Comparison of genetic algorithms to mathematical programming for the optimal design and operation of pumping stations

Since energy costs constitute the largest operational expenditure for nearly all water utilities worldwide, one of the greatest potential areas for energy cost-savings is the effective scheduling of daily pump operations. This paper focuses on the optimal control and operation of water distribution systems by means of two methods for solving the governing equations. The first method mathematically solves the large-nonlinear model using Lagrange Multipliers; the second approach obtains the optimum design and operation using the latest advances in genetic algorithms (GAs). The GA model automatically determines the least annual cost of the pump stations and their operation while satisfying target hydraulic performance requirements. The solution includes the selection of pump type, capacity, and the number of units, as well as scheduling the operation of irrigation pumps that result in minimum design and operating cost for a given set of demand curves. Computation is driven in both methods by an objective function that includes both operating and capital costs and the various performance and hydraulic constraints. Application of the two models to a real-world project shows not only considerable savings in cost and energy but also highlights the efficiency of GA approach for solving complex problems of this type.