AN ALGORITHM FOR OPTIMAL SCHEDULING OF A CLASS OF CASCADE WATER-SUPPLY SYSTEMS

The problem of determining overall optimized control schedules for a c lass of cascade water supply systems containing only fixed speed pumps is examined. The system control is by nature an on-off type. The opti mal scheduling problem can be formulated as dynamical optimal control problems with purely discrete symbols, discrete controls and also with continuous intermediate variables interrelated in a highly non-linear way. An efficient problem solver is proposed. Its high efficiency is achieved by exploiting, through a suitable decomposition, certain stru ctural properties of the problem. Lagrange relaxation is applied in or der to break down the time structure of discrete control variables. Th e decomposition also enables consideration of mixed integer optimizati on on purely static grounds. The dynamical optimization constitutes on ly that part of the solver which deals with entirely continuous variab les. There is a duality gap in the problem. However, certain, but not complete, information obtained through solving the dual problem (dual optimal information) is close to that which corresponds to the true (p rimal) optimal solution. This is an important property of the scheduli ng problem, which together with the problem structure creates a basis for the solver design.