107 research outputs found
A Computational Comparison of Optimization Methods for the Golomb Ruler Problem
The Golomb ruler problem is defined as follows: Given a positive integer n,
locate n marks on a ruler such that the distance between any two distinct pair
of marks are different from each other and the total length of the ruler is
minimized. The Golomb ruler problem has applications in information theory,
astronomy and communications, and it can be seen as a challenge for
combinatorial optimization algorithms. Although constructing high quality
rulers is well-studied, proving optimality is a far more challenging task. In
this paper, we provide a computational comparison of different optimization
paradigms, each using a different model (linear integer, constraint programming
and quadratic integer) to certify that a given Golomb ruler is optimal. We
propose several enhancements to improve the computational performance of each
method by exploring bound tightening, valid inequalities, cutting planes and
branching strategies. We conclude that a certain quadratic integer programming
model solved through a Benders decomposition and strengthened by two types of
valid inequalities performs the best in terms of solution time for small-sized
Golomb ruler problem instances. On the other hand, a constraint programming
model improved by range reduction and a particular branching strategy could
have more potential to solve larger size instances due to its promising
parallelization features
Compressive and Noncompressive Power Spectral Density Estimation from Periodic Nonuniform Samples
This paper presents a novel power spectral density estimation technique for
band-limited, wide-sense stationary signals from sub-Nyquist sampled data. The
technique employs multi-coset sampling and incorporates the advantages of
compressed sensing (CS) when the power spectrum is sparse, but applies to
sparse and nonsparse power spectra alike. The estimates are consistent
piecewise constant approximations whose resolutions (width of the piecewise
constant segments) are controlled by the periodicity of the multi-coset
sampling. We show that compressive estimates exhibit better tradeoffs among the
estimator's resolution, system complexity, and average sampling rate compared
to their noncompressive counterparts. For suitable sampling patterns,
noncompressive estimates are obtained as least squares solutions. Because of
the non-negativity of power spectra, compressive estimates can be computed by
seeking non-negative least squares solutions (provided appropriate sampling
patterns exist) instead of using standard CS recovery algorithms. This
flexibility suggests a reduction in computational overhead for systems
estimating both sparse and nonsparse power spectra because one algorithm can be
used to compute both compressive and noncompressive estimates.Comment: 26 pages, single spaced, 9 figure
GPGPU for Difficult Black-box Problems
AbstractDifficult black-box problems arise in many scientific and industrial areas. In this paper, efficient use of a hardware accelerator to implement dedicated solvers for such problems is discussed and studied based on an example of Golomb Ruler problem. The actual solution of the problem is shown based on evolutionary and memetic algorithms accelerated on GPGPU. The presented results prove that GPGPU outperforms CPU in some memetic algorithms which can be used as a part of hybrid algorithm of finding near optimal solutions of Golomb Ruler problem. The presented research is a part of building heterogenous parallel algorithm for difficult black-box Golomb Ruler problem
Towards hybrid methods for solving hard combinatorial optimization problems
Tesis doctoral leída en la Escuela Politécnica Superior de la Universidad Autónoma de Madrid el 4 de septiembre de 200
A Unified Framework for Integer Programming Formulation of Graph Matching Problems
Graph theory has been a powerful tool in solving difficult and complex problems arising in all disciplines. In particular, graph matching is a classical problem in pattern analysis with enormous applications. Many graph problems have been formulated as a mathematical program then solved using exact, heuristic and/or approximated-guaranteed procedures. On the other hand, graph theory has been a powerful tool in visualizing and understanding of complex mathematical programming problems, especially integer programs. Formulating a graph problem as a natural integer program (IP) is often a challenging task. However, an IP formulation of the problem has many advantages. Several researchers have noted the need for natural IP formulation of graph theoretic problems. The aim of the present study is to provide a unified framework for IP formulation of graph matching problems. Although there are many surveys on graph matching problems, however, none is concerned with IP formulation. This paper is the first to provide a comprehensive IP formulation for such problems. The framework includes variety of graph optimization problems in the literature. While these problems have been studied by different research communities, however, the framework presented here helps to bring efforts from different disciplines to tackle such diverse and complex problems. We hope the present study can significantly help to simplify some of difficult problems arising in practice, especially in pattern analysis
Constraint programming on a heterogeneous multicore architecture
