Roadside LiDAR placement for cooperative traffic detection by a novel chance constrained stochastic simulation optimization approach

Light Detection and Ranging (LiDAR) plays a pivotal role in localization, thereby meeting the imperative to accurately discern vehicle positions and road states for enhanced services in Intelligent Transportation Systems (ITS). As the cooperative perception among multiple LiDARs is necessitated by localization applications spanning extensive road networks, the strategic placement of LiDARs significantly impacts localization outcomes. This research proposes a chance constrained stochastic simulation-based optimization (SO) model for Roadside LiDAR (RSL) placement to maximize the expected value of mean Average Precision (mAP) subject to a budgeted number of RSLs and a chance constraint of ensuring a specific recall value under traffic uncertainties. Importantly, the assessment of a specific RSL placement plan employs a data-driven deep learning approach based on a high-fidelity co-simulator, which is inherently characterized by black-box nature, high computational costs and stochasticity. To address these challenges, a novel Gaussian Process Regression-based Approximate Knowledge Gradient (GPR-AKG) sampling algorithm is designed. In numerical experiments on a bi-directional eight-lane highway, the RSL placement plan optimized by GPR-AKG attains an impressive mAP of 0.829 while ensuring compliance with the chance constraint, and outperforms empirically designed alternatives. The cooperative vehicle detection and tracking under the optimized plan can effectively address false alarms and missed detections caused by heavy vehicle occlusions, and generate highly complete and smooth vehicle trajectories. Meanwhile, the analyses of detection coverage and average effective work duration validate the reasonability of prioritizing the center-mounted RSLs in the optimized plan. The balance analysis of mAP and the number of deployed RSLs confirms the scientific validity of deploying 20 RSLs in the optimized plan. In conclusion, the GPR-AKG algorithm exhibits promise in resolving chance constrained stochastic SO problems marked by black-box evaluations, high computational costs, high dimensions, stochasticity, and diverse decision variable types, offering potential applicability across various engineering domains.