Efficient curvature-constrained least cost route optimization on parallel architectures

Abstract

When choosing a path for a linear infrastructure between two terminals, several types of constraints apply for installation and operational criteria. For offshore pipelines or cables, curvature constraints are typically important not only due to the flexural rigidity but also the maneuverability of the laying vessels. Roads are subject to similar curvature constraints to ensure the safety of users travelling at the design speed. Yet, such constraints are not taken into account in traditional least cost routing methods, often based on Dijkstra’s algorithm. Post-process smoothing is often necessary, resulting in non-optimal routes. We present a new method for least cost route optimization, allowing to incorporate the curvature constraints into the primary calculations as opposed to a post-determination consideration. With this technique, smoothing of the least cost route becomes unnecessary, preserving its optimal character. Optimization algorithms for the trajectories of forward-moving vehicles were adapted for the routing of linear infrastructures and modified to include an angular discretization of variable resolution, resulting in faster and more accurate results. In addition to the inclusion of curvature constraints, the proposed method offers a higher flexibility in terms of local route orientation compared to the traditional Dijkstra’s algorithm, producing routes of lower cost. The numerical solver was implemented on parallel architectures, to compute optimal routes on realistic domains in reasonable computational times. For personal computers with a few computing cores, the OpenMP implementation on Central Processing Units does not significantly increase the iteration count and provides significant speedups. For certain configurations, the use of Graphical Processing Units reduces further the computational time.