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At least 253 records · Page 14

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NASA NTRS1985

The role of service areas in the optimization of FSS orbital and frequency assignments

A relationship is derived, on a single-entry interference basis, for the minimum allowable spacing between two satellites as a function of electrical parameters and service-area geometries. For circular beams, universal curves relate the topocentric satellite spacing angle to the service-area separation angle measured at the satellite. The corresponding geocentric spacing depends only weakly on the mean longitude of the two satellites, and this is true also for alliptical antenna beams. As a consequence, if frequency channels are preassigned, the orbital assignment synthesis of a satellite system can be formulated as a mixed-integer programming (MIP) problem or approximated by a linear programming (LP) problem, with the interference protection requirements enforced by constraints while some linear function is optimized. Possible objective-function choices are discussed and explicit formulations are presented for the choice of the sum of the absolute deviations of the orbital locations from some prescribed ideal location set. A test problem is posed consisting of six service areas, each served by one satellite, all using elliptical antenna beams and the same frequency channels. Numerical results are given for the three ideal location prescriptions for both the MIP and LP formulations. The resulting scenarios also satisfy reasonable aggregate interference protection requirements.

Levis, C. A.↗

NASA NTRS1986

Engineering calculations for communications satellite systems planning

Observed solution times were analyzed for the extended gradient and cyclic coordinate search procedures. The times used in the analysis come from computer runs made during a previously-reported experiment conducted to assess the quality of the solutions to a BSS synthesis problem found by the two search methods. The results of a second experiment with a Fixed Satellite Service (FSS) test problem are also presented. Computational results are summarized for mixed integer programming approaches for solving FSS synthesis problems. A promising heuristic algorithm is described. A synthesis model is discussed for orbital arc allotment optimization. Research plans for the near future are also presented.

Reilly, C. H.↗

NASA NTRS1986

On orbital allotments for geostationary satellites

The following satellite synthesis problem is addressed: communication satellites are to be allotted positions on the geostationary arc so that interference does not exceed a given acceptable level by enforcing conservative pairwise satellite separation. A desired location is specified for each satellite, and the objective is to minimize the sum of the deviations between the satellites' prescribed and desired locations. Two mixed integer programming models for the satellite synthesis problem are presented. Four solution strategies, branch-and-bound, Benders' decomposition, linear programming with restricted basis entry, and a switching heuristic, are used to find solutions to example synthesis problems. Computational results indicate the switching algorithm yields solutions of good quality in reasonable execution times when compared to the other solution methods. It is demonstrated that the switching algorithm can be applied to synthesis problems with the objective of minimizing the largest deviation between a prescribed location and the corresponding desired location. Furthermore, it is shown that the switching heuristic can use no conservative, location-dependent satellite separations in order to satisfy interference criteria.

Gonsalvez, David J. A.↗

NASA NTRS1987

Engineering calculations for communications satellite systems planning

A procedure is described that was used to calculate minimum required satellite separations based on total link carrier to interference requirements. Also summarized are recent results with a switching algorithm for satellite synthesis problems. Analytic solution value bounds for two of the satellite synthesis models studied are described. Preliminary results from an empirical study of alternate mixed integer programming models for satellite synthesis are presented. Research plans for the near future are discussed.

Reilly, Charles H.↗

NASA NTRS1987

A satellite system synthesis model for orbital arc allotment optimization

A mixed integer programming formulation of a satellite system synthesis problem if presented, which is referred to as the arc allotment problem (AAP). Each satellite administration is to be allotted a weighted-length segment of the geostationary orbital arc within which its satellites may be positioned at any longitudes. The objective function maximizes the length of the unweighted arc segment allotted to every administration, subject to single-entry co-channel interference restrictions and constraints imposed by the visible arc for each administration. Useful relationships between special cases of AAP and another satellite synthesis problem are established. Solutions to two example problems are presented.

Reilly, Charles H.↗

NASA NTRS1988

A k-permutation algorithm for Fixed Satellite Service orbital allotments

A satellite system synthesis problem, the satellite location problem (SLP), is addressed in this paper. In SLP, orbital locations (longitudes) are allotted to geostationary satellites in the Fixed Satellite Service. A linear mixed-integer programming model is presented that views SLP as a combination of two problems: (1) the problem of ordering the satellites and (2) the problem of locating the satellites given some ordering. A special-purpose heuristic procedure, a k-permutation algorithm, that has been developed to find solutions to SLPs formulated in the manner suggested is described. Solutions to small example problems are presented and analyzed.

