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We present the mapping of a class of simplified air traffic management (ATM) problems (strategic conflict resolution) to quadratic unconstrained boolean optimization (QUBO) problems. The mapping is performed through an original representation of the conflict-resolution problem in terms of a conflict graph, where nodes of the graph represent flights and edges represent a potential conflict between flights. The representation allows a natural decomposition of a real world instance related to wind-optimal trajectories over the Atlantic ocean into smaller subproblems, that can be discretized and are amenable to be programmed in quantum annealers. In the study, we tested the new programming techniques and we benchmark the hardness of the instances using both classical solvers and the D-Wave 2X and D-Wave 2000Q quantum chip. The preliminary results show that for reasonable modeling choices the most challenging subproblems which are programmable in the current devices are solved to optimality with 99% of probability within a second of annealing time., Comment: Paper accepted for publication on: IEEE Transactions on Intelligent Transportation Systems

Air traffic in the North Atlantic oceanic airspace (NAT) experiences very strong winds caused by jet streams. Flying wind-optimal trajectories increases individual flight efficiency, which is advantageous when operating in the NAT. However, as the NAT is highly congested during peak hours, a large number of potential conflicts between flights are detected for the sets of wind-optimal trajectories. Conflict resolution performed at the strategic level of flight planning can significantly reduce the airspace congestion. However, being completed far in advance, strategic planning can only use predicted environmental conditions that may significantly differ from the real conditions experienced further by aircraft. The forecast uncertainties result in uncertainties in conflict prediction, and thus, conflict resolution becomes less efficient. This work considers wind uncertainties in order to improve the robustness of conflict resolution in the NAT. First, the influence of wind uncertainties on conflict prediction is investigated. Then, conflict resolution methods accounting for wind uncertainties are proposed.

North Atlantic oceanic airspace accommodates more than 1000 flights daily, and is subjected to very strong winds. Flying wind-optimal trajectories yields time and fuel savings for each individual flight. However, when taken together, these trajectories induce a large amount of potential en-route conflicts. This paper analyses the detected conflicts, figuring out conflict distribution in time and space. It further describes an optimization algorithm aimed at reducing the number of conflicts for a daily set of flights on strategic level. Several trajectory modification strategies are discussed, followed with simulation results. Finally, an algorithm improvement is presented aiming at better preserving the trajectory optimality.

The efficiency of oceanic flights is low due to limited navigational and communication equipment, congestion and airspace restrictions. The availability of Automated Dependent Surveillance-Broadcast (ADS-B) and other improvements provides opportunity for better strategic planning of trajectories. Transatlantic flights between US and Europe constitute one of the busiest oceanic airspace regions in the world. This paper examines the benefits of a wind-optimal trajectory concept with a strategic de-confliction component compared to the current flight planning using the North Atlantic Tracks. The methodology generates a wind-optimal route for each aircraft and a strategic reduction in the potential conflicts between aircraft by a combination of small adjustments to departure times and rerouting. The de-confliction is achieved by optimization techniques involving simulated annealing with local gradient searching. The fuel burn for the tracks in today's Organized Track System are compared with the corresponding quantities for the wind-optimized routes to evaluate the potential benefits of flying wind-optimal routes in North Atlantic Airspace. The analysis is based on air traffic between US and Europe during July 2012. The potential fuel savings depend on existing inefficiencies in current flight plans, atmospheric conditions and location of the city-pairs. The paper provides both aggregate results and detailed examination of some of the most popular city-pairs. Results show that strategic planning can improve the efficiency of flight trajectories by 3 to 5 depending on city-pairs and aircraft type. This translates into a potential fuel savings in the range of (420-970) kg per flight for a Boeing 767-300, the most widely used aircraft between the city-pairs in this study.

This study examines three possible approaches to improving the speed in generating wind-optimal routes for air traffic at the national or global level. They are: (a) using the resources of a supercomputer, (b) running the computations on multiple commercially available computers and (c) implementing those same algorithms into NASA’s Future ATM Concepts Evaluation Tool (FACET) and compares those to a standard implementation run on a single CPU. Wind-optimal aircraft trajectories are computed using global air traffic schedules. The run time and wait time on the supercomputer for trajectory optimization using various numbers of CPUs ranging from 80 to 10,240 units are compared with the total computational time for running the same computation on a single desktop computer and on multiple commercially available computers for potential computational enhancement through parallel processing on the computer clusters. This study also re-implements the trajectory optimization algorithm for further reduction of computational time through algorithm modifications and integrates that with FACET to facilitate the use of the new features which calculate time-optimal routes between worldwide airport pairs in a wind field for use with existing FACET applications. The implementations of trajectory optimization algorithms use MATLAB, Python, and Java programming languages. The performance evaluations are done by comparing their computational efficiencies and based on the potential application of optimized trajectories. The paper shows that in the absence of special privileges on a supercomputer, a cluster of commercially available computers provides a good option for computing wind-optimal trajectories for national and global air traffic system studies.

