180,975 research outputs found
Relationship between clustering and algorithmic phase transitions in the random k-XORSAT model and its NP-complete extensions
We study the performances of stochastic heuristic search algorithms on
Uniquely Extendible Constraint Satisfaction Problems with random inputs. We
show that, for any heuristic preserving the Poissonian nature of the underlying
instance, the (heuristic-dependent) largest ratio of constraints per
variables for which a search algorithm is likely to find solutions is smaller
than the critical ratio above which solutions are clustered and
highly correlated. In addition we show that the clustering ratio can be reached
when the number k of variables per constraints goes to infinity by the
so-called Generalized Unit Clause heuristic.Comment: 15 pages, 4 figures, Proceedings of the International Workshop on
Statistical-Mechanical Informatics, September 16-19, 2007, Kyoto, Japan; some
imprecisions in the previous version have been correcte
Behavior of heuristics and state space structure near SAT/UNSAT transition
We study the behavior of ASAT, a heuristic for solving satisfiability
problems by stochastic local search near the SAT/UNSAT transition. The
heuristic is focused, i.e. only variables in unsatisfied clauses are updated in
each step, and is significantly simpler, while similar to, walksat or Focused
Metropolis Search. We show that ASAT solves instances as large as one million
variables in linear time, on average, up to 4.21 clauses per variable for
random 3SAT. For K higher than 3, ASAT appears to solve instances at the ``FRSB
threshold'' in linear time, up to K=7.Comment: 12 pages, 6 figures, longer version available as MSc thesis of first
author at http://biophys.physics.kth.se/docs/ardelius_thesis.pd
Random Costs in Combinatorial Optimization
The random cost problem is the problem of finding the minimum in an
exponentially long list of random numbers. By definition, this problem cannot
be solved faster than by exhaustive search. It is shown that a classical
NP-hard optimization problem, number partitioning, is essentially equivalent to
the random cost problem. This explains the bad performance of heuristic
approaches to the number partitioning problem and allows us to calculate the
probability distributions of the optimum and sub-optimum costs.Comment: 4 pages, Revtex, 2 figures (eps), submitted to PR
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A mapping strategy for MIMD computers
In this paper, a heuristic mapping approach which maps parallel programs, described by precedence graphs, to MIMD architectures, described by system graphs, is presented. The complete execution time of a parallel program is used as a measure, and the concept of critical edges is utilized as the heuristic to guide the search for a better initial assignment and subsequent refinement. An important feature is the use of a termination condition of the refinement process. This is based on deriving a lower bound on the total execution time of the mapped program. When this has been reached, no further refinement steps are necessary. The algorithms have been implemented and applied to the mapping of random problem graphs to various system topologies, including hypercubes, meshes, and random graphs. The results show reductions in execution times of the mapped programs of up to 77 percent over random mapping
State Transition Algorithm
In terms of the concepts of state and state transition, a new heuristic
random search algorithm named state transition algorithm is proposed. For
continuous function optimization problems, four special transformation
operators called rotation, translation, expansion and axesion are designed.
Adjusting measures of the transformations are mainly studied to keep the
balance of exploration and exploitation. Convergence analysis is also discussed
about the algorithm based on random search theory. In the meanwhile, to
strengthen the search ability in high dimensional space, communication strategy
is introduced into the basic algorithm and intermittent exchange is presented
to prevent premature convergence. Finally, experiments are carried out for the
algorithms. With 10 common benchmark unconstrained continuous functions used to
test the performance, the results show that state transition algorithms are
promising algorithms due to their good global search capability and convergence
property when compared with some popular algorithms.Comment: 18 pages, 28 figure
Heuristic pattern search for bound constrained minimax problems
This paper presents a pattern search algorithm and its hybridization
with a random descent search for solving bound constrained minimax problems.
The herein proposed heuristic pattern search method combines the Hooke and
Jeeves (HJ) pattern and exploratory moves with a randomly generated approxi-
mate descent direction. Two versions of the heuristic algorithm have been applied
to several benchmark minimax problems and compared with the original HJ pat-
tern search algorithm
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