Multiobjective Analysis in Optimal Solution of Hydraulic Networks

The optimal design of closed hydraulic networks with pumping stations and different flow rate conditions is considered. The main difficulties in determination of optimal solutions for such problems are related to: (1) Nonlinearity of objective functions and constraints equations; and (2) heterogeneity between construction costs and management costs. In fact it is not easy to consider in the objective function both initial construction costs, which are related to the pipe weight, and management costs, which arise later and are essentially related to the pumping energy. Therefore it appears to be more reasonable to use multiobjective techniques. These techniques are used in order to define the optimal Pareto set in the space of the objective functions: each step of the sequence is analyzed by reduced gradient methods, with pipe diameters chosen in a range of standard values. The constraints are related to: (1) Minimum values of piezometric head at the nodes; and (2) maximum values of velocities in the branches.