6,983 research outputs found
Improving the Asymmetric TSP by Considering Graph Structure
Recent works on cost based relaxations have improved Constraint Programming
(CP) models for the Traveling Salesman Problem (TSP). We provide a short survey
over solving asymmetric TSP with CP. Then, we suggest new implied propagators
based on general graph properties. We experimentally show that such implied
propagators bring robustness to pathological instances and highlight the fact
that graph structure can significantly improve search heuristics behavior.
Finally, we show that our approach outperforms current state of the art
results.Comment: Technical repor
Phase Transitions and Backbones of the Asymmetric Traveling Salesman Problem
In recent years, there has been much interest in phase transitions of
combinatorial problems. Phase transitions have been successfully used to
analyze combinatorial optimization problems, characterize their typical-case
features and locate the hardest problem instances. In this paper, we study
phase transitions of the asymmetric Traveling Salesman Problem (ATSP), an
NP-hard combinatorial optimization problem that has many real-world
applications. Using random instances of up to 1,500 cities in which intercity
distances are uniformly distributed, we empirically show that many properties
of the problem, including the optimal tour cost and backbone size, experience
sharp transitions as the precision of intercity distances increases across a
critical value. Our experimental results on the costs of the ATSP tours and
assignment problem agree with the theoretical result that the asymptotic cost
of assignment problem is pi ^2 /6 the number of cities goes to infinity. In
addition, we show that the average computational cost of the well-known
branch-and-bound subtour elimination algorithm for the problem also exhibits a
thrashing behavior, transitioning from easy to difficult as the distance
precision increases. These results answer positively an open question regarding
the existence of phase transitions in the ATSP, and provide guidance on how
difficult ATSP problem instances should be generated
Learning in stochastic neural networks for constraint satisfaction problems
Researchers describe a newly-developed artificial neural network algorithm for solving constraint satisfaction problems (CSPs) which includes a learning component that can significantly improve the performance of the network from run to run. The network, referred to as the Guarded Discrete Stochastic (GDS) network, is based on the discrete Hopfield network but differs from it primarily in that auxiliary networks (guards) are asymmetrically coupled to the main network to enforce certain types of constraints. Although the presence of asymmetric connections implies that the network may not converge, it was found that, for certain classes of problems, the network often quickly converges to find satisfactory solutions when they exist. The network can run efficiently on serial machines and can find solutions to very large problems (e.g., N-queens for N as large as 1024). One advantage of the network architecture is that network connection strengths need not be instantiated when the network is established: they are needed only when a participating neural element transitions from off to on. They have exploited this feature to devise a learning algorithm, based on consistency techniques for discrete CSPs, that updates the network biases and connection strengths and thus improves the network performance
Macrostate Data Clustering
We develop an effective nonhierarchical data clustering method using an
analogy to the dynamic coarse graining of a stochastic system. Analyzing the
eigensystem of an interitem transition matrix identifies fuzzy clusters
corresponding to the metastable macroscopic states (macrostates) of a diffusive
system. A "minimum uncertainty criterion" determines the linear transformation
from eigenvectors to cluster-defining window functions. Eigenspectrum gap and
cluster certainty conditions identify the proper number of clusters. The
physically motivated fuzzy representation and associated uncertainty analysis
distinguishes macrostate clustering from spectral partitioning methods.
Macrostate data clustering solves a variety of test cases that challenge other
methods.Comment: keywords: cluster analysis, clustering, pattern recognition, spectral
graph theory, dynamic eigenvectors, machine learning, macrostates,
classificatio
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