Evaluation of genetic algorithms using discrete and continuous methods for pump optimization of water distribution systems

• Evolutionary optimization method (e.g. GA) is suited for optimizing pumping system.
• Discrete and continuous methods applied for coding GA for optimizing pumping system.
• Discrete method needs more computer storage in comparison with continuous method.
• Mutation and crossover steps of continuous method may generate infeasible children.

A considerable portion of costs associated with delivering municipal drinking water is related to energy usage. This energy consumption also has environmental implications resulting from the pollutants emitted at power generation plants. Optimizing the cost and environmental emission of energy consumption by strategically scheduling pumping cycles is a multi-objective nonlinear problem that contains considerable number of constraints. The solution space of this type of problem even for a small water network can be very large and finding the boundaries associated with the solution space is quite difficult. Evolutionary optimization methods, such as genetic algorithm, are well suited for solving this kind of problem. In this paper, two methods for describing the pump optimization problem within a genetic algorithm solution framework are considered. Each leads to different methods for conducting crossover and mutation steps of the genetic algorithm. Results are presented when these methods are used with a novel pump optimization software, Pollutant Emission and Pump Station Optimization (PEPSO) using a hydraulic model of a moderately sized municipal drinking water system located in Monroe, MI, USA. Advantages and disadvantages of each method are discussed. Results highlight the need for genetic algorithm coding methods which circumvent infeasible solutions.