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NASA NTRS2010

Air Traffic Sector Configuration Change Frequency

A Mixed Integer Linear Programming method is used for creating sectors in Fort Worth, Cleveland, and Los Angeles centers based on several days of good-weather traffic data. The performance of these sectors is studied when they are subjected to traffic data from different days. Additionally, the advantage of using different sector designs at different times of day with varying traffic loads is examined. Specifically, traffic data from 10 days are used for design, and 47 other days are played back to test if the traffic-counts stay below the design values used in creating the partitions. The primary findings of this study are as follows. Sectors created with traffic from good-weather days can be used on other good-weather days. Sector configurations created with two hours of traffic can be used for 6 to 12 hours without exceeding the peak-count requirement. Compared to using a single configuration for the entire day, most of the sector-hour reduction is achieved by using two sector configurations -one during daytime hours and one during nighttime hours.

Chatterji, Gano B.↗

NASA NTRS2017

Optimization Routine for Generating Medical Kits for Spaceflight Using the Integrated Medical Model

The Integrated Medical Model (IMM) is a MATLAB model that provides probabilistic assessment of the medical risk associated with human spaceflight missions.Different simulations or profiles can be run in which input conditions regarding both mission characteristics and crew characteristics may vary. For each simulation, the IMM records the total medical events that occur and “treats” each event with resources drawn from import scripts. IMM outputs include Total Medical Events (TME), Crew Health Index (CHI), probability of Evacuation (pEVAC), and probability of Loss of Crew Life (pLOCL).The Crew Health Index is determined by the amount of quality time lost (QTL). Previously, an optimization code was implemented in order to efficiently generate medical kits. The kits were optimized to have the greatest benefit possible, given amass and/or volume constraint. A 6-crew, 14-day lunar mission was chosen for the simulation and run through the IMM for 100,000 trials. A built-in MATLAB solver, mixed-integer linear programming, was used for the optimization routine. Kits were generated in 10% increments ranging from 10%-100% of the benefit constraints. Conditions wheremass alone was minimized, volume alone was minimized, and where mass and volume were minimizedjointly were tested.

Medical Kit↗

NASA NTRS2017

Optimization of Airport Surface Traffic: A Case-Study of Incheon International Airport

This study aims to develop a controllers' decision support tool for departure and surface management of ICN. Airport surface traffic optimization for Incheon International Airport (ICN) in South Korea was studied based on the operational characteristics of ICN and airspace of Korea. For surface traffic optimization, a multiple runway scheduling problem and a taxi scheduling problem were formulated into two Mixed Integer Linear Programming (MILP) optimization models. The Miles-In-Trail (MIT) separation constraint at the departure fix shared by the departure flights from multiple runways and the runway crossing constraints due to the taxi route configuration specific to ICN were incorporated into the runway scheduling and taxiway scheduling problems, respectively. Since the MILP-based optimization model for the multiple runway scheduling problem may be computationally intensive, computation times and delay costs of different solving methods were compared for a practical implementation. This research was a collaboration between Korea Aerospace Research Institute (KARI) and National Aeronautics and Space Administration (NASA).

surface management↗

NASA NTRS2017

Optimization of Airport Surface Traffic: A Case-Study of Incheon International Airport

This study aims to develop a controllers decision support tool for departure and surface management of ICN. Airport surface traffic optimization for Incheon International Airport (ICN) in South Korea was studied based on the operational characteristics of ICN and airspace of Korea. For surface traffic optimization, a multiple runway scheduling problem and a taxi scheduling problem were formulated into two Mixed Integer Linear Programming (MILP) optimization models. The Miles-In-Trail (MIT) separation constraint at the departure fix shared by the departure flights from multiple runways and the runway crossing constraints due to the taxi route configuration specific to ICN were incorporated into the runway scheduling and taxiway scheduling problems, respectively. Since the MILP-based optimization model for the multiple runway scheduling problem may be computationally intensive, computation times and delay costs of different solving methods were compared for a practical implementation. This research was a collaboration between Korea Aerospace Research Institute (KARI) and National Aeronautics and Space Administration (NASA).

