Massively Parallel Dantzig-Wolfe Decomposition Applied to Traffic Flow Scheduling

Optimal scheduling of air traffic over the entire National Airspace System is a computationally difficult task. To speed computation, Dantzig-Wolfe decomposition is applied to a known linear integer programming approach for assigning delays to flights. The optimization model is proven to have the block-angular structure necessary for Dantzig-Wolfe decomposition. The subproblems for this decomposition are solved in parallel via independent computation threads. Experimental evidence suggests that as the number of subproblems/threads increases (and their respective sizes decrease), the solution quality, convergence, and runtime improve. A demonstration of this is provided by using one flight per subproblem, which is the finest possible decomposition. This results in thousands of subproblems and associated computation threads. This massively parallel approach is compared to one with few threads and to standard (non-decomposed) approaches in terms of solution quality and runtime. Since this method generally provides a non-integral (relaxed) solution to the original optimization problem, two heuristics are developed to generate an integral solution. Dantzig-Wolfe followed by these heuristics can provide a near-optimal (sometimes optimal) solution to the original problem hundreds of times faster than standard (non-decomposed) approaches. In addition, when massive decomposition is employed, the solution is shown to be more likely integral, which obviates the need for an integerization step. These results indicate that nationwide, real-time, high fidelity, optimal traffic flow scheduling is achievable for (at least) 3 hour planning horizons

Incorporating User Preferences Within an Optimal Traffic Flow Management Framework

The effectiveness of future decision support tools for Traffic Flow Management in the National Airspace System will depend on two major factors: computational burden and collaboration. Previous research has focused separately on these two aspects without consideration of their interaction. In this paper, their explicit combination is examined. It is shown that when user preferences are incorporated with an optimal approach to scheduling, runtime is not adversely affected. A benefit-cost ratio is used to measure the influence of user preferences on an optimal solution. This metric shows user preferences can be accommodated without inordinately, negatively affecting the overall system delay. Specifically, incorporating user preferences will increase delays proportionally to increased user satisfaction

Fast-time demand-capacity balancing optimizer for collaborative air traffic flow management

This paper builds on top of a collaborative ATFM framework previously published, which demonstrated a potential in significant pre-tactical system delay reduction over the current European ATFM practices. In this paper, we aim to raise the technology readiness level (TRL) of the original works, focusing on improving the tractability of its DCB optimizer. To this end, we apply a Dantzig-Wolfe (DW) decomposition approach and use high performance computing (HPC) techniques to attempt the solution in a short time. The main contribution of this paper is to mitigate the computational burden faced by previous approaches, which will make all the contributions demonstrated therein more operationally feasible.Postprint (published version

The Coupled Operational Systems: A Linear Optimisation Review

The purpose of this review is to summarise the existing literature on the operational systems as to explain the current state of understanding on the coupled operational systems. The review only considers the linear optimisation of the operational systems. Traditionally, the operational systems are classified as decoupled, tightly coupled, and loosely coupled. Lately, the coupled operational systems were classified as systems of time-sensitive and time-insensitive operational cycle, systems employing one mix and different mixes of factors of production, and systems of single-linear, single-linear-fractional, and multi-linear objective. These new classifications extend the knowledge about the linear optimisation of the coupled operational systems and reveal new objective-improving models and new state-of-the-art methodologies never discussed before. Business areas affected by these extensions include product assembly lines, cooperative farming, gas/oil reservoir development, maintenance service throughout multiple facilities, construction via different locations, flights traffic control in aviation, game reserves, and tramp shipping in maritime cargo transport

Application of decomposition techniques in a wildfire suppression optimization model

Resource assignment and scheduling models provides an automatic and fast decision support system for wildfire suppression logistics. However, this process generates challenging optimization problems in many real-world cases, and the computational time becomes a critical issue, especially in realistic-size instances. Thus, to overcome that limitation, this work studies and applies a set of decomposition techniques such as augmented Lagrangian, branch and price, and Benders decomposition’s to a wildfire suppression model. Moreover, a reformulation strategy, inspired by Benders’ decomposition, is also introduced and demonstrated. Finally, a numerical study comparing the behavior of the proposals using different problem sizes is conductedThis research work is supported by the R+D+I project grants PID2020-116587GB-I00 and PID2021-124030NB (C31 and C32), funded by MCIN/AEI/10.13039/501100011033/ and by “ERDF A way of making Europe”/EU. Second author investigation is funded by the Xunta de Galicia (contract post-doctoral 2019-2022). We acknowledge the computational resources provided by CESGA. Third author acknowledges support from the Xunta de Galicia through the ERDF (ED431C-2020-14 and ED431G 2019/01), and “CITIC”S

