An athlete–referee dual learning system for real-time optimization with large-scale complex constraints

Constrained optimization (CO) has made a profound impact in solving many real-world problems. Due to the high computation burden in exact solvers, data-driven CO based on machine learning techniques is recently receiving extensive research interests for its capability to solve CO problems in real time. The existing data-driven CO approaches only serve for optimization problems with rather simple constraints that can be directly incorporated into model training. However, constraints that are computationally infeasible or burdensome to evaluate are commonly experienced in realistic optimization applications, especially in the engineering sector. This paper proposes an athlete–referee dual learning system (ARDLS) for end-to-end CO with large-scale complex constraints, where an athlete model is trained as the main optimizer while a referee model is trained as a probabilistic constraint classifier to guide the athlete training. A risk-based constrained loss function is designed to fine-tune the athlete model for constraint satisfaction. A case study on electric power system emergency control application is conducted to validate the proposed ARDLS, where the testing results demonstrate the excellent capability of ARDLS to improve the likelihood of satisfying large-scale complex constraints in CO. © 2023 The Authors. Published by Elsevier B.V.