Improving Computational Efficiency of Model Predictive Control Genetic Algorithms for Real-Time Decision Support

Enabling real-time decision support, particularly under conditions of uncertainty, requires computationally efficient algorithms that can rapidly generate recommendations. In this paper, a suite of model predictive control (MPC) genetic algorithms are developed and tested offline to explore their value for reducing CSOs during real-time use in a deep-tunnel sewer system. MPC approaches include the micro-GA, the probability-based compact GA, and domain-specific GA methods that reduce the number of decision variable values analyzed within the sewer hydraulic model, thus reducing algorithm search space. Minimum fitness and constraint values achieved by all GA approaches, as well as computational times required to reach the minimum values, are compared to large population sizes with long convergence times.

Optimization results for a subset of the Chicago combined sewer system indicate that genetic algorithm variations with coarse decision variable representation, eventually transitioning to the entire range of decision variable values, are most efficient at addressing the CSO control problem. Although diversity-enhancing micro-GAs evaluate a larger search space and exhibit shorter convergence times, these representations do not reach minimum fitness and constraint values. The domain-specific GAs prove to be the most efficient and are used to test CSO sensitivity to energy costs, CSO penalties, and pressurization constraint values. The results show that CSO volumes are highly dependent on the tunnel pressurization constraint, with reductions of 13% to 77% possible with less conservative operational strategies. Because current management practices may not account for varying costs at CSO locations and electricity rate changes in the summer and winter, the sensitivity of the results is evaluated for variable seasonal and diurnal CSO penalty costs and electricity-related system maintenance costs, as well as different sluice gate constraint levels. These findings indicate that optimal operating strategies are governed by tunnel pressurization constraint values regardless of the CSO penalty and energy costs.