The large-scale charging scheduling problem for fleet batteries: Lagrangian decomposition with time-block reformulations

TL;DR

This paper introduces a novel Lagrangian decomposition approach with time-block reformulations for large-scale fleet battery charging scheduling, significantly improving solution quality and computational efficiency over existing methods.

Contribution

It develops a new, tighter time-block reformulation and an ergodic-iterate-based local search, advancing optimization techniques for large-scale battery charging problems.

Findings

Achieved 43% lower objective value than state-of-the-art methods

Obtained near-optimal solutions in 71% of instances

Provided feasible solutions for all tested instances

Abstract

There is a rise in the need for efficient battery charging methods due to the high penetration of electromobility solutions. Battery swapping, a technique in which fully or partially depleted batteries are exchanged and then transported to a central facility for charging, introduces a unique scheduling problem. For scenarios involving a large number of batteries, commercial solvers and existing methods do not yield optimal or near-optimal solutions in a reasonable time due to high computational complexity. Our study presents a novel approach that combines variable layering with Lagrangian decomposition. We develop a new, tighter time-block reformulation for one of the Lagrangian sub-problems, enhancing convergence rates when used with our partial-variable fixing Lagrangian heuristic. We also propose an ergodic-iterate-based local search method to further improve the solution quality. Lower bounds are improved by learning the relation between Lagrangian multipliers and electricity cost. Our extensive benchmarks show superior computational performance against commercial solvers. We achieved, on average, a 43% lower objective value compared to state-of-the-art methods. In 71% of the instances, we obtained near-optimal solutions (optimality gap less than 6%), and 93% of the instances were below 10%. We obtained feasible solutions for all instances, compared to only 65% feasibility using incumbent methods. The developed exact method aims to support future research on charging scheduling, especially important for micromobility industry, vehicle-to-grid (V2G) applications, and second-life utilization of batteries. Furthermore, the developed polyhedral insights can be useful in other scheduling problems with a common underlying mathematical structure.