Wastewater treatment process optimization in stochastic game based on multiagent deep reinforcement learning

Frequent changes in process conditions and production materials make the papermaking wastewater treatment process (PWTP) inherently nonlinear and dynamically uncertain. Meanwhile, the industry is under increasing pressure to achieve coordinated pollution control and carbon reduction. Therefore, ensuring compliance with wastewater discharge standards while simultaneously reducing operational costs, energy consumption, and greenhouse gas (GHG) emissions remains a critical challenge. To this end, this study proposes a multi-objective optimization approach that integrates Kriging and High-Dimensional Model Representation (HDMR) with multi-agent deep reinforcement learning (MADRL) for the papermaking wastewater treatment process (PWTP). In this work, the biochemical and sedimentation processes were modeled using the Benchmark Simulation Model No. 1 (BSM1). A Kriging-HDMR-based surrogate model was developed to estimate the GHG emissions of the process in real time by integrating biochemical mechanisms and data-driven models. This surrogate model was embedded within a reinforcement learning framework to construct a multi-agent "exploring-observing-employing" dynamic optimization system. The MADRL strategy enables collaborative multi-objective optimization for both pollution reduction and carbon mitigation. Simulation results demonstrate that, compared to the BSM1 benchmark control, the proposed policy achieves a 3.52% reduction in operational costs, a 26.38% reduction in energy consumption, and a 7.9% reduction in GHG emissions, while maintaining compliance with effluent quality standards and achieving robust performance.