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Results for “combinatorial optimization problem”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1989

Minimizing distortion and internal forces in truss structures by simulated annealing

Inaccuracies in the length of members and the diameters of joints of large truss reflector backup structures may produce unacceptable levels of surface distortion and member forces. However, if the member lengths and joint diameters can be measured accurately it is possible to configure the members and joints so that root-mean-square (rms) surface error and/or rms member forces is minimized. Following Greene and Haftka (1989) it is assumed that the force vector f is linearly proportional to the member length errors e(sub M) of dimension NMEMB (the number of members) and joint errors e(sub J) of dimension NJOINT (the number of joints), and that the best-fit displacement vector d is a linear function of f. Let NNODES denote the number of positions on the surface of the truss where error influences are measured. The solution of the problem is discussed. To classify, this problem was compared to a similar combinatorial optimization problem. In particular, when only the member length errors are considered, minimizing d(sup 2)(sub rms) is equivalent to the quadratic assignment problem. The quadratic assignment problem is a well known NP-complete problem in operations research literature. Hence minimizing d(sup 2)(sub rms) is is also an NP-complete problem. The focus of the research is the development of a simulated annealing algorithm to reduce d(sup 2)(sub rms). The plausibility of this technique is its recent success on a variety of NP-complete combinatorial optimization problems including the quadratic assignment problem. A physical analogy for simulated annealing is the way liquids freeze and crystallize. All computational experiments were done on a MicroVAX. The two interchange heuristic is very fast but produces widely varying results. The two and three interchange heuristic provides less variability in the final objective function values but runs much more slowly. Simulated annealing produced the best objective function values for every starting configuration and was faster than the two and three interchange heuristic.

Kincaid, Rex K.↗
NASA NTRS2012

Design of Spacecraft Missions to Remove Multiple Orbital Debris Objects

The amount of hazardous debris in Earth orbit has been increasing, posing an evergreater danger to space assets and human missions. In January of 2007, a Chinese ASAT test produced approximately 2600 pieces of orbital debris. In February of 2009, Iridium 33 collided with an inactive Russian satellite, yielding approximately 1300 pieces of debris. These recent disastrous events and the sheer size of the Earth orbiting population make clear the necessity of removing orbital debris. In fact, experts from both NASA and ESA have stated that 10 to 20 pieces of orbital debris need to be removed per year to stabilize the orbital debris environment. However, no spacecraft trajectories have yet been designed for removing multiple debris objects and the size of the debris population makes the design of such trajectories a daunting task. Designing an efficient spacecraft trajectory to rendezvous with each of a large number of orbital debris pieces is akin to the famous Traveling Salesman problem, an NP-complete combinatorial optimization problem in which a number of cities are to be visited in turn. The goal is to choose the order in which the cities are visited so as to minimize the total path distance traveled. In the case of orbital debris, the pieces of debris to be visited must be selected and ordered such that spacecraft propellant consumption is minimized or at least kept low enough to be feasible. Emergent Space Technologies, Inc. has developed specialized algorithms for designing efficient tour missions for near-Earth asteroids that may be applied to the design of efficient spacecraft missions capable of visiting large numbers of orbital debris pieces. The first step is to identify a list of high priority debris targets using the Analytical Graphics, Inc. SOCRATES website and then obtain their state information from Celestrak. The tour trajectory design algorithms will then be used to determine the itinerary of objects and v requirements. These results will shed light on how many debris pieces can be visited for various amounts of propellant, which launch vehicles can accommodate such missions, and how much margin is available for debris removal system payloads.

