Fair Multiple Traveling Salesman Problem - An Alternative to the Min-Max Multiple Traveling Salesman Problem
Explore the source record for details and available documents.
97 MATHEMATICS AND COMPUTING↗
SEARCH · Search NASA
Results for “TRAVELING SALESMAN 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.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
WHAMII - An enumeration and insertion procedure with binomial bounds for the stochastic time-constrained traveling salesman problem
This paper presents an algorithm (WHAMII) designed to solve the Artificial Intelligence Design Challenge at the 1987 AIAA Guidance, Navigation and Control Conference. The problem under consideration is a stochastic generalization of the traveling salesman problem in which travel costs can incur a penalty with a given probability. The variability in travel costs leads to a probability constraint with respect to violating the budget allocation. Given the small size of the problem (eleven cities), an approach is considered that combines partial tour enumeration with a heuristic city insertion procedure. For computational efficiency during both the enumeration and insertion procedures, precalculated binomial probabilities are used to determine an upper bound on the actual probability of violating the budget constraint for each tour. The actual probability is calculated for the final best tour, and additional insertions are attempted until the actual probability exceeds the bound.
Dahl, Roy W.↗
Neural Network Solves "Traveling-Salesman" Problem
Experimental electronic neural network solves "traveling-salesman" problem. Plans round trip of minimum distance among N cities, visiting every city once and only once (without backtracking). This problem is paradigm of many problems of global optimization (e.g., routing or allocation of resources) occuring in industry, business, and government. Applied to large number of cities (or resources), circuits of this kind expected to solve problem faster and more cheaply.
Thakoor, Anilkumar P.↗
A Simple Algorithm for the Metric Traveling Salesman Problem
An algorithm was designed for a wire list net sort problem. A branch and bound algorithm for the metric traveling salesman problem is presented for this. The algorithm is a best bound first recursive descent where the bound is based on the triangle inequality. The bounded subsets are defined by the relative order of the first K of the N cities (i.e., a K city subtour). When K equals N, the bound is the length of the tour. The algorithm is implemented as a one page subroutine written in the C programming language for the VAX 11/750. Average execution times for randomly selected planar points using the Euclidean metric are 0.01, 0.05, 0.42, and 3.13 seconds for ten, fifteen, twenty, and twenty-five cities, respectively. Maximum execution times for a hundred cases are less than eleven times the averages. The speed of the algorithms is due to an initial ordering algorithm that is a N squared operation. The algorithm also solves the related problem where the tour does not return to the starting city and the starting and/or ending cities may be specified. It is possible to extend the algorithm to solve a nonsymmetric problem satisfying the triangle inequality.
Grimm, M. J.↗
Fault-tolerance of a neural network solving the traveling salesman problem
This study presents the results of a fault-injection experiment that stimulates a neural network solving the Traveling Salesman Problem (TSP). The network is based on a modified version of Hopfield's and Tank's original method. We define a performance characteristic for the TSP that allows an overall assessment of the solution quality for different city-distributions and problem sizes. Five different 10-, 20-, and 30- city cases are sued for the injection of up to 13 simultaneous stuck-at-0 and stuck-at-1 faults. The results of more than 4000 simulation-runs show the extreme fault-tolerance of the network, especially with respect to stuck-at-0 faults. One possible explanation for the overall surprising result is the redundancy of the problem representation.
Protzel, P.↗
A Hybrid Traveling Salesman Problem - Squeaky Wheel Optimization Planner for Earth Observational Scheduling
We outline a hybrid planner for scheduling Observa- tion Requests on an Earth observing satellite, subject to a variety of constraints for the ASPEN (Chien et al. 2000) Eagle Eye adaptation (Knight, Donnellan, and Green 2013) that combines Squeaky Wheel Optimiza- tion (Joslin and Clements 1999) with sliding observa- tion planning (Aldinger et al. 2013). The Earth Ob- serving Satellite (EOS) planning problem (Globus et al. 2004) is reformulated as time-varying travel time TSP with interval constraints (Ichoua, Gendreau, and Potvin 2003). The replanning/ ll stage of the hybrid scheduler marginally improves schedule quality for all bus agilities examined, but has more impact on lower agility observers. The squeaky wheel stage primarily a ects overall schedule quality by satisfying high pri- ority requests, while the replanner reduces starvation of lower value requests.
Trowbridge, Michael↗
Analog Processor To Solve Optimization Problems
Proposed analog processor solves "traveling-salesman" problem, considered paradigm of global-optimization problems involving routing or allocation of resources. Includes electronic neural network and auxiliary circuitry based partly on concepts described in "Neural-Network Processor Would Allocate Resources" (NPO-17781) and "Neural Network Solves 'Traveling-Salesman' Problem" (NPO-17807). Processor based on highly parallel computing solves problem in significantly less time.
Duong, Tuan A.↗
Discrete optimizing.
Discrete optimization problem approach and evaluation of results of applying it to variety of traveling salesman problems
OPTIMIZATION↗
Fault tolerance of artificial neural networks with applications in critical systems
This paper investigates the fault tolerance characteristics of time continuous recurrent artificial neural networks (ANN) that can be used to solve optimization problems. The principle of operations and performance of these networks are first illustrated by using well-known model problems like the traveling salesman problem and the assignment problem. The ANNs are then subjected to 13 simultaneous 'stuck at 1' or 'stuck at 0' faults for network sizes of up to 900 'neurons'. The effects of these faults is demonstrated and the cause for the observed fault tolerance is discussed. An application is presented in which a network performs a critical task for a real-time distributed processing system by generating new task allocations during the reconfiguration of the system. The performance degradation of the ANN under the presence of faults is investigated by large-scale simulations, and the potential benefits of delegating a critical task to a fault tolerant network are discussed.
