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Results for “Mixed integer linear programming”

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DOE OSTI2025

Optimal Mitigation Planning For Adversarial Scenarios

We propose a generalized framework which performs an optimal partitioning of a limited budget into various organizational sectors in order to improve the cybersecurity of a smart device or component in the Cyber Physical Energy System (CPS). The framework identifies the adversarial threats and possible attack sequences which can be performed to exploit cyber vulnerabilities of the component. Thereafter, we formulate an Mixed Integer Linear Programming (MILP) optimization problem which aims to evaluate the optimal budget partitions in order to minimize the number of highly likely attack sequences. Though we provide results for using the framework in CPES, the proposed methodology can be extended for multiple domains with a set of known adversarial and mitigation actions.

Purohit, Sumit [Pacific Northwest National Laborat↗

DOE OSTI2025

New Results on Communication- and Memory-Aware Load Balancing Model and Algorithms

While load balancing in distributed-memory computing has been well-studied, we present an innovative approach to this problem: a unified, reduced-order model that combines three key components to describe “work” in a distributed system: computation, communication, and memory. Our model enables an optimizer to explore complex tradeoffs in task placement, such as augmented parallelism, at the expense of data replication increasing memory usage. We propose a fully distributed, heuristic-based load balancing optimization algorithm, and demonstrate that it quickly finds close-to-optimal solutions. We formalize the complex optimization problem as a mixed-integer linear program, and compare it to our strategy. Finally, we show that when applied to an electromagnetics code, our approach obtains up to 2.3x speedups for the imbalanced execution.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Optimal Design of Food Packaging Considering Waste Management Technologies to Achieve Circular Economy

Plastic packaging plays a fundamental role in the food industry, avoiding food waste and facilitating food access. The increasing plastic production and the lack of appropriate plastic waste management technologies represent a threat to the environmental and human welfare. Therefore, there is an urgent need to identify sustainable packaging solutions. Circular economy (CE) promotes reducing waste and increasing recycling practices to achieve sustainability. In this work, we propose a CE framework based on multi-objective optimization, considering both economic and environmental impacts, to identify optimal packaging designs and waste management technologies. Using mixed-integer linear programming (MILP), techno-economic analysis (TEA), and life cycle assessment (LCA), this work aims to build the first steps in packaging design, informing about the best packaging alternatives and the optimal technology or technologies to process packaging waste. For the economic analysis, we consider the minimum increase in price (MIP) when adding recycling to the cost of each packaging solution, while for the environmental analysis, the greenhouse gas emissions impact was considered. A case study on ground coffee packaging is used to illustrate the proposed framework. The results demonstrate that the multilayer bag option is the most convenient when considering both the chosen economic and environmental impacts.

Life Cycle Analysis↗

NASA NTRS1982

A DSN optimal spacecraft scheduling model

A computer model is described which uses mixed-integer linear programming to provide optimal DSN spacecraft schedules given a mission set and specified scheduling requirements. A solution technique is proposed which uses Bender's Method and a heuristic starting algorithm.

Webb, W. A.↗

NASA NTRS1985

An optimal spacecraft scheduling model for the NASA deep space network

Webb, W. A.↗

NASA NTRS2009

Air Traffic Sector Configuration Change Frequency

Several techniques for partitioning airspace have been developed in the literature. The question of whether a region of airspace created by such methods can be used with other days of traffic, and the number of times a different partition is needed during the day is examined in this paper. Both these aspects are examined for the Fort Worth Center airspace sectors. A Mixed Integer Linear Programming method is used with actual air traffic data of ten high-volume low-weather-delay days for creating sectors. Nine solutions were obtained for each two-hour period of the day by partitioning the center airspace into two through 18 sectors in steps of two sectors. Actual track-data were played back with the generated partitions for creating histograms of the traffic-counts. The best partition for each two-hour period was then identified based on the nine traffic-count distributions. Numbers of sectors in such partitions were analyzed to determine the number of times a different configuration is needed during the day. One to three partitions were selected for the 24-hour period, and traffic data from ten days were played back to test if the traffic-counts stayed below the threshold values associated with these partitions. Results show that these partitions are robust and can be used for longer durations than they were designed for

Chatterji, Gano Broto↗

NASA NTRS2010

Incorporating Active Runway Crossings in Airport Departure Scheduling

A mixed integer linear program is presented for deterministically scheduling departure and ar rival aircraft at airport runways. This method addresses different schemes of managing the departure queuing area by treating it as first-in-first-out queues or as a simple par king area where any available aircraft can take-off ir respective of its relative sequence with others. In addition, this method explicitly considers separation criteria between successive aircraft and also incorporates an optional prioritization scheme using time windows. Multiple objectives pertaining to throughput and system delay are used independently. Results indicate improvement over a basic first-come-first-serve rule in both system delay and throughput. Minimizing system delay results in small deviations from optimal throughput, whereas minimizing throughput results in large deviations in system delay. Enhancements for computational efficiency are also presented in the form of reformulating certain constraints and defining additional inequalities for better bounds.

Gupta, Gautam↗

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

A Markov Decision Process Framework for Optimal Airport Reconfiguration

The airport runway configuration is defined as a combination set of runways for arrivals and departures used at a point during operation of the airport. An optimal configuration of these runways depends on a number of factors, including traffic demand, wind magnitude and direction, other adverse weather conditions, and noise restrictions, among others. Based on the current state of these factors and predictions of traffic demand and weather conditions, runway configuration changes are made and coordinated between tower controller, other air traffic control facilities, pilots, and ground personnel. Reconfigurations can be quite disruptive to airport operations; minimizing their frequency and scheduling them well in advance is essential for mitigating some of the added workload for controllers and pilots. Unfortunately, deciding on an appropriate time to change is challenging for human decision makers. Not only do multiple factors need to be evaluated, but the uncertainty in their forecasts must also be considered. Previous optimization methods, such as mixed linear integer programming, have been proposed. Although these methods can reason over a large set of variables, they do not systematically handle the uncertainty associated with weather movement, traffic demands, and other variables. In this work, we introduce a Markov Decision Process (MDP)-based decision making framework which can reason effectively over the inherent uncertainties and make optimal decisions on if/when to change the airport configuration. In a prototype implementation, we present a single runway with three aircraft and utilize knowledge of the forecasted wind speed and direction to determine whether to keep or change the current runway configuration. Our aim through this work is to present a framework for airport reconfiguration which can be scalable to additional aircraft, multiple runways, and various input parameters. This technique will optimize the airport reconfiguration procedure by providing a proactive approach, optimizing not just at the next optimal opportunity for a reconfiguration based on varying atmospheric and traffic conditions in the terminal airspace, but also anticipating future necessary reconfigurations. This will eliminate the inefficiencies of frequent changes currently associated with runway reconfiguration procedures.

runway reconfiguration↗

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 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↗