising approaches to overcome this limitation are to perform Gaussian Processes (GP) regression to model the mismatch and use Bayesian optimization techniques. Aiming to initiate a further discussion of the numerical problems expected with the application of these new approaches, the objective of this work is to study the effect of the optimizer on the performance of randomly initialized RTO systems in the presence of measurement noise. For this, we consider the MA with GPs adaptation (MA-GP) and a new approach using constrained Bayesian optimization through the Expected Improvement with Constraints (EIC) acquisition function. Based on the convergence to the plant optimum, iteration feasibility and computational cost, the performance of deterministic nonlinear optimization algorithms (Sequential Quadratic Programming (SQP) and Nelder-Mead Simplex (NM)) and an evolutionary heuristic (Differential Evolution (DE)) are compared. For two benchmark models available in the literature, it is illustrated that the SQP and NM algorithms may fail to find the optimum during the RTO system iterations. As a result, the system’s performance is degraded, presenting higher variability and sensitivity to the initialization step. For a confidence interval of 95%, DE outperformed the other algorithms, although it requires a higher computational effort. Furthermore, it is possible to prove the proposed technique’s potential via constrained Bayesian optimization. By allowing the use of the unrestricted NM algorithm, it becomes efficient when compared to MA-GP with SQP, requiring at the same time a low computational cost. However, its convergence is still uncertain and its performance is inferior to MA-GP, especially for problems where the plant’s optimal operating point is at the intersection of its constraints.