Barbee, Brent W.↗
NASA NTRS2006

Exploiting Quantum Resonance to Solve Combinatorial Problems

Quantum resonance would be exploited in a proposed quantum-computing approach to the solution of combinatorial optimization problems. In quantum computing in general, one takes advantage of the fact that an algorithm cannot be decoupled from the physical effects available to implement it. Prior approaches to quantum computing have involved exploitation of only a subset of known quantum physical effects, notably including parallelism and entanglement, but not including resonance. In the proposed approach, one would utilize the combinatorial properties of tensor-product decomposability of unitary evolution of many-particle quantum systems for physically simulating solutions to NP-complete problems (a class of problems that are intractable with respect to classical methods of computation). In this approach, reinforcement and selection of a desired solution would be executed by means of quantum resonance. Classes of NP-complete problems that are important in practice and could be solved by the proposed approach include planning, scheduling, search, and optimal design.

Zak, Michail↗
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 NTRS1992

The damper placement problem for large flexible space structures

The damper placement problem for large flexible space truss structures is formulated as a combinatorial optimization problem. The objective is to determine the p truss members of the structure to replace with active (or passive) dampers so that the modal damping ratio is as large as possible for all significant modes of vibration. Equivalently, given a strain energy matrix with rows indexed on the modes and the columns indexed on the truss members, we seek to find the set of p columns such that the smallest row sum, over the p columns, is maximized. We develop a tabu search heuristic for the damper placement problems on the Controls Structures Interaction (CSI) Phase 1 Evolutionary Model (10 modes and 1507 truss members). The resulting solutions are shown to be of high quality.

Kincaid, Rex K.↗
NASA NTRS2010

An Optimizing Space Data-Communications Scheduling Method and Algorithm with Interference Mitigation, Generalized for a Broad Class of Optimization Problems

NASA's space data-communications infrastructure, the Space Network and the Ground Network, provide scheduled (as well as some limited types of unscheduled) data-communications services to user spacecraft via orbiting relay satellites and ground stations. An implementation of the methods and algorithms disclosed herein will be a system that produces globally optimized schedules with not only optimized service delivery by the space data-communications infrastructure but also optimized satisfaction of all user requirements and prescribed constraints, including radio frequency interference (RFI) constraints. Evolutionary search, a class of probabilistic strategies for searching large solution spaces, constitutes the essential technology in this disclosure. Also disclosed are methods and algorithms for optimizing the execution efficiency of the schedule-generation algorithm itself. The scheduling methods and algorithms as presented are adaptable to accommodate the complexity of scheduling the civilian and/or military data-communications infrastructure. Finally, the problem itself, and the methods and algorithms, are generalized and specified formally, with applicability to a very broad class of combinatorial optimization problems.

Rash, James L.↗
NASA NTRS2018

XY vs X Mixer in Quantum Alternating Operator Ansatz for Optimization Problems with Constraints

Quantum Approximate Optimization Algorithm, further generalized as Quantum Alternating Operator Ansatz (QAOA), is a family of algorithms for combinatorial optimization problems. It is a leading candidate to run on emerging universal quantum computers to gain insight into quantum heuristics. In constrained optimization, penalties are often introduced so that the ground state of the cost Hamiltonian encodes the solution (a standard practice in quantum annealing). An alternative is to choose a mixing Hamiltonian such that the constraint corresponds to a constant of motion and the quantum evolution stays in the feasible subspace. Better performance of the algorithm is speculated due to a much smaller search space. We consider problems with a constant Hamming weight as the constraint. We also compare different methods of generating the generalized W-state, which serves as a natural initial state for the Hamming-weight constraint. Using graph-coloring as an example, we compare the performance of using XY model as a mixer that preserves the Hamming weight with the performance of adding a penalty term in the cost Hamiltonian.

quantum computing↗
NASA NTRS2014

An Optimizing Space Data-Communications Scheduling Method and Algorithm with Interference Mitigation, Generalized for a Broad Class of Optimization Problems