taxi scheduler↗

NASA NTRS2018

Next Generation Aircraft Design Considering Airline Operations and Economics

Traditional approaches to design and optimization of a new system often use a system-centric objective and do not take into consideration how the operator will use this new system alongside other existing systems. When the new system design is incorporated into the broader group of systems, the performance of the operator-level objective can be sub-optimal due to the unmodeled interaction between the new system and the other systems. Among the few available references that describe attempts to address this disconnect, most follow an MDO (Multidisciplinary Design Optimization)-motivated sequential decomposition approach of first designing a very good system and then providing this system to the operator who, decides the best way to use this new system along with the existing systems. This paper addresses this issue by including aircraft design, airline operations, and revenue management "subspaces"; and presents an approach that could simultaneously solve these subspaces posed as a monolithic optimization problem rather than the traditional approach described above. The monolithic approach makes the problem an expensive Mixed Integer Non-Linear Programming problem, which are extremely difficult to solve. To address the problem, we use a recently developed optimization framework that simultaneously solves the subspaces to capture the "synergy" in the problem that the previous decomposition approaches did not exploit, addresses mixed-integer/discrete type design variables in an efficient manner, and accounts for computationally expensive analysis tools. This approach solves an 11-route airline network problem consisting of 94 decision variables including 33 integer and 61 continuous type variables. Simultaneously solving the subspaces leads to significant improvement in the fleet-level objective of the airline when compared to the previously developed sequential subspace decomposition approach.

Roy, Satadru↗

NASA NTRS2018

Comparison of First-Come First-Served and Optimization Based Scheduling Algorithms for Integrated Departure and Arrival Management

Korea Aerospace Research Institute (KARI) and National Aeronautics and Space Administration (NASA) are investigating scheduling algorithms that will be a part of an integrated arrival and departure management system. Inha University, one of the Korean collaborators of KARI, developed an Extended First-Come First-Served (EFCFS) algorithm that is robust and efficient. However, since the EFCFS algorithm sequentially computes the schedule based on priority, the end results may not be optimal for system efficiency. The approach based on Mixed Integer Linear Programming (MILP) originally developed by NASA and modified by KARI is known to produce better schedules at the expense of computational cost. In this paper, the two different scheduling approaches are compared using common traffic scenarios and constraints at Incheon International Airport. Capabilities to apply weight class based wake turbulence runway separation minima and Miles-in-Trail (MIT) restrictions at selected meter fixes are added to the previously developed EFCFS scheduler. Based on historic data, 40 departures and 20 arrivals are chosen in a one-hour period and 100 scenarios were created by randomly assigning gate numbers, gate departure times, and runway landing times. With the current runway separation requirements, MILP resulted in about ten to twenty percent smaller average delays depending on the constraints. With artificially increased separation minima, the difference between MILP and EFCFS became more noticeable. However, the EFCFS was about ten times faster with smaller variations among different scenarios and constraints. The comparison suggests that the MILP-based algorithm has a small advantage at the current traffic level; however, has potential to be more effective in higher demand or severe weather situations. The EFCFS algorithm may be better suited for real-time applications or investigating larger scale scheduling problems.

air traffic optimization↗

NASA NTRS2015

Optimizing Integrated Arrival, Departure and Surface Operations Under Uncertainty

In airports and surrounding terminal airspaces, the integration of arrival, departure and surface scheduling and routing have the potential to improve the operations efficiency. Recent research had developed mixed-integer-linear programming algorithm-based scheduler for integrated arrival and departure operations in the presence of uncertainty. This paper extends to the surface previous research performed by the authors to integrate taxiway and runway operations. The developed algorithm is capable of computing optimal aircraft schedules and routings that reflects the integration of air and ground operations. A preliminary study case is conducted for a set of thirteen aircraft evolving in a model of the Los Angeles International airport and surrounding terminal areas. Using historical data, a representative traffic scenario is constructed and probabilistic distributions of pushback delay and arrival gate delay are obtained. To assess the benefits of optimization, a First- Come-First-Serve algorithm approach comparison is realized. Evaluation results demonstrate that the optimization can help identifying runway sequencing and schedule that reduce gate waiting time without increasing average taxi times.

Bosson, Christabelle↗

NASA NTRS2015

Integration of Uncertain Ramp Area Aircraft Trajectories and Generation of Optimal Taxiway Schedules at Charlotte Douglas (CLT) Airport

The integration of aircraft maneuver characteristics into an optimal taxiway scheduling solution is challenging due to the uncertainties that are intrinsic to ramp area aircraft trajectories. To address the challenge, we build a stochastic model of ramp area aircraft trajectories that is used to generate a probabilistic measure of conflict within the Charlotte Douglas International Airport (CLT) ramp area. Parameters of the conflict distributions are estimated and passed to a Mixed Integer Linear Program that solves for an optimal taxiway schedule constrained to be conflict free in the presence of trajectory uncertainties. Here we extend our previous research by accounting for departing and arriving aircraft whereas our prior formulation only accounted for departing aircraft.

