37 research outputs found
Preliminary study on restarts for CSP algorithms
O uso de técnicas de restarts para resolver problemas de satisfação de restrições (CSPs),
utilizando algoritmos de procura com retrocesso, é considerado pouco importante. Neste artigo
propomos conduzir um estudo preliminar sobre o impacto da utilização de restarts nestes
algoritmos. Mostramos que o conhecido problema da n-rainhas tem uma distribuição heavy-tail.
Apresentamos evidências empíricas de que os restarts podem efectivamente melhorar o tempo
necessário para encontrar a solução das n-rainhas. Implementamos ainda uma heurística de
decisão baseada em conflitos e mostramos empiricamente que esta heurística, em conjunto com
os restarts, melhora ainda mais o tempo de execução dos algoritmos
Variable Annealing Length and Parallelism in Simulated Annealing
In this paper, we propose: (a) a restart schedule for an adaptive simulated
annealer, and (b) parallel simulated annealing, with an adaptive and
parameter-free annealing schedule. The foundation of our approach is the
Modified Lam annealing schedule, which adaptively controls the temperature
parameter to track a theoretically ideal rate of acceptance of neighboring
states. A sequential implementation of Modified Lam simulated annealing is
almost parameter-free. However, it requires prior knowledge of the annealing
length. We eliminate this parameter using restarts, with an exponentially
increasing schedule of annealing lengths. We then extend this restart schedule
to parallel implementation, executing several Modified Lam simulated annealers
in parallel, with varying initial annealing lengths, and our proposed parallel
annealing length schedule. To validate our approach, we conduct experiments on
an NP-Hard scheduling problem with sequence-dependent setup constraints. We
compare our approach to fixed length restarts, both sequentially and in
parallel. Our results show that our approach can achieve substantial
performance gains, throughout the course of the run, demonstrating our approach
to be an effective anytime algorithm.Comment: Tenth International Symposium on Combinatorial Search, pages 2-10.
June 201
Fine-grained Search Space Classification for Hard Enumeration Variants of Subset Problems
We propose a simple, powerful, and flexible machine learning framework for
(i) reducing the search space of computationally difficult enumeration variants
of subset problems and (ii) augmenting existing state-of-the-art solvers with
informative cues arising from the input distribution. We instantiate our
framework for the problem of listing all maximum cliques in a graph, a central
problem in network analysis, data mining, and computational biology. We
demonstrate the practicality of our approach on real-world networks with
millions of vertices and edges by not only retaining all optimal solutions, but
also aggressively pruning the input instance size resulting in several fold
speedups of state-of-the-art algorithms. Finally, we explore the limits of
scalability and robustness of our proposed framework, suggesting that
supervised learning is viable for tackling NP-hard problems in practice.Comment: AAAI 201
Restart Strategies for Constraint-Handling in Generative Design Systems
Product alternatives suggested by a generative design system often need to be evaluated on qualitative criteria. This evaluation necessitates that several feasible solutions which fulfill all technical constraints can be proposed to the user of the system. Also, as concept development is an iterative process, it is important that these solutions are generated quickly; i.e., the system must have a low convergence time. A problem, however, is that stochastic constraint-handling techniques can have highly unpredictable convergence times, spanning several orders of magnitude, and might sometimes not converge at all. A possible solution to avoid the lengthy runs is to restart the search after a certain time, with the hope that a new starting point will lead to a lower overall convergence time, but selecting an optimal restart-time is not trivial. In this paper, two strategies are investigated for such selection, and their performance is evaluated on two constraint-handling techniques for a product design problem. The results show that both restart strategies can greatly reduce the overall convergence time. Moreover, it is shown that one of the restart strategies can be applied to a wide range of constraint-handling techniques and problems, without requiring any fine-tuning of problem-specific parameters
Accelerating SAT solving with best-first-search
Solvers for Boolean satisfiability (SAT), like other algorithms for NP-complete problems, tend to have a heavy-tailed runtime distribution. Successful SAT solvers make use of frequent restarts to mitigate this problem by abandoning unfruitful parts of the search space after some time. Although frequent restarting works fairly well, it is a quite simplistic technique that does not do anything explicitly to make the next try better than the previous one. In this paper, we suggest a more sophisticated method: using a best-first-search approach to quickly move between different parts of the search space. This way, the search can always focus on the most promising region. We investigate empirically how the performance of frequent restarts, best-first-search, and a combination of the two compare to each other. Our findings indicate that the combined method works best, improving 36-43\% on the performance of frequent restarts on the used set of benchmark problems
Understanding heavy tails in a bounded world or, is a truncated heavy tail heavy or not?
We address the important question of the extent to which random variables and
vectors with truncated power tails retain the characteristic features of random
variables and vectors with power tails. We define two truncation regimes, soft
truncation regime and hard truncation regime, and show that, in the soft
truncation regime, truncated power tails behave, in important respects, as if
no truncation took place. On the other hand, in the hard truncation regime much
of "heavy tailedness" is lost. We show how to estimate consistently the tail
exponent when the tails are truncated, and suggest statistical tests to decide
on whether the truncation is soft or hard. Finally, we apply our methods to two
recent data sets arising from computer networks
On the Maximum Satisfiability of Random Formulas
Maximum satisfiability is a canonical NP-hard optimization problem that
appears empirically hard for random instances. Let us say that a Conjunctive
normal form (CNF) formula consisting of -clauses is -satisfiable if there
exists a truth assignment satisfying of all clauses
(observe that every -CNF is 0-satisfiable). Also, let denote a
random -CNF on variables formed by selecting uniformly and independently
out of all possible -clauses. It is easy to prove that for every
and every in , there is such that if , then the
probability that is -satisfiable tends to 0 as tends to
infinity. We prove that there exists a sequence such that if
then the probability that is
-satisfiable tends to 1 as tends to infinity. The sequence
tends to 0 exponentially fast in