Reilly, Charles H.↗

NASA NTRS1988

A satellite system synthesis model for orbital arc allotment optimization

A mixed-integer programming formulation is presented of a satellite system synthesis problem, or geostationary-orbital-planning synthesis problem, which is refered to as the arc allotment problem (AAP). Each satellite administration is to be allotted a weighted-length segment of the geostationary orbital arc within which its satellites may be positioned at any longitude. The objective function maximizes the length of the unweighted arc segment allotted to every administration, subject to single-entry cochannel interference restrictions and constraints imposed by the visible arc for each administration. Useful relationships between special cases of AAP and another satellite synthesis problem are established. Solutions to two example problems are presented.

Reilly, Charles H.↗

NASA NTRS1988

Engineering calculations for solving the orbital allotment problem

Four approaches for calculating downlink interferences for shaped-beam antennas are described. An investigation of alternative mixed-integer programming models for satellite synthesis is summarized. Plans for coordinating the various programs developed under this grant are outlined. Two procedures for ordering satellites to initialize the k-permutation algorithm are proposed. Results are presented for the k-permutation algorithms. Feasible solutions are found for 5 of the 6 problems considered. Finally, it is demonstrated that the k-permutation algorithm can be used to solve arc allotment problems.

Reilly, C.↗

NASA NTRS1990

Finding fixed satellite service orbital allotments with a k-permutation algorithm

A satellite system synthesis problem, the satellite location problem (SLP), is addressed. In SLP, orbital locations (longitudes) are allotted to geostationary satellites in the fixed satellite service. A linear mixed-integer programming model is presented that views SLP as a combination of two problems: the problem of ordering the satellites and the problem of locating the satellites given some ordering. A special-purpose heuristic procedure, a k-permutation algorithm, has been developed to find solutions to SLPs. Solutions to small sample problems are presented and analyzed on the basis of calculated interferences.

Reilly, Charles H.↗

NASA NTRS1992

Towards a theory of automated elliptic mesh generation

The theory of elliptic mesh generation is reviewed and the fundamental problem of constructing computational space is discussed. It is argued that the construction of computational space is an NP-Complete problem and therefore requires a nonstandard approach for its solution. This leads to the development of graph-theoretic, combinatorial optimization and integer programming algorithms. Methods for the construction of two dimensional computational space are presented.

Cordova, J. Q.↗

NASA NTRS2000

Analysis and Modeling of Ground Operations at Hub Airports

Building simple and accurate models of hub airports can considerably help one understand airport dynamics, and may provide quantitative estimates of operational airport improvements. In this paper, three models are proposed to capture the dynamics of busy hub airport operations. Two simple queuing models are introduced to capture the taxi-out and taxi-in processes. An integer programming model aimed at representing airline decision-making attempts to capture the dynamics of the aircraft turnaround process. These models can be applied for predictive purposes. They may also be used to evaluate control strategies for improving overall airport efficiency.

Atkins, Stephen↗

NASA NTRS2003

Runway Operations Planning: A Two-Stage Heuristic Algorithm

Anagnostakis, Ioannis↗

NASA NTRS2003

Runway Operations Planning: A Two-Stage Solution Methodology

The airport runway is a scarce resource that must be shared by different runway operations (arrivals, departures and runway crossings). Given the possible sequences of runway events, careful Runway Operations Planning (ROP) is required if runway utilization is to be maximized. Thus, Runway Operations Planning (ROP) is a critical component of airport operations planning in general and surface operations planning in particular. From the perspective of departures, ROP solutions are aircraft departure schedules developed by optimally allocating runway time for departures given the time required for arrivals and crossings. In addition to the obvious objective of maximizing throughput, other objectives, such as guaranteeing fairness and minimizing environmental impact, may be incorporated into the ROP solution subject to constraints introduced by Air Traffic Control (ATC) procedures. Generating optimal runway operations plans was approached in with a 'one-stage' optimization routine that considered all the desired objectives and constraints, and the characteristics of each aircraft (weight class, destination, Air Traffic Control (ATC) constraints) at the same time. Since, however, at any given point in time, there is less uncertainty in the predicted demand for departure resources in terms of weight class than in terms of specific aircraft, the ROP problem can be parsed into two stages. In the context of the Departure Planner (OP) research project, this paper introduces Runway Operations Planning (ROP) as part of the wider Surface Operations Optimization (SOO) and describes a proposed 'two stage' heuristic algorithm for solving the Runway Operations Planning (ROP) problem. Focus is specifically given on including runway crossings in the planning process of runway operations. In the first stage, sequences of departure class slots and runwy crossings slots are generated and ranked based on departure runway throughput under stochastic conditions. In the second stage, the departure class slots are populated with specific flights from the pool of available aircraft, by solving an integer program. Preliminary results from the algorithm implementation on real-world traffic data are included.