NASA's space data-communications infrastructure-the Space Network and the Ground Network-provide scheduled (as well as some limited types of unscheduled) data-communications services to user spacecraft. The Space Network operates several orbiting geostationary platforms (the Tracking and Data Relay Satellite System (TDRSS)), each with its own servicedelivery antennas onboard. The Ground Network operates service-delivery antennas at ground stations located around the world. Together, these networks enable data transfer between user spacecraft and their mission control centers on Earth. Scheduling data-communications events for spacecraft that use the NASA communications infrastructure-the relay satellites and the ground stations-can be accomplished today with software having an operational heritage dating from the 1980s or earlier. An implementation of the scheduling methods and algorithms disclosed and formally specified herein will produce globally optimized schedules with not only optimized service delivery by the space data-communications infrastructure but also optimized satisfaction of all user requirements and prescribed constraints, including radio frequency interference (RFI) constraints. Evolutionary algorithms, a class of probabilistic strategies for searching large solution spaces, is the essential technology invoked and exploited in this disclosure. Also disclosed are secondary methods and algorithms for optimizing the execution efficiency of the schedule-generation algorithms themselves. The scheduling methods and algorithms as presented are adaptable to accommodate the complexity of scheduling the civilian and/or military data-communications infrastructure within the expected range of future users and space- or ground-based service-delivery assets. Finally, the problem itself, and the methods and algorithms, are generalized and specified formally. The generalized methods and algorithms are applicable to a very broad class of combinatorial-optimization problems that encompasses, among many others, the problem of generating optimal space-data communications schedules.

ground stations↗
NASA NTRS1986

Intractable computations without local minima

An NP-complete problem which is not a spin-glass is exhibited. The NP-complete problem 3-satisfiability is also embedded into a continuous analog system with no hills in the energy landscape obstructing solution of the problem. There is, however, a large flat plateau. This shows how sculpting of the energy surfaces of continuous analog systems to remove hills may fail to aid solution of embedded combinatorial optimization problems.

Baum, Eric B.↗
NASA NTRS1987

Optimal mapping of irregular finite element domains to parallel processors

Mapping the solution domain of n-finite elements into N-subdomains that may be processed in parallel by N-processors is an optimal one if the subdomain decomposition results in a well-balanced workload distribution among the processors. The problem is discussed in the context of irregular finite element domains as an important aspect of the efficient utilization of the capabilities of emerging multiprocessor computers. Finding the optimal mapping is an intractable combinatorial optimization problem, for which a satisfactory approximate solution is obtained here by analogy to a method used in statistical mechanics for simulating the annealing process in solids. The simulated annealing analogy and algorithm are described, and numerical results are given for mapping an irregular two-dimensional finite element domain containing a singularity onto the Hypercube computer.

Flower, J.↗
NASA NTRS1993

Optimization of blade arrangement in a randomly mistuned cascade using simulated annealing

This paper presents preliminary results of an investigation on mistuning of bladed-disk assemblies aimed at capturing the benefits of mistuning on stability, while at the same time, minimizing the adverse effects on response by solving the following problem: given a set of N turbine blades, each being a small random perturbation of the same nominal blade, determine the best arrangement of the N blades in a mistuned cascade with regard to aeroelastic response. In the studies reported here, mistuning of the blades is restricted to small differences in torsional stiffness. The large combinatorial optimization problem of seeking the best arrangement by blade exchanges is solved using a simulated annealing algorithm.

Thompson, Edward A.↗
NASA NTRS2017

Quantum Approximate Optimization with Hard and Soft Constraints

Challenging computational problems arising in the practical world are frequently tackled by heuristic algorithms. Small universal quantum computers will emerge in the next year or two, enabling a substantial broadening of the types of quantum heuristics that can be investigated beyond quantum annealing. The immediate question is What experiments should we prioritize that will give us insight into quantum heuristics? One leading candidate is the quantum approximate optimization algorithm (QAOA) metaheuristic. Here, we provide a framework for designing QAOA circuits for a variety of combinatorial optimization problems with both hard constraints that must be met and soft constraints whose violation we wish to minimize. We work through a number of examples, and discuss design principles and implementation considerations.

