Optimization of Multi-Quality Water Networks: Can Simple Optimization Heuristics Compete with Nonlinear Solvers?

Abstract

Optimal management of water systems tends to be very complex, especially when water quality aspects are included. This paper addresses the management of multi-quality water networks over a fixed time horizon. The problem is formulated as an optimization program that minimizes cost by determining the optimal flow distribution that satisfies the water quantity and quality requirement in the demand nodes. The resulted model is nonlinear and non-convex due to bilinear terms in the mass balance equations of blending multi-quality flow. This results in several local optima, making the process of solving large-scale problems to global optimality very challenging. One classical approach to deal with this challenge is to use a multi-start procedure in which off-the-shelf local optimization solvers are initialized with several random initial points. Then the final optimal solution is considered as the lowest objective value over the different runs. This will lead to a cumbersome and slow solution process for large-scale problems. In light of the above, this study supports using ultra-fast simple optimization heuristics, which despite their moderate accuracy, can still reach the optimum solution when run many times using a multi-start procedure. As such, the final solution from simple optimization heuristics can compete with off-the-shelf nonlinear solvers in terms of accuracy and efficiency. The paper presents a simple optimization heuristic, which is specially tailored for the problem and compares its performance with a state-of-the-art nonlinear solver on large-scale systems.