Equity-Transformer: Solving NP-Hard Min-Max Routing Problems as Sequential Generation with Equity Context
Jiwoo Son, Minsu Kim, Sanghyeok Choi, Hyeonah Kim, Jinkyoo Park
Abstract
Min-max routing problems aim to minimize the maximum tour length among multiple agents as they collaboratively visit all cities, i.e., the completion time. These problems include impactful real-world applications but are known as NP-hard. Existing methods are facing challenges, particularly in large-scale problems that require the coordination of numerous agents to cover thousands of cities. This paper proposes Equity-Transformer to solve large-scale min-max routing problems. First, we model min-max routing problems into sequential planning, reducing the complexity and enabling the use of a powerful Transformer architecture. Second, we propose key inductive biases that ensure equitable workload distribution among agents. The effectiveness of Equity-Transformer is demonstrated through its superior performance in two representative min-max routing tasks: the min-max multi-agent traveling salesman problem (min-max mTSP) and the min-max multi-agent pick-up and delivery problem (min-max mPDP). Notably, our method achieves significant reductions of runtime, approximately 335 times, and cost values of about 53% compared to a competitive heuristic (LKH3) in the case of 100 vehicles with 1,000 cities of mTSP. We provide reproducible source code: https://github.com/kaist-silab/equity-transformer.
BibTeX
@article{Son_Kim_Choi_Kim_Park_2024, title={Equity-Transformer: Solving NP-Hard Min-Max Routing Problems as Sequential Generation with Equity Context}, volume={38}, url={https://ojs.aaai.org/index.php/AAAI/article/view/30007}, DOI={10.1609/aaai.v38i18.30007}, abstractNote={Min-max routing problems aim to minimize the maximum tour length among multiple agents as they collaboratively visit all cities, i.e., the completion time. These problems include impactful real-world applications but are known as NP-hard. Existing methods are facing challenges, particularly in large-scale problems that require the coordination of numerous agents to cover thousands of cities. This paper proposes Equity-Transformer to solve large-scale min-max routing problems. First, we model min-max routing problems into sequential planning, reducing the complexity and enabling the use of a powerful Transformer architecture. Second, we propose key inductive biases that ensure equitable workload distribution among agents. The effectiveness of Equity-Transformer is demonstrated through its superior performance in two representative min-max routing tasks: the min-max multi-agent traveling salesman problem (min-max mTSP) and the min-max multi-agent pick-up and delivery problem (min-max mPDP). Notably, our method achieves significant reductions of runtime, approximately 335 times, and cost values of about 53% compared to a competitive heuristic (LKH3) in the case of 100 vehicles with 1,000 cities of mTSP. We provide reproducible source code: https://github.com/kaist-silab/equity-transformer.}, number={18}, journal={Proceedings of the AAAI Conference on Artificial Intelligence}, author={Son, Jiwoo and Kim, Minsu and Choi, Sanghyeok and Kim, Hyeonah and Park, Jinkyoo}, year={2024}, month={Mar.}, pages={20265-20273} }