taxiway schedule↗

NASA NTRS2017

MColl: Monte Collocation Trajectory Design Tool

In this paper we describe a prototype low-thrust optimization software being developed at JPL. The software tool is based on a collocation algorithm where a trajectory discretization is fitted and adjusted until the underlying dynamics equations of motion are satisfied. The resulting large scale non-linear programming problem may either be optimized with IPOPT or KNITRO. The user specifies path constraints, boundary constraints, and objectives. We describe the collocation algorithm as well as various mesh refinement strategies, and apply the software tool to solve various example problems.

Grebow, Daniel J.↗

NASA NTRS2019

Image Processing Methods for Coronal Hole Segmentation, Matching, and Map Classification

The paper presents the results from a multi-year effort to develop and validate image processing methods forselecting the best physical models based on solar image observations. The approach consists of selecting the physical models based on their agreement with coronal holes extracted from the images. Ultimately, the goal is to use physical models to predict geomagnetic storms. We decompose the problem into three subproblems: (i) coronal hole segmentation based on physical constraints, (ii) matching clusters of coronal holes between different maps, and (iii) physical map classification. For segmenting coronal holes, we develop a multi-modal method that uses segmentation maps from three different methods to initialize a level-set method that evolves the initial coronal hole segmentation to the magnetic boundary. Then, we introducea new method based on Linear Programming for matchingclusters of coronal holes. The final matching is then performedusing Random Forests. The methods were carefully validatedusing consensus maps derived from multiple readers, manualclustering, manual map classification, and method validation for50 maps. The proposed multi-modal segmentation method significantly outperformed SegNet, U-net, Henney-Harvey, and FCNby providing accurate boundary detection. Overall, the methodgave a 95.5% map classification accuracy.

Jatla, Venkatesh↗

NASA NTRS2017

GTOC9: Methods and Results from the Jet Propulsion Laboratory Team

The removal of 123 pieces of debris from the Sunsynchronous LEO environment is accomplished by a 10-spacecraft campaign wherein the spacecraft, flying in succession over an 8-yr period, rendezvous with a series of the debris objects, delivering a de-orbit package at each one before moving on to the next object by means of impulsive manoeuvres. This was the GTOC9 problem, as posed by the European Space Agency. The methods used by the Jet Propulsion Laboratory team are described, along with the winning solution found by the team. Methods include branch-and-bound searches that exploit the natural nodal drift to compute long chains of rendezvous with debris objects, beam searches for synthesising campaigns, ant colony optimisation, and a genetic algorithm. Databases of transfers between all bodies on a fine time grid are made, containing an easyto- compute yet accurate estimate of the transfer V . Lastly, a final non-linear programming optimisation is performed to ensure the trajectories meet all the constraints and are locally optimal in initial mass.

Sims, Jon↗

NASA NTRSDate not supplied

Scheduling Position, Navigation and Time Service Requests from Non-dedicated Lunar Constellations

This paper presents a centralized scheduler that satisfies user requests for Position, Navigation, and Time (PNT) services from an ad-hoc, non-dedicated orbital constellation around the Moon. Traditional, dedicated GNSS networks provide service 24/7, which allows users to acquire localization services at-will. For ad-hoc networks, a coordinated schedule is needed to ensure Quality of Service (QoS) guarantees for user localization, while satisfying non-dedicated assets’ usage constraints. This scheduler bridges this coordination gap by leveraging Mixed Integer-Linear Programming (MILP) to schedule this “as-needed” localization service while respecting the constraints on each asset. In upcoming decades there is expected to be a substantial increase in Lunar missions. Many of these missions will feature low-cost surface assets near the moon’s polar regions and small-sat science missions in orbit. Most missions need PNT capabilities to ensure safe operations and meet their science objectives, but low-cost missions may not be able to support the large power, mass, and weight that a weak GNSS or DSN based navigation solution would entail. Asset localization has been demonstrated using a decentralized extended Kalman Filter (DEKF) in the previously presented Lunar Autonomous PNT System (LAPS). Within the LAPS simulation environment, a module has been developed to generate the coordinated user-asset schedules described above; this Service Scheduler Module (SSM) allows for complete end-to-end testing of the entire system. Within SSM, a user service request consists of a location on the Lunar surface, a cumulative service duration, and a window in which service must occur. SSM takes as input these requests and the LAPS-predicted positional degree of precision as the QoS for each available set of orbital assets. A simple, baseline MILP model is formulated to provide the highest-precision service balanced across all requests. To reflect the non-dedicated nature of the constellation, this baseline model is augmented with additional asset-specific load capacity constraints or availability constraints. The load capacity constraints limit total time spent providing service, and the availability constraints reflect blockout times or availability windows when the assets are not otherwise occupied. SSM outputs two schedules: the user schedule to indicate their service times and expected QoS, and a satellite schedule to be transmitted to the orbiting constellation, describing when each non-dedicated asset provides PNT service. SSM is predominantly implemented in MATLAB and allows the use of any MILP solver to generate the resulting schedules. This paper describes the SSM - LAPS interface, how the output of LAPS is used to construct the MILP, and how SSM provides user localization service while satisfying constraints. It will also demonstrate the tool’s flexibility for formulating schedules for the end user and the constellation, focusing on scenarios that match real-world proposed missions. It will detail how SSM can be used to compare the addition of load capacity constraints, satellite availability constraints, and QoS guarantees for the users. Finally, we describe how SSM can be used to support the design of the ad-hoc constellation itself. The resulting integrated capability will support the design of future ad-hoc Lunar PNT networks, enabling high-quality, low-cost Lunar exploration