Aircraft flying over the airspace of different countries are subject to over-flight charges. These charges vary from country to country. Airspace charges, while necessary to support the communication, navigation and surveillance services, may lead to aircraft flying routes longer than wind-optimal routes and produce additional carbon dioxide and other gaseous emissions. This paper develops an optimal route between city pairs by modifying the cost function to include an airspace cost whenever an aircraft flies through a controlled airspace without landing or departing from that airspace. It is assumed that the aircraft will fly the trajectory at a constant cruise altitude and constant speed. The computationally efficient optimal trajectory is derived by solving a non-linear optimal control problem. The operational strategies investigated in this study for minimizing aircraft fuel burn and emissions include flying fuel-optimal routes and flying cost-optimal routes that may completely or partially reduce airspace charges en route. The results in this paper use traffic data for transatlantic flights during July 2012. The mean daily savings in over-flight charges, fuel cost and total operation cost during the period are 17.6 percent, 1.6 percent, and 2.4 percent respectively, along the cost- optimal trajectories. The transatlantic flights can potentially save $600,000 in fuel cost plus $360,000 in over-flight charges daily by flying the cost-optimal trajectories. In addition, the aircraft emissions can be potentially reduced by 2,070 metric tons each day. The airport pairs and airspace regions that have the highest potential impacts due to airspace charges are identified for possible reduction of fuel burn and aircraft emissions for the transatlantic flights. The results in the paper show that the impact of the variation in fuel price on the optimal routes is to reduce the difference between wind-optimal and cost-optimal routes as the fuel price increases. The additional fuel consumption is quantified using the 30 percent variation in fuel prices during March 2014 to March 2015.

The design of arrival and departure routes from an airport has to balance the conflicting requirements of fuel efficiency, airport capacity utilization and community emission and noise considerations. The commonly used tools for aircraft noise assessment are the FAA’s Integrated Noise Model (INM) and Aviation Environmental Design Tool (AEDT). These tools are suitable to generate precise noise contours. However, they are harder to use with other tools for route design optimization involving evaluation of a large number of aircraft trajectories. A simplified aircraft noise computation tool, named AIRNOISE, is developed for preliminary aircraft noise-reduction route design in this paper. AIRNOISE computes aircraft noise based on the same SAE-AIR-1845 procedures used by INM and AEDT. AIRNOISE does not consider components related to terrain and atmosphere adjustments. As a result, it is not only computationally efficient but also flexible to use for customized aircraft profiles. The aircraft noise results are compared with the FAA’s AEDT2b and show that the level of accuracy achieved by AIRNOISE can be used to reduce the number of route design options to a small number from a large pool for subsequent accurate analysis by INM.

The impact of aircraft emissions and contrails on the environment adds an additional aspect to aircraft trajectory optimization. This study developed a three-dimensional trajectory optimization algorithm for trans-Atlantic flights in cruise to generate aircraft trajectories that minimize environmental impacts due to CO2 emissions and contrails in the presence of winds. The climate-optimal trajectory is developed using dynamic programming that adjusts a wind-optimal aircraft heading while determining the optimal locations, altitudes and times for en-route step climbs. Flying wind-optimal routes minimize aircraft travel time, fuel burn and associated emissions during cruise while adjusting aircraft heading and en-route step climbs at the optimal locations and times minimize climate impact of contrails. This capability integrates an air traffic management simulation with aircraft fuel burn and emissions models, contrail formation and dispersion models, simplified climate response models, and a common climate metric. A study was conducted to evaluate the potential cost and benefits of flying climate-optimal routes in North Atlantic Airspace and their impacts to the Organized Track System design based on the trans-Atlantic air traffic during a day, July 12, 2012. Results show eastbound flights achieved a larger environmental benefit with less additional fuel burn than westbound flights that operated in strong headwinds that caused more additional fuel burn and aircraft emissions to avoid traversing contrails favorable regions.

