Abstract
In this paper, we have suggested a penalty method to modify the combinatorial optimization problem with the linear constraints to a global optimization problem with linear constraints. It also deals with a topic of vital significance of pump operation optimization in a water system. In this connection we have done a lot of work to formulate a model based on a simplified flow volume balance to resolve the problem of optimal pump operation settings of switching "ON" and "OFF" with the reduced gradient method. This global solution approach incorporates some benefits for practical application to a real system as is shown in the case study.