Making A Trade-Off Between Cost and Distance By A Differentiable Way

Zishang Chen, Longhe Lin, Qi Qi

Keywords: Transportation Planning, Combinatorial Optimization, Cost Distance Problem, Gradient Descent

TL;DR: We propose the first gradient-based framework for Cost-Distance problem.

Abstract: The Cost-Distance problem, introduced by Meyerson, which is a natural abstraction for modeling UAV logistics networks, seeks a network design that simultaneously minimizes construction cost and the weighted routing distances from multiple sources to a designated root. Existing methods exhibit a strong dependence on the number of sources and are difficult to parallelize, which hinders their scalability on large graphs. We propose Cost-Distance Policy Gradient (CDPG), the first gradient-based framework for this problem. CDPG relaxes the discrete subgraph selection into a probabilistic adjacency matrix and formulates the Cost-Distance objective as an expectation, enabling efficient optimization via policy gradients. Our algorithm achieves the time complexity of $\mathcal{O}(m\log n)$, faster than the previous fastest approximation algorithm's $\mathcal{O}(|S|(m+n\log n))$ in graphs with dense sources. Extensive experiments across 9 real-world Unmanned Aerial Vehicle (UAV) logistics scenarios in the Guangdong-Hong Kong-Macao Greater Bay Area demonstrate that CDPG significantly outperforms approximation algorithms, continuous relaxation baselines, and heuristic search methods. Our code is available at: \url{https://anonymous.4open.science/r/iclr_cdpg-8737}.

Primary Area: other topics in machine learning (i.e., none of the above)

Submission Number: 7874