Reduction of the search space for the optimization problem of the design of the pumping station through the automatic identification of infeasible flow distributions

Abstract

The pumping station design is a critical process in water distribution networks. This set of decisions will have an immediate impact on construction costs and determine energy consumption over the entire lifetime of the system. However, the minimization of investment and operational costs at the same time is a complex problem that has been approached from different perspectives. To achieve this goal, in recent years, it has been shown that it is possible to optimize the selection of pumps, accessories, and control systems while optimizing the flow distribution provided by the pumping stations by using the setpoint curve. However, the huge number of possible combinations and the non-linearity of the equations rule out the use of exact methods to solve the proposed mathematical model. Despite this, some metaheuristic techniques, specifically population-based evolutionary algorithms, have shown good performance against case studies in networks with a high level of simplification. Each objective function evaluation involves at least one hydraulic simulation during the analysis periods. Therefore, the computational effort grows considerably as the size of the network increases, affecting the efficiency of these algorithms and limiting their use to smaller networks. Thus, optimization of the design of pumping stations in real-size networks is a problem that has not yet been fully resolved. To reduce the number of evaluations of the objective function during the optimization process, this work presents a new method for the reduction of the search space based on the automatic identification of infeasible flow ranges as part of the network preprocessing. The method considers the maximum capacity of the available pumps, the minimum pressure required, and the demand patterns of the network. In this way, each pumping station has different restrictions for the decision variables of the mathematical model related to the flow contributions. From this point on, the algorithm does not waste any computational effort evaluating solutions that represent flow distributions previously classified as infeasible. Therefore, it is possible to accelerate the convergence of the algorithms while preserving the quality of the solutions obtained. This new method can be applied to any direct injection network. The amount of solution space reduction will depend on the characteristics of each network. To clarify, this work includes the analysis of one case study and a genetic algorithm was implemented to resolve the model. Finally, the results show a reduction of the solutions space of 80% for the largest network presented.