A Comparison of Optimization Methods for Path Finding Problem

Abstract—Optimizing travel time on a multi-lane highway with dynamically changing traffic density poses a 2-dimensional path optimization challenge. The temporal evolution of traffic density introduces a quasi-quadratic nature to the optimization problem, rendering quadratic optimization methods applicable. This research compares prevalent quadratic optimization techniques—specifically, the interior point method (IPM), sequential quadratic programming (SQP), and active set (AS) methods—in terms of both travel times and computational efficiency. A Monte-Carlo (MC) study is conducted, incorporating variables like the number of lanes, road length, and constraints on car speed (i.e., speed limits).Additionally, a novel path optimization approach, termed ’segmented path optimization,' is introduced. This method involves dividing the road into segments, optimizing each segment, merging their end and start points, and discretizing the optimal path. Through our comparative analysis, we find that the efficacy of these methods is context-dependent. There is no universally superior method, as each demonstrates its advantages under different conditions. However, the pipeline and the optimization flowchart may help the structuring of future works that contain the optimization processes, especially in artificial intelligence, smart recommendation, and GPS-based systems.