Anagnostakis, Ioannis↗

NASA NTRS2006

Assisting Public Organizations in Their Outsourcing Endeavors: A Decision Support Mode

There has been a tremendous growth in outsourcing practices in recent years. The public organizations in the United States have outsourced some functions and are now being compelled to outsource additional ones. While there are numerous studies that document and analyze outsourcing practices, there is limited research to guide public or governmental organizations in determining what functions to outsource. This study fills this gap by developing a decision support model for a typical public organization in determining what to outsource and how. A set of outsourcing decision factors is identified that can be used as parameters in the three integer programming formulations developed. These formulations are used as solution engines in the model. The first formulation identifies which functions are the best candidates for outsourcing given the organization's priorities. The other formulations place the functions into recommended contracts and re-assign displaced employees. Data from NASA Glenn Research Center in Ohio is used to test and analyze the model. Analysis indicates that cost and skills-related factors are the most sensitive parameters for the data tested. The model and the formulations are a relatively comprehensive package and may help guide outsourcing decisionmakers and policymakers in public organizations.

Kremic, TIbor↗

NASA NTRS2008

Efficient G(sup 4)FET-Based Logic Circuits

A total of 81 optimal logic circuits based on four-gate field-effect transistors (G(sup 4)4FETs) have been designed to implement all Boolean functions of up to three variables. The purpose of this development was to lend credence to the expectation that logic circuits based on G(sup 4)FETs could be more efficient (in the sense that they could contain fewer transistors), relative to functionally equivalent logic circuits based on conventional transistors. A G(sup 4)FET a combination of a junction field-effect transistor (JFET) and a metal oxide/semiconductor field-effect transistor (MOSFET) superimposed in a single silicon island and can therefore be regarded as two transistors sharing the same body. A G(sup 4)FET can also be regarded as a single device having four gates: two side junction-based gates, a top MOS gate, and a back gate activated by biasing of a silicon-on-insulator substrate. Each of these gates can be used to control the conduction characteristics of the transistor; this possibility creates new options for designing analog, radio-frequency, mixed-signal, and digital circuitry. One such option is to design a G(sup 4)FET to function as a three-input NOT-majority gate, which has been shown to be a universal and programmable logic gate. Optimal NOT-majority-gate, G(sup 4)FET-based logic-circuit designs were obtained in a comparative study that also included formulation of functionally equivalent logic circuits based on NOR and NAND gates implemented by use of conventional transistors. In the study, the problem of finding the optimal design for each logic function and each transistor type was solved as an integer-programming optimization problem. Considering all 81 non-equivalent Boolean functions included in the study, it was found that in 63% of the cases, fewer logic gates (and, hence, fewer transistors) would be needed in the G(sup 4)FET-based implementations.

Vatan, Farrokh↗

NASA NTRS2009

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.

Rios, Joseph Lucio↗

NASA NTRS2010

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.

Mukherjee, Avijit↗

NASA NTRS2012

Efficient Computation of Separation-Compliant Speed Advisories for Air Traffic Arriving in Terminal Airspace

A class of problems in air traffic management asks for a scheduling algorithm that supplies the air traffic services authority not only with a schedule of arrivals and departures, but also with speed advisories. Since advisories must be finite, a scheduling algorithm must ultimately produce a finite data set, hence must either start with a purely discrete model or involve a discretization of a continuous one. The former choice, often preferred for intuitive clarity, naturally leads to mixed-integer programs, hindering proofs of correctness and computational cost bounds (crucial for real-time operations). In this paper, a hybrid control system is used to model air traffic scheduling, capturing both the discrete and continuous aspects. This framework is applied to a class of problems, called the Fully Routed Nominal Problem. We prove a number of geometric results on feasible schedules and use these results to formulate an algorithm that attempts to compute a collective speed advisory, effectively finite, and has computational cost polynomial in the number of aircraft. This work is a first step toward optimization and models refined with more realistic detail.

Sadovsky, Alexander V.↗