From nonlinear programming theory to practical optimization algorithms: A process engineering viewpoint

Abstract

As process optimization becomes an established and mature technology for process simulation, analysis and operation, it becomes important to consider larger and more creative problem formulations and applications, as well as the development of efficient algorithms to tackle them. Here, some novel process optimization applications are briefly reviewed in the following areas of process design and analysis:• treatment of constrained and nonsmooth simulation problems, particularly in phase equilibrium • synthesis of chemical reactor networks through the application of targeting strategies • more efficient strategies for process optimization and postoptimality analysis • treatment of uncertainty through multiperiod optimization problems • the role of automatic differentiation tools in process optimization An outline of the concepts behind each of these topics will be presented and process examples are briefly described in order to demonstrate the effectiveness of these optimization-based applications.

Measurement-based optimization of batch and repetitive processes using an integrated two-layer architecture

“…Three main variants of this method are direct single shooting, direct multiple shooting, and orthogonal collocation [see, e.g., 27,28]. The focus in this section is on the former approach, also known as direct sequential approach, but the following ideas can be readily extended to the other two approaches.…”

“…Moreover, in using derivative-based NLP techniques such as SQP, the first-order derivatives-and the second-order derivatives too if necessary-can be obtained from the numerical integration of the associated state-sensitivity or adjoint equations [28].…”

“…4. This solution was determined by first applying a direct sequential approach with a piecewise-constant control parameterization [28,44], and then refining the solution using an indirect shooting approach [23]. It consists of an upper bound, a lower bound, and an interior arc.…”

“…State-of-the-art numerical techniques for solving optimal control problems can be classified as direct methods, whereby the control trajectories are parameterized and an approximate optimal solution is computed by solving the resulting finite-dimensional optimization problem (NLP) [27,28]; and indirect methods, where one seeks for trajectories that satisfy the Pontryagin maximum principle, without the need to resort to a control parameterization [29,30]. Accordingly, NE updates can be computed from the linearization of either the parameterized optimal control problem, using NLP sensitivity theory [24], or of the original optimal control problem, using NE control theory [23].…”

Extension of modifier adaptation for controlled plants using static open-loop models

“…If a plant model is available, numerical optimization techniques can be used to compute a local [1] or even the global [2] solution. The problem to be solved then reads: u * (θ ) := arg min u φ (u, θ ) subject to g (u, θ ) ≤ 0, (1.2) where φ is the modeled cost function, g is the n g -dimensional vector of modeled plant constraints, and θ is an n θ -dimensional vector of model parameters.…”