Mixed-Integer Path-Stable Optimisation, with Applications in Model-Predictive Control of Water Systems

TL;DR

This paper introduces a branch-and-bound algorithm for solving mixed-integer non-convex non-linear optimal control problems with applications in water systems, providing global optimality guarantees.

Contribution

It develops a novel framework for mixed-integer path-stable optimization problems and implements deterministic solvers with proven global convergence.

Findings

Successfully applied to water system control problems

Achieved global optimal solutions for complex mixed-integer models

Demonstrated effectiveness of the method in practical scenarios

Abstract

Many systems exhibit a mixture of continuous and discrete dynamics. We consider a family of mixed-integer non-convex non-linear optimisation problems obtained in discretisations of optimal control of such systems. For this family, a branch-and-bound algorithm solves the discretised problem to global optimality. As an example, we consider water systems, where variations in flow and variations in water levels are continuous, while decisions related to fixed-speed pumps and whether gates that may be opened and closed are discrete. We show that the related optimal-control problems come from the family we introduce -- and implement deterministic solvers with global convergence guarantees.