A systematic mixed-integer differential evolution approach for water network operational optimization

The operational management of potable water distribution networks presents a great challenge to water utilities, as reflected by the complex interplay of a wide range of multidimensional and nonlinear factors across the water value chain including the network physical structure and characteristics, operational requirements, water consumption profiles and the structure of energy tariffs. Nevertheless, both continuous and discrete actuation variables can be involved in governing the water network, which makes optimizing such networks a mixed-integer and highly constrained decision-making problem. As such, there is a need to situate the problem holistically, factoring in multidimensional considerations, with a goal of minimizing water operational costs. This paper, therefore, proposes a systematic optimization methodology for (near) real-time operation of water networks, where the operational strategy can be dynamically updated using a model-based predictive control scheme with little human intervention. The hydraulic model of the network of interest is thereby integrated and successively simulated with different trial strategies as part of the optimization process. A novel adapted mixed-integer differential evolution (DE) algorithm is particularly designed to deal with the discrete-continuous actuation variables involved in the network. Simulation results on a pilot water network confirm the effectiveness of the proposed methodology and the superiority of the proposed mixed-integer DE in comparison with genetic algorithms. It also suggests that 23.69% cost savings can be achieved compared with the water utility's current operational strategy, if adaptive pricing is adopted for all the pumping stations.