AES-RTO: An Adaptive Evolution Strategy for Real-Time Economic Optimization of High-Dimensional Chemical Processes

Chemical processes operate under time-varying economic conditions, such as changes in raw-material prices and market demand. Such changes may shift the economically optimal operating point. For high-dimensional systems, real-time optimization becomes difficult because the solution time rises rapidly with the number of decision variables and can exceed the available control interval. To address that issue, this paper develops an adaptive evolution strategy-based real-time optimization framework, termed AES-RTO. The framework first applies economically weighted uniform manifold approximation and projection (UMAP) to project the high-dimensional operating space into a low-dimensional latent space while retaining the cost-related structure. AES searches this latent space by adjusting the step size, expanding the population when needed, and performing directionally guided long-range exploration. These operations broaden the search when the optimization stalls and help prevent early convergence in local regions. The suboptimal point obtained from the search is then supplied to a gradient-based RTO step as a warm start, reducing the iterations required for final refinement. The framework was evaluated on a single-stage continuous stirred-tank reactor (CSTR), a higher-dimensional cascade CSTR, and the Tennessee Eastman Process. Across these cases, it improved the initial search result relative to the derivative-free methods considered and remained applicable to processes with heterogeneous constraints. The results indicate that AES-RTO provides a computationally efficient route to economically favorable operating points on the benchmark models studied, under changing economic parameters.