(173g) Novel Feasible Path Optimization Algorithms for Optimal Process Design Using Rigorous Models

Energy crisis, environmental challenges and the pursuit of high economic profit are driving process engineers to design the most efficient chemical processes (Richard C. Pattison et al., 2016; Recker et al., 2014). To find the optimal design, process optimization problems should be formulated with accurate mathematical models to predict real-world behavior of a process and systematic optimization strategies to drive the process model towards the optimal point (Biegler, 2017). However, accurate models or so-called rigorous models are often strongly nonlinear, non-convex or even ill-conditioned, leading to convergence problems when they are solved directly.

The feasible path optimization algorithm is widely used to solve such highly complex optimization problems as a feasible path is followed in each optimization iteration, possibly leading to good convergence performance (Biegler, 2010). The feasible path algorithm decomposes the nonlinear optimization problems into two sub-problems including a small-scale optimization problem in the outer level and a process simulation problem in the inner level. While the small-scale optimization problem can be solved using existing gradient-based optimization algorithms, the process simulation problem can be solved using solution algorithms for nonlinear equations such as a Newton-based algorithm (Barton, 1992). As a result, the performance of the feasible path optimization algorithm strongly replies on the convergence of the process simulation problem, which is difficult to guarantee in the equation-oriented (EO) environment. The pseudo-transient continuation (PTC) modeling approach can significantly improve the convergence performance of the process simulation and hence enable to solve many challenging process flowsheet optimization problems (R. C. Pattison & Baldea, 2014; Tsay et al., 2019). There are two existing variants of the feasible path algorithm using PTC modelling approach including the time-relaxation-based optimization algorithm (R. C. Pattison & Baldea, 2014) and the PTC model-assisted steady-state optimization algorithm (Ma et al., 2018) The former often leads to computational inefficiency due to time-consuming dynamic simulations required during the optimization, while the latter is more computationally efficient but may fail to converge in some cases.

In this work, we propose three novel feasible path optimization algorithms to improve the convergence and computational efficiency. The first algorithm improves the original steady-state feasible path algorithm through resetting the initial point used for process simulation when the directly preceding point fails during the line search. The second algorithm enhances the time-relaxation-based optimization algorithm by incorporating the tolerances-relaxation integration method for the PTC simulation. The last algorithm is a hybrid algorithm through the effective combination of the steady-state simulation and the PTC simulation in the feasible path optimization framework. Two strategies are used to tackle the failure problem due to numerical noise in process simulation, especially when an ill-conditioned Hessian matrix and Jacobian matrix appear. These two strategies include the use of a smaller simulation tolerance and restarting the optimization with the default Hessian matrix and Lagrange multipliers from the point where the optimization fails.

Several complex process design problems from the literature (Ma et al., 2018; Ma et al., 2019) are used to illustrate the capability of the proposed three novel algorithms. The computational results demonstrate that the proposed algorithms can successfully solve these complex process design problems to local optimality. We also compare the performance of the proposed algorithms with the time-relaxation-based optimization algorithm and the PTC model-assisted steady-state optimization algorithm. It is shown that the proposed new algorithms have improved convergence and higher computational efficiency compared to the time-relaxation-based algorithm and the PTC model-assisted steady-state algorithm. It is also indicated that the improved steady-state feasible path algorithm and the hybrid algorithm are the most promising and are superior to other feasible path algorithms.

Reference

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Ma, Y., Luo, Y., & Yuan, X. (2019). Towards the really optimal design of distillation systems: Simultaneous pressures optimization of distillation systems based on rigorous models. Computers & Chemical Engineering, 126, 54-67.

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