Massively Parallel Optimal Solution to the Nationwide Traffic Flow Management Problem

Abstract

§NASA is developing algorithms and methodologies for efficient air-traffic management. Several researchers have adopted an optimization framework for solving problems such as flight scheduling, route assignment, flight rerouting, nationwide traffic flow management and dynamic airspace configuration. Computational complexity of these problems have led investigators to conclude that in many instances, real-time solutions are computationally infeasible, forcing the use of relaxed versions of the problem to manage computational complexity. The primary objective of this research is to accelerate optimization algorithms that play central roles in NASA’s ATM research, by parallel implementation on Graphics Processing Units (GPUs). This paper focuses on one of the optimization problems viz. the nationwide Traffic Flow Management Problem (TFMP) formulated by as a Binary Integer program. The Binary Integer program has a primal block angular structure that renders it amenable to the Dantzig-Wolfe decomposition algorithm. This research effort implemented a Simplex-based Dantzig-Wolfe (DW) decomposition solver on GPUs that exploits both coarse-grain and fine-grain parallelism. The implementation also exploits the sparsity in the problems, to manage both memory requirements and run-times for large-scale optimization problems. The GPU implementation was used to solve a TFM problem with 17,000 aircraft (linear program with 7 million constraints), in 15 seconds. The GPU implementation is 30 times faster than the exact same code running on the CPU. It is also 16 times faster than the NASA’s current solution that implements parallel DW decomposition using the GNU Linear Programming Kit (GLPK) on an 8-core computer with hyper-threading.