Accelerating Multi-Objective Evolutionary Algorithms for Cascade Hydropower Scheduling via a Physics-Embedded TCN

Cascade hydropower scheduling is a high-dimensional, tightly constrained multi-objective optimization problem in which classical genetic and evolutionary algorithms struggle to find feasible solutions. Under random initialization, algorithms such as the Non-dominated Sorting Genetic Algorithm II (NSGA-II), the Non-dominated Sorting Genetic Algorithm III (NSGA-III), and the Constrained Two-Archive Evolutionary Algorithm (C-TAEA) rarely produce any feasible solution when the feasible region occupies a vanishingly small fraction of the search space. This paper presents a three-phase framework that combines physics-guided deep learning with evolutionary computation to accelerate both NSGA-II and NSGA-III. The method trains a Physics-Embedded Temporal Convolutional Network (PeTCN) as a differentiable surrogate model that explicitly incorporates physical constraints, applies gradient-based inverse optimization to obtain a feasible or near-feasible solution of high quality, and warm-starts NSGA-II or NSGA-III with that solution for efficient Pareto front exploration. Experiments on a real-world six-station cascade system show that, under a 1500 s fixed-time budget across 20 independent runs, Boosted NSGA-II and Boosted NSGA-III both find feasible solutions in all runs. Boosted NSGA-II and Boosted NSGA-III both reach the first feasible solution within roughly 50–60 generations of Phase 3 search on average, whereas standard NSGA-II produces no feasible run within the same budget and standard NSGA-III requires thousands of generations among its successful runs. The mean final hypervolume reaches 43.84×106 for Boosted NSGA-II and 46.52×106 for Boosted NSGA-III, and both boosted algorithms reach a target hypervolume of 35.00×106 in all 10 target-hypervolume runs. These results demonstrate that coupling physics-embedded surrogates with gradient-based initialization is an effective strategy for constrained multi-objective problems in which feasible solutions are extremely sparse.