Optimizing Flight Departure Delay and Route Selection Under En Route Convective Weather

This paper presents a linear Integer Programming model for managing air traffic flow in the United States. The decision variables in the model are departure delays and predeparture reroutes of aircraft whose trajectories are predicted to cross weather-impacted regions of the National Airspace System. The model assigns delays to a set of flights while ensuring their trajectories are free of any conflicts with weather. In a deterministic setting, there is no airborne holding due to unexpected weather incursion in a flight s path. The model is applied to solve a large-scale traffic flow management problem with realistic weather data and flight schedules. Experimental results indicate that allowing rerouting can reduce departure delays by nearly 57%, but it is associated with an increase in total airborne time due to longer routes flown by aircraft. The computation times to solve this problem were significantly lower than those reported in the earlier studies

Decomposition techniques for large scale stochastic linear programs

Stochastic linear programming is an effective and often used technique for incorporating uncertainties about future events into decision making processes. Stochastic linear programs tend to be significantly larger than other types of linear programs and generally require sophisticated decomposition solution procedures. Detailed algorithms based uponDantzig-Wolfe and L-Shaped decomposition are developed and implemented. These algorithms allow for solutions to within an arbitrary tolerance on the gap between the lower and upper bounds on a problem\u27s objective function value. Special procedures and implementation strategies are presented that enable many multi-period stochastic linear programs to be solved with two-stage, instead of nested, decomposition techniques. Consequently, abroad class of large scale problems, with tens of millions of constraints and variables, can be solved on a personal computer. Myopic decomposition algorithms based upon a shortsighted view of the future are also developed. Although unable to guarantee an arbitrary solution tolerance, myopic decomposition algorithms may yield very good solutions in a fraction of the time required by Dantzig-Wolfe/L-Shaped decomposition based algorithms.In addition, derivations are given for statistics, based upon Mahalanobis squared distances,that can be used to provide measures for a random sample\u27s effectiveness in approximating a parent distribution. Results and analyses are provided for the applications of the decomposition procedures and sample effectiveness measures to a multi-period market investment model

A Perspective on NASA Ames Air Traffic Management Research

This paper describes past and present air-traffic-management research at NASA Ames Research Center. The descriptions emerge from the perspective of a technical manager who supervised the majority of this research for the last four years. Past research contributions built a foundation for calculating accurate flight trajectories to enable efficient airspace management in time. That foundation led to two predominant research activities that continue to this day - one in automatically separating aircraft and the other in optimizing traffic flows. Today s national airspace uses many of the applications resulting from research at Ames. These applications include the nationwide deployment of the Traffic Management Advisor, new procedures enabling continuous descent arrivals, cooperation with industry to permit more direct flights to downstream way-points, a surface management system in use by two cargo carriers, and software to evaluate how well flights conform to national traffic management initiatives. The paper concludes with suggestions for prioritized research in the upcoming years. These priorities include: enabling more first-look operational evaluations, improving conflict detection and resolution for climbing or descending aircraft, and focusing additional attention on the underpinning safety critical items such as a reliable datalink

Traffic Flow Management Using Aggregate Flow Models and the Development of Disaggregation Methods

A linear time-varying aggregate traffic flow model can be used to develop Traffic Flow Management (tfm) strategies based on optimization algorithms. However, there are no methods available in the literature to translate these aggregate solutions into actions involving individual aircraft. This paper describes and implements a computationally efficient disaggregation algorithm, which converts an aggregate (flow-based) solution to a flight-specific control action. Numerical results generated by the optimization method and the disaggregation algorithm are presented and illustrated by applying them to generate TFM schedules for a typical day in the U.S. National Airspace System. The results show that the disaggregation algorithm generates control actions for individual flights while keeping the air traffic behavior very close to the optimal solution