The aircraft-induced climate impact has drawn attention in recent years. Aviation operations affect the environment mainly through the release of carbon-dioxide, nitrogen-oxides, and by the formation of contrails. Recent research has shown that altering trajectories can reduce aviation environmental cost by reducing Absolute Global Temperature Change Potential, a climate assessment metric that adapts a linear system for modeling the global temperature response to aviation emissions and contrails. However, these methods will increase fuel consumption that leads to higher fuel costs imposed on airlines. The goal of this work is to identify ights for which the environmental cost of climate impact reduction outweighs the increase in operational cost on an individual aircraft basis. Environmental cost is quanti ed using the monetary social cost of carbon. The increase in operational cost is considering cost of additional fuel usage only. For this paper, an algorithm has been developed that modi es the trajectories of ights to evaluate the e ect of environ- mental cost and operational cost of ights in the United States National Airspace System. The algorithm identi es ights for which the environmental cost of climate impact can be reduced and modi es their trajectories to achieve maximum environmental net bene t, which is the di erence between reduction in environmental cost and additional operational cost. The result shows on a selected day, 16% of the ights among eight major airlines, or 2,043 ights, can achieve environmental net bene t using weather forecast data, resulting in net bene t of around $500,000. The result also suggests that the long-haul ights would be better candidates for cost-ecient climate impact reduction than the short haul ights. The algorithm will help to identify the characteristics of ights that are capable of applying cost-ecient climate impact reduction strategy.

North Atlantic Tracks are trans-Atlantic routes across the busiest oceanic airspace in the world. This study analyzes and compares current flight-plan routes to wind-optimal routes for trans-Atlantic flights in terms of aircraft fuel burn, emissions and the associated climate impact. The historical flight track data recorded by EUROCONTROL's Central Flow Management Unit is merged with data from FAA's Enhanced Traffic Management System to provide an accurate flight movement database containing the highest available flight path resolution in both systems. The combined database is adopted for airspace simulation integrated with aircraft fuel burn and emissions models, contrail models, simplified climate response models, and a common climate metric to assess the climate impact of flight routes within the Organized Track System (OTS). The fuel burn and emissions for the tracks in the OTS are compared with the corresponding quantities for the wind-optimized routes to evaluate the potential environmental benefits of flying wind-optimal routes in North Atlantic Airspace. The potential fuel savings and reduction in emissions depend on existing inefficiencies in current flight plans, atmospheric conditions and location of the city-pairs. The potential benefits are scaled by comparing them with actual flight tests that have been conducted since 2010 between a few city-pairs in the transatlantic and trans-pacific region to improve fuel consumption and reduce the environmental impact of aviation.

Aircraft operations need to meet the combined requirements of safety, efficiency, capacity and reduced environmental impact. Aircraft routes can be made efficient by flying wind optimal routes. However, the desire to reduce the impact of aviation emissions and contrails may result in trajectories, which deviate from wind optimal trajectories leading to extra fuel use. The lifetime associated with different emissions and contrails varies from a few hours to several hundred years. The impact of certain gases depends on the amount and location of the emission, and the decision-making horizon, in years, when the impact is estimated. The Absolute Global Temperature Potential (AGTP) is used as a metric to measure the combined effects of emissions and contrails. This paper extends earlier work by the authors to include the effect of oxides of nitrogen in the development of aircraft trajectories to reduce the combined effects of carbon dioxide, oxides of nitrogen (NOX) and contrails. The methodology is applied to air traffic in the continental US. The paper shows the trade-offs between reducing emissions and the cost of extra fuel using a fuel sensitivity index, defined as the reduction in AGTP per kg of fuel. The paper shows the performance of the optimization strategy for decision intervals of 10, 25 and 100 years. Based on the simplified models, the inclusion of NOX emissions has a slight influence on the minimal climate impact trajectories when the decision horizons are around 25 years.

The rapid growth of air traffic has drawn attention to aircraft-induced environmental impact. Aviation operations affect the environment mainly through the release of emissions and by the formation of contrails. Recent research has shown that altering aircraft cruise altitudes can reduce aviation environmental impact by reducing Absolute Global Temperature Change Potential, a climate assessment metric that adapts a linear system for modeling the global temperature response to aviation emissions and contrails. However, these methods will increase fuel consumption that leads to higher operational costs imposed on airlines resulting in reluctance to adopt a new routing strategy. This paper evaluates the tradeoff between environmental impact reduction and the corresponding added operational costs for enroute air traffic. The concept of social cost of carbon and the carbon auction price from California's recent cap-and-trade system were used to provide estimates and a methodology to evaluate environmental costs for carbon dioxide emissions and contrail formations. Depending on the specific environmental policy, the strategy is considered favorable when the reduction in environmental costs exceeds the increase in operational costs. The results show how the net environmental bene t varies with different decision-making time horizons, different carbon and fuel costs, and different days. The study provides guidance towards the development of the environmental reduction strategies.