Hadfield, Stuart↗
NASA NTRS1989

Optimal placement of excitations and sensors by simulated annealing

The optimal placement of discrete actuators and sensors is posed as a combinatorial optimization problem. Two examples for truss structures were used for illustration; the first dealt with the optimal placement of passive dampers along existing truss members, and the second dealt with the optimal placement of a combination of a set of actuators and a set of sensors. Except for the simplest problems, an exact solution by enumeration involves a very large number of function evaluations, and is therefore computationally intractable. By contrast, the simulated annealing heuristic involves far fewer evaluations and is best suited for the class of problems considered. As an optimization tool, the effectiveness of the algorithm is enhanced by introducing a number of rules that incorporate knowledge about the physical behavior of the problem. Some of the suggested rules are necessarily problem dependent.

Salama, Moktar↗
NASA NTRS1992

Minimizing distortion in truss structures - A Hopfield network solution

Distortions in truss structures can result from random errors in element lengths that are typical of a manufacturing process. These distortions may be minimized by an optimal selection of elements from those available for placement between the prescribed nodes - a combinatorial optimization problem requiring significant investment of computational resource for all but the smallest problems. The present paper describes a formulation in which near-optimal element assignments are obtained as minimum-energy stable states, of an analogous Hopfield neural network. This requires mapping of the optimization problem into an energy function of the appropriate Liapunov form. The computational architecture is ideally suited to a parallel processor implementation and offers significant savings in computational effort. A numerical implementation of the approach is discussed with reference to planar truss problems.

Fu, B.↗
NASA NTRS1993

Optimal placement of tuning masses on truss structures by genetic algorithms

Optimal placement of tuning masses, actuators and other peripherals on large space structures is a combinatorial optimization problem. This paper surveys several techniques for solving this problem. The genetic algorithm approach to the solution of the placement problem is described in detail. An example of minimizing the difference between the two lowest frequencies of a laboratory truss by adding tuning masses is used for demonstrating some of the advantages of genetic algorithms. The relative efficiencies of different codings are compared using the results of a large number of optimization runs.

Ponslet, Eric↗
NASA NTRS1993

Minimizing distortion in truss structures -- a Hopfield network solution

Distortions in truss structures can result from random errors in elemental lengths that are typical of a manufacturing process. These distortions may be minimized by an optimal selection of elements from those available for placement between the prescribed nodes -- a combinatorial optimization problem requiring significant investment of computational resource for all but the smallest problems. The present paper describes a formulation in which near-optimal element assignments are obtained as minimum energy, stable states, of an analogous Hopfield neural network. This requires mapping of the optimization problem into an energy function of the appropriate Lyapunov form. The computational architecture is ideally suited to a parallel processor implementation and offers significant savings in computational effort. A numerical implementation of the approach is discussed with reference to planar truss problems.

Fu, B.↗
NASA NTRS1995

Aerospace applications on integer and combinatorial optimization

Research supported by NASA Langley Research Center includes many applications of aerospace design optimization and is conducted by teams of applied mathematicians and aerospace engineers. This paper investigates the benefits from this combined expertise in formulating and solving integer and combinatorial optimization problems. Applications range from the design of large space antennas to interior noise control. A typical problem. for example, seeks the optimal locations for vibration-damping devices on an orbiting platform and is expressed as a mixed/integer linear programming problem with more than 1500 design variables.

Padula, S. L.↗
NASA NTRS1995

Aerospace applications of integer and combinatorial optimization

Research supported by NASA Langley Research Center includes many applications of aerospace design optimization and is conducted by teams of applied mathematicians and aerospace engineers. This paper investigates the benefits from this combined expertise in solving combinatorial optimization problems. Applications range from the design of large space antennas to interior noise control. A typical problem, for example, seeks the optimal locations for vibration-damping devices on a large space structure and is expressed as a mixed/integer linear programming problem with more than 1500 design variables.

Padula, S. L.↗