Graphical Deterministic Equivalent Algorithm for Robust Process Optimization

The uncertainty of process parameters is always a challenge during the design of chemical processes. There are several ways to consider uncertainty during process optimization, for example: stochastic programming, chance-constrained programming, and robust optimization (Li and Grossman, 2021). Robust optimization, in particular, yields the highest risk avoidance, i.e. to plan for the worst-case scenario (Li and Grossman, 2021). In this contribution, a graphical method is proposed to estimate the robust optimum of an optimization problem, given a bounded uncertainty set. This method is based on the Monte Carlo method to find a combination of uncertain parameters that would give the robust optimum. With the robust uncertain parameter as the input, the optimization problem can be solved deterministically to obtain the robust optimum. To demonstrate the method, a reactor-separator system with recycle, where the uncertain parameters follow Gaussian distribution is used. The proposed method was benchmarked and compared against PyROS solver that is based on the Generalized Robust Cutting Set algorithm (Isenberg et al., 2021). The results show that compared to the more robust PyROS solver, the graphical method with 5000 samples gives a 3% difference in the objective value function with 33% computation time requirement. The speed can be increased further by utilizing parallelization during the feasibility checks of each sample.