Optimization of Critical Infrastructure with Fluids

Abstract

Many of the world's most critical infrastructure systems control the motion of fluids. Despite their importance, the design, operation, and restoration of these infrastructures are sometimes carried out suboptimally. One reason for this is the intractability of optimization problems involving fluids, which are often constrained by partial differential equations or nonconvex physics. To address these challenges, this dissertation focuses on developing new mathematical programming and algorithmic techniques for optimization problems involving difficult nonlinear constraints that model a fluid's behavior. These new contributions bring many important problems within the realm of tractability.

The first focus of this dissertation is on surface water systems. Specifically, we introduce the Optimal Flood Mitigation Problem, which optimizes the positioning of structural measures to protect critical assets with respect to a predefined flood scenario. Two solution approaches are then developed. The first leverages mathematical programming but does not tractably scale to realistic scenarios. The second uses a physics-inspired metaheuristic, which is found to compute good quality solutions for realistic scenarios.

The second focus is on potable water distribution systems. Two foundational problems are considered. The first is the optimal water network design problem, for which we derive a novel convex reformulation, then develop an algorithm found to be more effective than the current state of the art on select instances. The second is the optimal pump scheduling (or Optimal Water Flow) problem, for which we develop a mathematical programming relaxation and various algorithmic techniques to improve convergence.

The final focus is on natural gas pipeline systems. Two novel problems are considered. The first is the Maximal Load Delivery (MLD) problem for gas pipelines, which aims at finding a feasible steady-state operating point that maximizes load delivery for a severely damaged gas network. The second is the joint gas-power MLD problem, which couples damaged gas and power networks at gas-fired generators. In both problems, convex relaxations of nonconvex dynamical constraints are developed to increase tractability.