As bibliotecas para programação com restrições são úteis ao desenvolverem-se aplicações em linguagens de programação normalmente mais utilizadas pois não necessitam que os programadores aprendam uma. Nova, linguagem, fornecendo ferramentas de programação declarativa para utilização com os sistemas convencionais. Algumas soluções para programação com restrições favorecem completude, tais como sistemas baseados em propagação. Outras estão mais interessadas em obter uma boa solução rapidamente, rejeitando a necessidade de encontram todas as soluções; esta sendo a alternativa utilizada nos sistemas de pesquisa local. Conceber soluções híbridas (propagação + pesquisa local) parece prometedor pois as vantagens de ambas alternativas podem ser combinadas numa única solução. As arquiteturas paralelas são cada vez mais comuns, em parte devido à disponibilidade em grande escala, de sistemas individuais mas também devido à tendência em generalizar o uso de processadores multicore ou seja., processadores com várias unidades de processamento. Nesta tese é proposta uma. Arquitetura para resolvedores de restrições mistos, de pendendo de métodos de propagação e pesquisa local, a qual foi concebida para funcionar eficazmente numa arquitetura. Heterogéneo multiprocessador. /ABSTRACT - Constraint programming libraries are useful when building applications developed mostly in mainstrearn programming languages: they do not require the developers to acquire skills for a new language, providing instead declarative programming tools for use within conventional systems. Some approaches to constraint programming favour completeness, such as propagation-based systems. Others are more interested in getting to a good solution fast, regardless of whether all solutions may be found; this approach is used in local search systems. Designing hybrid approaches (propagation + local search) seems promising since the advantages may be combined into a single approach. Parallel architectures are becoming more commonplace, partly due to the large-scale availability of individual systems but also because of the trend towards generalizing the use of multicore microprocessors. In this thesis an architecture for mixed constraint solvers is proposed, relying both on propagation and local search, which is designed to function effectively in a heterogeneous multicore architecture
AN EMPIRICAL STUDY OF DIFFERENT BRANCHING STRATEGIES FOR CONSTRAINT SATISFACTION PROBLEMS
Many real life problems can be formulated as constraint satisfaction problems (CSPs). Backtracking search algorithms are usually employed to solve CSPs and in backtracking search the choice of branching strategies can be critical since they specify how a search algorithm can instantiate a variable and how a problem can be reduced into subproblems; that is, they define a search tree. In spite of the apparent importance of the branching strategy, there have been only a few empirical studies about different branching strategies and they all have been tested exclusively for numerical constraints. In this thesis, we employ the three most commonly used branching strategies in solving finite domain CSPs. These branching strategies are described as follows: first, a branching strategy with strong commitment assigns its variables in the early stage of the search as in k-Way branching; second, 2-Way branching guides a search by branching one side with assigning a variable and the other with eliminating the assigned value; third, the domain splitting strategy, based on the least commitment principle, branches by dividing a variable's domain rather than by assigning a single value to a variable. In our experiments, we compared the efficiency of different branching strategies in terms of their execution times and the number of choice points in solving finite domain CSPs. Interestingly, our experiments provide evidence that the choice of branching strategy for finite domain problems does not matter much in most cases--provided we are using an effective variable ordering heuristic--as domain splitting and 2-Way branching end up simulating k-Way branching. However, for an optimization problem with large domain size, the branching strategy with the least commitment principle can be more efficient than the other strategies. This empirical study will hopefully interest other practitioners to take different branching schemes into consideration in designing heuristics
Constraint programming on hierarchical multiprocessor systems
The work reported in this thesis is about constraint processing in the context of hierarchical
multiprocessor systems, including distributed systems. More speci cally, it develops
techniques and a system to help bringing the power available in today's multiprocessing
networked systems into the constraint processing eld.
Solving constraint speci ed problems is a process which lends itself naturally to
parallelisation, as it usually implies going through very large search spaces, looking for
a solution. Parallel constraint solving draws on the idea of dividing the search space
among several workers, so the search may proceed faster, and thanks to the declarative
nature of constraint programming, the parallelisation happens transparently as far as
the user is concerned. However, to fully take advantage of the parallel computing power
available, techniques must be developed to help ensure that the workers executing the
search are kept busy at all times, which is an issue tackled by this work; RESUMO: Esta tese debruça-se sobre a programação por restrições no contexto dos sistemas multiprocessador
hierárquicos, incluindo os sistemas distribuídos. Mais especificamente, o
trabalho elaborado desenvolve as técnicas de resolução de problemas de satisfação de
restrições recorrendo ao paralelismo.
A actualidade do tema prende-se com a cada vez maior divulgação de que são objecto
os sistemas multiprocessador que, juntamente com a omnipresença das redes de
computadores, põe à nossa disposição uma capacidade de cálculo que necessita de ser
posta a uso, o que tarda em acontecer. Nesta tese desenvolve-se um sistema que permite
tirar partido desses recursos através do processamento de restrições
A programação por restrições é um paradigma declarativo, em que o utilizador não
tem de se preocupar com o controlo da computação, e a introdução de paralelismo nesta
área pode realizar-se transparentemente. Por outro lado, o processo de pesquisa de
soluções para problemas especificados por restrições adapta-se particularmente bem a
ser paralelizado.
Este tese apresenta uma abordagem _à resolução paralela de restrições, que junta
paralelismo local, sob a forma de trabalhadores, com paralelismo distribuído, em que os
actores são as equipas. O sistema construído, destinado a sistemas distribuídos de larga
escala, que _é descrito e os seus resultados apresentados, inclui distribuição de trabalho,
através de roubo de trabalho. Este funciona, localmente, sem a colaboração do roubado
e, remotamente, com colaboração, num ambiente em que todas as equipas cooperam na
procura da solução
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