Optimal Localization of Pressure Reducing Valves in Water Distribution Systems by a Reformulation Approach

Leakage reduction represents one of the most challenging tasks in managing water distribution systems (WDSs). An effective way to leakage reduction is to carry out network operational pressure management through optimizing locations and regulations for pressure reducing valves (PRVs) and system pressures. This leads to a mixed-integer nonlinear program (MINLP) with a large number of binary variables which make it difficult to solve by an available software package. In this study, instead of directly solving the MINLP problem, we reformulate it to a mathematical program with complementarity constraints which can be efficiently solved by available NLP algorithms. The binary variables are replaced by continuous ones with complementarity constraints to be satisfied by a penalization scheme. To improve the quality of the solution and also to accelerate the convergence, in each relaxed NLP the results of the binary variables are rounded to binary values with which the NLP problem is solved again to achieve a MINLP solution. The final solution will be determined by the best one among the MINLP solutions. The results from two case studies reveal new and better combinations of PRVs as compared with those given in the literature.