Integrating Column Generation and Large Neighborhood Search for Bus Driver Scheduling with Complex Break Constraints

2025-05-05

AI Summary

This paper addresses the Bus Driver Scheduling Problem (BDSP), aiming to minimize operational costs while enhancing driver satisfaction under complex legal and collective bargaining constraints on working hours, rest periods, and qualification requirements. We propose a hybrid exact algorithm that tightly integrates Column Generation (CG) with Large Neighborhood Search (LNS): feasible duty columns generated during CG are reused to enrich LNS neighborhood structures, and the Resource-Constrained Shortest Path Problem (RCSPP) subproblem is accelerated via enhanced labeling techniques. Our Branch-and-Price framework achieves state-of-the-art (SOTA) performance on full-scale instances: optimal solutions for small instances; significantly reduced optimality gaps for medium-scale instances; and consistent superiority over an LNS baseline that treats CG as a black-box subroutine. The approach thus advances both computational efficiency and solution quality in BDSP optimization.

Technology Category

• Planning, Routing, and Scheduling: Learning for Planning and Scheduling
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Economics, Online Markets and Human Computation: The sharing economy
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

The Bus Driver Scheduling Problem (BDSP) is a combinatorial optimization problem with the goal to design shifts to cover prearranged bus tours. The objective takes into account the operational cost as well as the satisfaction of drivers. This problem is heavily constrained due to strict legal rules and collective agreements. The objective of this article is to provide state-of-the-art exact and hybrid solution methods that can provide high-quality solutions for instances of different sizes. This work presents a comprehensive study of both an exact method, Branch and Price (B&P), as well as a Large Neighborhood Search (LNS) framework which uses B&P or Column Generation (CG) for the repair phase to solve the BDSP. It further proposes and evaluates a novel deeper integration of B&P and LNS, storing the generated columns from the LNS subproblems and reusing them for other subproblems, or to find better global solutions. The article presents a detailed analysis of several components of the solution methods and their impact, including general improvements for the B&P subproblem, which is a high-dimensional Resource Constrained Shortest Path Problem (RCSPP), and the components of the LNS. The evaluation shows that our approach provides new state-of-the-art results for instances of all sizes, including exact solutions for small instances, and low gaps to a known lower bound for mid-sized instances. Conclusions: We observe that B&P provides the best results for small instances, while the tight integration of LNS and CG can provide high-quality solutions for larger instances, further improving over LNS which just uses CG as a black box. The proposed methods are general and can also be applied to other rule sets and related optimization problems

Problem

• Optimize bus driver scheduling with complex break constraints
• Develop exact and hybrid methods for diverse instance sizes
• Integrate Branch and Price with Large Neighborhood Search

Innovation

• Combines Column Generation and Large Neighborhood Search
• Integrates B&P and LNS for improved solutions
• Stores and reuses columns for global optimization