Swarm↗

NASA NTRSDate not supplied

Planning Satellite Swarm Measurements for Climate Models: Comparing Dynamic Constraint Processing and MILP Methods

We present D-SHIELD, a challenging climate science application to plan coordinated measurements (observations) for a constellation of satellites, each containing two different sensors, each with 61 pointing angle options. The L-band and P-band radar sensors collect data fed into a soil moisture model which tracks and predicts soil moisture across 1.67 million Ground Positions (GP). Soil moisture is an important predictor of wildfires, and then a predictor of floods, landslides and debris flow after a fire. Each measurement covers multiple GP due to the sensor footprint. Each GP has a "model error" which represents the uncertainty of the the soil moisture state prediction. Model error changes at different rates for each GP as the time since last observation increases and after significant events like rain. The planner's goal is to select measurements which maximize soil moisture model improvement (reduce model uncertainty). This problem is combinatorically explosive, involving many degrees of freedom for planner choices. Good domain heuristics can find solutions within a reasonable time for our application needs but cannot be proven optimal. In this paper we compare two different planning approaches to this problem: Dynamic Constraint Processing (DCP) and Mixed Integer Linear Programming (MILP). We match inputs and metrics for both DCP and MILP algorithms to enable a direct apples-to-apples comparison. We demonstrate and discuss the trades between DCP flexibility and performance vs. MILP's promise of provable optimality.

Rich Levinson↗

NASA NTRSDate not supplied

Aerial Vehicle Routing and Scheduling for UAS Traffic Management: A Monte Carlo Tree Search Approach

Numerous unmanned aircraft systems operating at low altitudes to deliver goods and services may one day become ubiquitous in our cities. In the Unmanned Aircraft Systems (UAS) Traffic Management (UTM) framework, such a concept is envisioned, where aerial vehicles operate beyond visual line of sight (BVLOS) within specifically reserved and time stamped “corridors” in the airspace. For example, these corridors or operational intent volumes can connect an aerial vehicle’s origin site to its destination site for package delivery operations. There may also be more than one corridor available for an aerial vehicle to choose from and often different corridors may intersect with one another. Thus, it is imperative to ensure flight trajectories belonging to different aerial vehicles are not in conflict. Per the UTM CONOPs, we assume that a vehicle almost always stays inside its corridor or operational volume. This work provides a framework for strategic deconfliction of UTM or package delivery drones, where we schedule the departure time of all vehicles subject to various temporal constraints (including the corridor deconfliction at the intersections). We present the “multi-route weighted package delivery problem” which serves as an exemplifying model for strategic deconfliction in UTM. In the multi-route weighted package delivery problem, a graph network is given which consists of a set of depots (source) and drop-off (destination) nodes, with multiple routes (defined as a sequence of waypoints) connecting the depots to drop-off nodes. In addition, routes are weighted by the associated ground risk and total travel distance for package delivery. The goal is for a known set of aerial vehicles to depart from the depots, choose a route and take off time, while avoiding conflicts with other aerial vehicles, and minimizing both risk and distance traveled. We provide a mixed integer linear programming (MILP) formulation of the problem, as well as a heuristic solution based on Monte Carlo Tree Search (MCTS) – a method used in game theory and artificial intelligence – to overcome limitations inherent to optimal solvers. Computational results show the advantages of using MCTS over the MILP formulation; the former can provide a sub-optimal solution quickly, and may sometimes even reach an optimal solution, whereas the latter may not even produce a solution in reasonable time. Furthermore, results from both the MILP formulation and MCTS methods were validated using a preliminary agent-based simulator implementing the UTM concept of operations. Thus, the MCTS method can be seen as a scalable solution to the complex multi-route weighted package delivery problem and may possibly be extended to similar complex optimization problems.

