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Highlights • An enhanced surrogate assisted framework for constrained global optimization is proposed. • Maximizing probability of improvement approach is used for selecting infill points. • Kriging meta-models of objective and constraints functions are updated in every iteration. • Meta-model of objective function is local optimized when it's sufficient mature. • Numerical results indicate that the framework is suitable for use in solving computationally expensive and constrained black-box optimization. Abstract An enhanced surrogate assisted framework, based on Probability of Improvement (PI) method, is proposed in this paper. We made some modifications to the original PI approach to enhance the performance of the modeling and optimization framework, leading to fewer rigorous simulations to find the optimal solution without loss of accuracy. We also extended the algorithm for handling general constraints using a fully probabilistic approach. The behavior of the proposed framework was investigated through a set of 9 Unconstrained Test Functions (UTF), 7 Constrained Optimization Problems (COP) and 3 Chemical Engineering Problems (CEP). The numerical results indicate that a lower number of rigorous model simulations were needed for optimizing UTF compared to the classic PI method and that the proposed framework was capable of achieving sustained near optimal solutions for COP and CEP. These results indicate that the proposed framework is suitable for solving computationally expensive constrained black-box optimization problems. [ABSTRACT FROM AUTHOR]

Highlights • A novel piecewise state feedback controller is introduced. • The chemical process optimal control problem is formulated as an optimal control problem of switched dynamical systems. • A gradient-based parallel optimization algorithm is developed for solving the optimal control. • Convergence results indicate that the gradient-based parallel optimization algorithm is global convergent. • Three chemical process optimal control problems are given to illustrate the effectiveness of the proposed algorithm. Abstract This paper considers an optimal control problem of chemical processes with a novel piecewise state-feedback controller. Firstly, the chemical process optimal control problem is formulated as a switched dynamical system optimal control problem, which can be transformed into a parameter optimization problem. Next, to achieve rapid convergence from remote starting points, we propose a novel gradient-based optimization algorithm, which is suitable to a parallel implementation because the step is improved by updating its direction as well as its length simultaneously before moving to the next iteration, and the step computation involves only the inner products of vectors. Then, the convergent properties of the parameter optimization problem to the original optimal control problem are discussed. Finally, the numerical simulation results show that the gradient-based parallel optimization algorithm is an effective alternative method for solving the chemical process optimal control problems. [ABSTRACT FROM AUTHOR]