Bayesian Optimization with Unknown Constraints for the Design and Real-Time Control of Stormwater Systems

Despite the prevalence of input-constrained optimization methods in the design and control of stormwater systems, these methods often do not align with the stated desires of designers. For example, it is often specified that flooding must not occur under real-time control (RTC). However, this constraint is defined in the output space and thereby has an a priori unknown relationship to the controllable inputs. Bayesian optimization with unknown constraints (BOUC) accurately approximates these constraints defined in the output space. We demonstrate the utility of BOUC in the structural and operational design of five drainage networks from the real-time control benchmarking library pystorms. We also address four limitations in the original version of pystorms: (1) the cost function for some scenarios is not strongly influenced by the actuators provided; (2) other scenarios have cost functions lenient enough that local rule-based controllers are sufficient to score perfectly; (3) sensor and actuator faults and noise are not represented, though they are a key challenge of practical RTC implementation; and (4) the benchmark controllers necessary to avoid an inappropriate comparison of the performance of new control algorithms with the passive system are not included. We present revised scenarios improving feasibility (1) and increasing discriminative power (2) while implementing randomized faults (3). Heuristic local and coordinated controllers are tuned using BOUC tobenchmark future control algorithms (4). This study introduces an optimization method well-suited to stormwater design and operation while also expanding an existing benchmarking tool to support further development and fair comparison of methods.