Choosing an Optimization Method for Water Resources Problems Based on the Features of Their Solution Spaces

Abstract

One of the main challenges for solving complex water-resources optimization is choosing an appropriate solution method. An important feature of optimization problems is the convexity and extent of their solution spaces. The solution space is the set whose elements are all the reservoir releases that meet the optimization problem’s constraints and are thus feasible. The solution space of optimization problems can be convex or nonconvex. This study presents a method for determining the convexity or nonconvexity of the optimization problem solution space. The convexity and the extent of the solution space for a water-supply and a hydropower-production reservoir operation problem are evaluated by the proposed method. It is shown that the solution spaces of the former and latter problems are convex and nonconvex, respectively. The dependence of the solution spaces of the two reservoir operation problems on changes in evaporation, water demand for the water-supply reservoir, power plant capacity (PPC) for the hydropower reservoir, dead storage, reservoir capacity, and reservoir inflow is evaluated. The results demonstrate that the generalized reduced gradient (GRG) method finds an optimal value faster and more accurately than does the genetic algorithm (GA) when solving the water-supply problem, and that the GRG search is trapped in a local optimum when solving the hydropower-production problem.