This paper evaluates a set of contrail reduction strategies based on environmental and operational costs. A linear climate model was first used to convert climate effects of carbon dioxide emissions and aircraft contrails to changes in Absolute Global Temperature Potential, a metric that measures the mean surface temperature change due to aircraft emissions and persistent contrail formations. The concept of social cost of carbon and the carbon auction price from recent California's cap-and-trade system were then used to relate the carbon dioxide emissions and contrail formations to an environmental cost index. The strategy for contrail reduction is based on minimizing contrail formations by altering the aircraft's cruising altitude. The strategy uses a user-defined factor to trade off between contrail reduction and additional fuel burn and carbon dioxide emissions. A higher value of tradeoff factor results in more contrail reduction but also more fuel burn and carbon emissions. The strategy is considered favorable when the net environmental cost benefit exceeds the operational cost. The results show how the net environmental benefit varies with different decision-making time-horizon and different carbon cost. The cost models provide a guidance to select the trade-off factor that will result in the most net environmental benefit.

Future air traffic management systems are required to balance the conflicting objectives of maximizing safety and efficiency of traffic flows while minimizing the climate impact of aviation emissions and contrails. Integrating emission and climate models together with air traffic simulations improve the understanding of the complex interaction between the physical climate system, carbon and other greenhouse gas emissions and aviation activity. This paper integrates a national-level air traffic simulation and optimization capability with simple climate models and carbon cycle models, and climate metrics to assess the impact of aviation on climate. The capability can be used to make trade-offs between extra fuel cost and reduction in global surface temperature change. The parameters in the simulation can be used to evaluate the effect of various uncertainties in emission models and contrails and the impact of different decision horizons. Alternatively, the optimization results from the simulation can be used as inputs to other tools that monetize global climate impacts like the FAA s Aviation Environmental Portfolio Management Tool for Impacts.

Cross-Polar routes offer new opportunities for air travel markets. Transpolar flights reduce travel times, fuel burns, and associated environmental emissions by flying direct paths between many North American and Asian cities. This study evaluates the potential benefits of flying wind-optimal polar routes and assessed their potential impact on climate change. An optimization algorithm is developed for transpolar flights to generate wind-optimal trajectories that minimize climate impact of aircraft, in terms of global warming potentials (relative to warming by one kg of CO2) of several types of emissions, while avoiding regions of airspace that facilitate persistent contrail formation. Estimations of global warming potential are incorporated into the objective function of the optimization algorithm to assess the climate impact of aircraft emissions discharged at a given location and altitude. The regions of airspace with very low ambient temperature and areas favorable to persistent contrail formation are modeled as undesirable regions that aircraft should avoid and are formulated as soft state constraints. The fuel burn and climate impact of cross-polar air traffic flying various types of trajectory including flight plan, great circle, wind-optimal, and contrail-avoidance are computed for 15 origin-destination pairs between major international airports in the U.S. and Asia. Wind-optimal routes reduce average fuel burn of flight plan routes by 4.4% on December 4, 2010 and 8.0% on August 7, 2010, respectively. The tradeoff between persistent contrail formation and additional global warming potential of aircraft emissions is investigated with and without altitude optimization. Without altitude optimization, the reduction in contrail travel times is gradual with increase in total fuel consumption. When altitude is optimized, a one percent increase in additional global warming potential, a climate impact equivalent to that of 4070kg and 4220kg CO2 emission, reduces 135 and 105 minutes persistent contrail formation per flight during a day with medium and high contrail formation, respectively.

This paper describes a class of strategies for reducing persistent contrail formation in the United States airspace. The primary objective is to minimize potential contrail formation regions by altering the aircraft's cruising altitude in a fuel-efficient way. The results show that the contrail formations can be reduced significantly without extra fuel consumption and without adversely affecting congestion in the airspace. The contrail formations can be further reduced by using extra fuel. For the day tested, the maximal reduction strategy has a 53% contrail reduction rate. The most fuel-efficient strategy has an 8% reduction rate with 2.86% less fuel-burnt compared to the maximal reduction strategy. Using a cost function which penalizes extra fuel consumed while maximizing the amount of contrail reduction provides a flexible way to trade off between contrail reduction and fuel consumption. It can achieve a 35% contrail reduction rate with only 0.23% extra fuel consumption. The proposed fuel-efficient contrail reduction strategy provides a solution to reduce aviation-induced environmental impact on a daily basis.