Protzel, Peter W.↗
Search Problems in Mission Planning and Navigation of Autonomous Aircraft
An architecture for the control of an autonomous aircraft is presented. The architecture is a hierarchical system representing an anthropomorphic breakdown of the control problem into planner, navigator, and pilot systems. The planner system determines high level global plans from overall mission objectives. This abstract mission planning is investigated by focusing on the Traveling Salesman Problem with variations on local and global constraints. Tree search techniques are applied including the breadth first, depth first, and best first algorithms. The minimum-column and row entries for the Traveling Salesman Problem cost matrix provides a powerful heuristic to guide these search techniques. Mission planning subgoals are directed from the planner to the navigator for planning routes in mountainous terrain with threats. Terrain/threat information is abstracted into a graph of possible paths for which graph searches are performed. It is shown that paths can be well represented by a search graph based on the Voronoi diagram of points representing the vertices of mountain boundaries. A comparison of Dijkstra's dynamic programming algorithm and the A* graph search algorithm from artificial intelligence/operations research is performed for several navigation path planning examples. These examples illustrate paths that minimize a combination of distance and exposure to threats. Finally, the pilot system synthesizes the flight trajectory by creating the control commands to fly the aircraft.
Krozel, James A.↗
Quantum-Inspired Maximizer
A report discusses an algorithm for a new kind of dynamics based on a quantum- classical hybrid-quantum-inspired maximizer. The model is represented by a modified Madelung equation in which the quantum potential is replaced by different, specially chosen 'computational' potential. As a result, the dynamics attains both quantum and classical properties: it preserves superposition and entanglement of random solutions, while allowing one to measure its state variables, using classical methods. Such optimal combination of characteristics is a perfect match for quantum-inspired computing. As an application, an algorithm for global maximum of an arbitrary integrable function is proposed. The idea of the proposed algorithm is very simple: based upon the Quantum-inspired Maximizer (QIM), introduce a positive function to be maximized as the probability density to which the solution is attracted. Then the larger value of this function will have the higher probability to appear. Special attention is paid to simulation of integer programming and NP-complete problems. It is demonstrated that the problem of global maximum of an integrable function can be found in polynomial time by using the proposed quantum- classical hybrid. The result is extended to a constrained maximum with applications to integer programming and TSP (Traveling Salesman Problem).
Zak, Michail↗
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.↗
A traveling-salesman-based approach to aircraft scheduling in the terminal area
An efficient algorithm is presented, based on the well-known algorithm for the traveling salesman problem, for scheduling aircraft arrivals into major terminal areas. The algorithm permits, but strictly limits, reassigning an aircraft from its initial position in the landing order. This limitation is needed so that no aircraft or aircraft category is unduly penalized. Results indicate, for the mix of arrivals investigated, a potential increase in capacity in the 3 to 5 percent range. Furthermore, it is shown that the computation time for the algorithm grows only linearly with problem size.
Luenberger, Robert A.↗
Simulation tests of the optimization method of Hopfield and Tank using neural networks
The method proposed by Hopfield and Tank for using the Hopfield neural network with continuous valued neurons to solve the traveling salesman problem is tested by simulation. Several researchers have apparently been unable to successfully repeat the numerical simulation documented by Hopfield and Tank. However, as suggested to the author by Adams, it appears that the reason for those difficulties is that a key parameter value is reported erroneously (by four orders of magnitude) in the original paper. When a reasonable value is used for that parameter, the network performs generally as claimed. Additionally, a new method of using feedback to control the input bias currents to the amplifiers is proposed and successfully tested. This eliminates the need to set the input currents by trial and error.
Paielli, Russell A.↗
WNN 92; Proceedings of the 3rd Workshop on Neural Networks: Academic/Industrial/NASA/Defense, Auburn Univ., AL, Feb. 10-12, 1992 and South Shore Harbour, TX, Nov. 4-6, 1992
The present conference discusses such neural networks (NN) related topics as their current development status, NN architectures, NN learning rules, NN optimization methods, NN temporal models, NN control methods, NN pattern recognition systems and applications, biological and biomedical applications of NNs, VLSI design techniques for NNs, NN systems simulation, fuzzy logic, and genetic algorithms. Attention is given to missileborne integrated NNs, adaptive-mixture NNs, implementable learning rules, an NN simulator for travelling salesman problem solutions, similarity-based forecasting, NN control of hypersonic aircraft takeoff, NN control of the Space Shuttle Arm, an adaptive NN robot manipulator controller, a synthetic approach to digital filtering, NNs for speech analysis, adaptive spline networks, an anticipatory fuzzy logic controller, and encoding operations for fuzzy associative memories.
Padgett, Mary L.↗
Scope of Various Random Number Generators in Ant System Approach for TSP
Experimented on heuristic, based on an ant system approach for traveling Salesman problem, are several quasi and pseudo-random number generators. This experiment is to explore if any particular generator is most desirable. Such an experiment on large samples has the potential to rank the performance of the generators for the foregoing heuristic. This is just to seek an answer to the controversial performance ranking of the generators in probabilistic/statically sense.
Sen, S. K.↗
Scope of Various Random Number Generators in ant System Approach for TSP
Experimented on heuristic, based on an ant system approach for traveling salesman problem, are several quasi- and pseudo-random number generators. This experiment is to explore if any particular generator is most desirable. Such an experiment on large samples has the potential to rank the performance of the generators for the foregoing heuristic. This is mainly to seek an answer to the controversial issue "which generator is the best in terms of quality of the result (accuracy) as well as cost of producing the result (time/computational complexity) in a probabilistic/statistical sense."
Sen, S. K.↗