Kenny Chour↗

NASA NTRS2022

Multi-Robot Assembly Scheduling for the Lunar Crater Radio Telescope on the Far-Side of the Moon

The Lunar Crater Radio Telescope (LCRT) is a pro- posed ultra-long-wavelength radio telescope to be constructed on the far side of the moon. The proposed telescope will be constructed by deploying a 1km wire mesh in a 3-5km crater using a team of wall-climbing DuAxel robots. In this work, we consider the problem of generating minimum-time assembly sequences for LCRT, using realistic models of travel speed and lighting. Specifically, we pose the assembly sequencing problem as a mixed-integer linear program (MILP), which we solve to global optimality using commercial solvers. We present methods for modeling time-varying travel and assembly times, based on variable lighting conditions (including crater shadowing), and show how such time-varying parameters can be incorporated into the MILP. Finally, we present numerical studies of our method, showing how makespan varies with the number of assembly robots.

Schwager, Mac↗

NASA NTRS2022

SatNet: A Benchmark for Satellite Scheduling Optimization

Satellites provide essential services such as networking and weather tracking, and the number of near-earth and deep space satellites are expected to grow rapidly in the coming years. Communications with terrestrial ground stations is one of the critical functionalities of any space mission. Satellite scheduling is a problem that has been scientifically investigated since the 1970s. A central aspect of this problem is the need to consider resource contention and satellite visibility constraints as they require line of sight. Due to the combinatorial nature of the problem, prior solutions such as linear programs and evolutionary algorithms require extensive compute capabilities to output a feasible schedule for each scenario. Machine learning based scheduling can provide an alternative solution by training a model with historical data and generating a schedule quickly with model inference. We present SatNet, a benchmark for satellite scheduling optimization based on historical data from the NASA Deep Space Network. We propose formulation of the satellite scheduling problem as a Markov Decision Process and use reinforcement learning (RL) policies to generate schedules. The nature of constraints imposed by SatNet differ from other combinatorial optimization problems such as vehicle routing studied in prior literature. Our initial results indicate that RL is an alternative optimization approach that can generate candidate solutions of comparable quality to existing state-of-the-practice results. However, we also find that RL policies overfit to the training dataset and do not generalize well to new data, thereby necessitating continued research on reusable and generalizable agents.

Wilson, Brian↗

NASA NTRSDate not supplied

Aerial Vehicle Routing and Scheduling for UAS Traffic Management: A Hybrid Monte Carlo Tree Search Approach

We present the Multi-Route Weighted Package Delivery Problem (MRWPDP) and a scalable solution methodology as a major step towards enabling an airspace deconfliction service for drone delivery operations. The problem is motivated by Strategic deconfliction under the FAA’s “Unmanned Aircraft Systems Traffic Management” Concept of Operations. MRWPDP falls under a class of vehicle routing and scheduling problems, and as such is NP-Hard. In MRWPDP, a graph network is given which consists of depots, drop-off sites, and multiple routes connecting the two. In addition, routes are weighted by the associated ground risk and total travel distance for package delivery. The goal is to optimally schedule the departure time and assign routes to a known set of vehicles at the depot. We propose a heuristic solution to the problem by borrowing techniques from Mixed Integer Linear Programming (MILP), Constraint Programming, and Monte Carlo Tree Search (MCTS). The resulting hybrid framework is MCTS with Bound-and-Prune (BP) and rapid simulated updates (U), or MCTS-BP-U. This approach is able to quickly provide a feasible solution for MRWPDP, even for large problem instances up to 1000 vehicles. We provide a MILP formulation of MRWPDP and compare its performance against MCTS-BP-U in terms of solution quality. An agent-based model simulation is conducted as a final step to validate the efficacy of our approach.

air traffic scheduling↗

NASA NTRSDate not supplied

Aerial Vehicle Routing and Scheduling for UAS Traffic Management: A Hybrid Monte Carlo Tree Search Approach

air traffic scheduling↗