There is increased awareness of anthropogenic factors affecting climate change and urgency to slow the negative impact. Greenhouse gases, oxides of Nitrogen and contrails resulting from aviation affect the climate in different and uncertain ways. This paper develops a flexible simulation and optimization software architecture to study the trade-offs involved in reducing emissions. The software environment is used to conduct analysis of two approaches for avoiding contrails using the concepts of contrail frequency index and optimal avoidance trajectories.

There are indications that persistent contrails can lead to adverse climate change, although the complete effect on climate forcing is still uncertain. A flight trajectory optimization algorithm with fuel and contrails models, which develops alternative flight paths, provides policy makers the necessary data to make tradeoffs between persistent contrails mitigation and aircraft fuel consumption. This study develops an algorithm that calculates wind-optimal trajectories for cruising aircraft while avoiding the regions of airspace prone to persistent contrails formation. The optimal trajectories are developed by solving a non-linear optimal control problem with path constraints. The regions of airspace favorable to persistent contrails formation are modeled as penalty areas that aircraft should avoid and are adjustable. The tradeoff between persistent contrails formation and additional fuel consumption is investigated, with and without altitude optimization, for 12 city-pairs in the continental United States. Without altitude optimization, the reduction in contrail travel times is gradual with increase in total fuel consumption. When altitude is optimized, a two percent increase in total fuel consumption can reduce the total travel times through contrail regions by more than six times. Allowing further increase in fuel consumption does not seem to result in proportionate decrease in contrail travel times.

Airspace capacity reduction due to convective weather impedes air traffic flows and causes traffic congestion. This study presents an algorithm that reroutes flights in the presence of winds, enroute convective weather, and congested airspace based on stochastic dynamic programming. A stochastic disturbance model incorporates into the reroute design process the capacity uncertainty. A trajectory-based airspace demand model is employed for calculating current and future airspace demand. The optimal routes minimize the total expected traveling time, weather incursion, and induced congestion costs. They are compared to weather-avoidance routes calculated using deterministic dynamic programming. The stochastic reroutes have smaller deviation probability than the deterministic counterpart when both reroutes have similar total flight distance. The stochastic rerouting algorithm takes into account all convective weather fields with all severity levels while the deterministic algorithm only accounts for convective weather systems exceeding a specified level of severity. When the stochastic reroutes are compared to the actual flight routes, they have similar total flight time, and both have about 1% of travel time crossing congested enroute sectors on average. The actual flight routes induce slightly less traffic congestion than the stochastic reroutes but intercept more severe convective weather.

The optimization of traffic flows in congested airspace with varying convective weather is a challenging problem. One approach is to generate shortest routes between origins and destinations while meeting airspace capacity constraint in the presence of uncertainties, such as weather and airspace demand. This study focuses on development of an optimal flight path search algorithm that optimizes national airspace system throughput and efficiency in the presence of uncertainties. The algorithm is based on dynamic programming and utilizes the predicted probability that an aircraft will deviate around convective weather. It is shown that the running time of the algorithm increases linearly with the total number of links between all stages. The optimal routes minimize a combination of fuel cost and expected cost of route deviation due to convective weather. They are considered as alternatives to the set of coded departure routes which are predefined by FAA to reroute pre-departure flights around weather or air traffic constraints. A formula, which calculates predicted probability of deviation from a given flight path, is also derived. The predicted probability of deviation is calculated for all path candidates. Routes with the best probability are selected as optimal. The predicted probability of deviation serves as a computable measure of reliability in pre-departure rerouting. The algorithm can also be extended to automatically adjust its design parameters to satisfy the desired level of reliability.

A health monitoring system based on analytical redundancy is developed for satellites on elliptical orbits. First, the dynamics of the satellite including orbital mechanics and attitude dynamics is modelled as a periodic system. Then, periodic fault detection filters are designed to detect and identify the satellite's actuator and sensor faults. In addition, parity equations are constructed using the algebraic redundant relationship among the actuators and sensors. Furthermore, a residual processor is designed to generate the probability of each of the actuator and sensor faults by using a sequential probability test. Finally, the health monitoring system, consisting of periodic fault detection lters, parity equations and residual processor, is evaluated in the simulation in the presence of disturbances and uncertainty.