SPO-VCS: An End-to-End Smart Predict-then-Optimize Framework with Alternating Differentiation Method for Relocation Problems in Large-Scale Vehicle Crowd Sensing

TL;DR

The paper tackles biased sensing coverage in vehicle crowd sensing by coupling demand prediction for non-dedicated vehicles with a constrained relocation optimization for dedicated vehicles in an end-to-end SPO framework. It introduces a QP-based optimization layer embedded in a neural network and solves it with an explicit unrolling of ADMM iterations, enabling gradient flow for joint training. Through two real-world datasets (Hong Kong and Chengdu), SPO-A demonstrates superior matching accuracy and scalability over traditional PTO and SPO-C baselines, particularly in large-scale networks, by directly optimizing task-specific distribution matching rather than minimizing upstream prediction error alone. The approach shows robust performance across multiple target distributions and DV/NDV control ratios, with sensitivity analyses confirming practical applicability and suggesting avenues for further efficiency improvements and broader transportation applications.

Abstract

Ubiquitous mobile devices have catalyzed the development of vehicle crowd sensing (VCS). In particular, vehicle sensing systems show great potential in the flexible acquisition of spatio-temporal urban data through built-in sensors under diverse sensing scenarios. However, vehicle systems often exhibit biased coverage due to the heterogeneous nature of trip requests and routes. To achieve a high sensing coverage, a critical challenge lies in optimally relocating vehicles to minimize the divergence between vehicle distributions and target sensing distributions. Conventional approaches typically employ a two-stage predict-then-optimize (PTO) process: first predicting real-time vehicle distributions and subsequently generating an optimal relocation strategy based on the predictions. However, this approach can lead to suboptimal decision-making due to the propagation of errors from upstream prediction. To this end, we develop an end-to-end Smart Predict-then-Optimize (SPO) framework by integrating optimization into prediction within the deep learning architecture, and the entire framework is trained by minimizing the task-specific matching divergence rather than the upstream prediction error. Methodologically, we formulate the vehicle relocation problem by quadratic programming (QP) and incorporate a novel unrolling approach based on the Alternating Direction Method of Multipliers (ADMM) within the SPO framework to compute gradients of the QP layer, facilitating backpropagation and gradient-based optimization for end-to-end learning. The effectiveness of the proposed framework is validated by real-world taxi datasets in Hong Kong. Utilizing the alternating differentiation method, the general SPO framework presents a novel concept of addressing decision-making problems with uncertainty, demonstrating significant potential for advancing applications in intelligent transportation systems.

Figures (18)

• Figure 1: An illustration of the sensing procedure in the VCS framework.
• Figure 2: The end-to-end SPO framework of the vehicle sensing problem.
• Figure 3: The variable relationship in different modules.
• Figure 4: Illustration of the computational graph.
• Figure 5: A comparison of the explicit and implicit differentiation method. (a) and (c) show the forward and backward pass through the implicit differentiation method by KKT, (b) and (d) depict the forward and backward pass through the alternating differentiation method.