DGA: a differential relaxation of genetic algorithms for receding-horizon control of nonlinear systems

Abstract

The growing complexity of industrial cyber-physical systems demands control strategies capable of handling strong nonlinearities, tight actuator constraints, and competing objectives under real-time requirements. Although Genetic Algorithms (GAs) are widely used in this class of problems, their non-differentiable operators prevent integration with modern gradient-based and decision-aware learning frameworks. This work proposes a Differentiable Genetic Algorithm (DGA) formulated as a smooth relaxation of a real-coded GA with simulated binary crossover and polynomial mutation, replacing hard components with distributional representations to enable gradient propagation through the evolutionary search process while preserving population-based exploration. The DGA layer is embedded within a receding-horizon control framework and evaluated on a nonlinear boiler drum–turbine unit with actuator magnitude and rate constraints. Results show improved tracking accuracy, smoother control signals, and balanced constraint activity compared to classical and rejection-based GA-MPC variants. Computational benchmarking further demonstrates that the proposed distributional relaxation achieves comparable solution quality to EvoGrad while substantially reducing runtime. These results show that evolutionary optimization and differentiable learning can be unified within a coherent framework for constrained nonlinear control.