Multiperiod Hypergraph Models for Water Systems Optimization

Abstract

Mathematical models describing water resources systems optimization are characterized by a large number of variables and constraints, which are needed to describe the physical components of the system, its functional ties, and its operating modalities. Some special algebraic structures allow its representation as a pure hypergraph flow problem. The hypergraph structure is derived from a multiperiod network describing the spatial and temporal structure of the physical system. As a crucial feature in modeling functional relations and in describing scenario changes in the system, with the hypergraph approach it is possible to reach a close correspondence between the components of the physical problem and those of the mathematical model. In this paper a water resources management model including a reservoir design problem is studied, and the methodology is tested by the hypergraph simplex algorithm on a real water resources system on the island of Sardinia (Italy) in a extended time horizon. The results obtained show that this technique is very competitive in this kind of problem.