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.

Optimal Traffic Flow Scheduling Using High-Performance Computing

“…Only in the special case of identical flights does the GPU perform significantly better than a multithreaded CPU. In this case, acceleration of up to nine times was observed using the GPU-based solver and, for smaller problems, larger acceleration values have been reported [26]. The fact that realistic problems, including the ones presented here, do not adhere to this ideal is also exhibited by the flattening of the execution time curve as a function of the number of concurrent threads in Fig.…”

“…Strength of the LP relaxation for very large problems has been noted in [23]. The problem described here is significantly larger than those described in [23] or later works demonstrating GPU-based decomposition [26], namely, in terms of the number of master problem constraints. An attempt was made to reduce the number of constraints by removing inactive constraints, but this approach does not work well for diverse schedules over a large timeframe.…”

“…Recent work [23,24] has shown that techniques such as the Dantzig-Wolfe (DW) decomposition [25] can exploit the unique block matrix structure of the LP and solve the problem using parallel computation and, in the process, significantly reduce the computation time, even for problems composed of a large number of flights over a large geographical area. Tandale et al [26] have demonstrated an implementation of the decomposition on graphics processing units. The results in that work were based on preliminary simulations that replicated a small set of flights multiple times to generate larger problems.…”

Applying Graph Theory to Problems in Air Traffic Management

“…Traffic Flow Management [27][28][29][30][31][32][33] (TFM) is concerned with choreographing the flow of air traffic across the national airspace system (NAS) based on demand and available capacity. It consists of a number of strategic programs and practices conducted by the Federal Aviation Administration (FAA) to ensure safety, while at the same time trying to minimize the costs associated with delays incurred.…”

A solution to the inverse problem of mathematical modeling of structural mechanics for beam elements

“…In the solution it is intended to use such properties of the problem as the sparsification of the obtained matrices being investigated, as well as the fact that it reduces well to the task of linear programming, making it possible to utilize effectively the possibilities of contemporary heterogeneous systems. There are a number of studies on the possibility of using heterogeneous systems for solving linear programming problems; in particular, [1] and [5] presented algorithms for solving linear programming problems on GPGPU systems from NVIDIA with CUDA (Compute Unified Device…”