37,638 research outputs found
Space-Efficient Parallel Algorithms for Combinatorial Search Problems
We present space-efficient parallel strategies for two fundamental
combinatorial search problems, namely, backtrack search and branch-and-bound,
both involving the visit of an -node tree of height under the assumption
that a node can be accessed only through its father or its children. For both
problems we propose efficient algorithms that run on a -processor
distributed-memory machine. For backtrack search, we give a deterministic
algorithm running in time, and a Las Vegas algorithm requiring
optimal time, with high probability. Building on the backtrack
search algorithm, we also derive a Las Vegas algorithm for branch-and-bound
which runs in time, with high probability. A
remarkable feature of our algorithms is the use of only constant space per
processor, which constitutes a significant improvement upon previous algorithms
whose space requirements per processor depend on the (possibly huge) tree to be
explored.Comment: Extended version of the paper in the Proc. of 38th International
Symposium on Mathematical Foundations of Computer Science (MFCS
Using genetic algorithms to solve combinatorial optimization problems
Genetic algorithms are stochastic search techniques based on the mechanics of natural selection and natural genetics. Genetic algorithms differ from traditional analytical methods by using genetic operators and historic cumulative information to prune the search space and generate plausible solutions. Recent research has shown that genetic algorithms have a large range and growing number of applications.
The research presented in this thesis is that of using genetic algorithms to solve some typical combinatorial optimization problems, namely the Clique, Vertex Cover and Max Cut problems. All of these are NP-Complete problems. The empirical results show that genetic algorithms can provide efficient search heuristics for solving these combinatorial optimization problems.
Genetic algorithms are inherently parallel. The Connection Machine system makes parallel implementation of these inherently parallel algorithms possible. Both sequential genetic algorithms and parallel genetic algorithms for Clique, Vertex Cover and Max Cut problems have been developed and implemented on the SUN4 and the Connection Machine systems respectively
A GPU-accelerated Branch-and-Bound Algorithm for the Flow-Shop Scheduling Problem
Branch-and-Bound (B&B) algorithms are time intensive tree-based exploration
methods for solving to optimality combinatorial optimization problems. In this
paper, we investigate the use of GPU computing as a major complementary way to
speed up those methods. The focus is put on the bounding mechanism of B&B
algorithms, which is the most time consuming part of their exploration process.
We propose a parallel B&B algorithm based on a GPU-accelerated bounding model.
The proposed approach concentrate on optimizing data access management to
further improve the performance of the bounding mechanism which uses large and
intermediate data sets that do not completely fit in GPU memory. Extensive
experiments of the contribution have been carried out on well known FSP
benchmarks using an Nvidia Tesla C2050 GPU card. We compared the obtained
performances to a single and a multithreaded CPU-based execution. Accelerations
up to x100 are achieved for large problem instances
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Combinatorial optimization and metaheuristics
Today, combinatorial optimization is one of the youngest and most active areas of discrete mathematics. It is a branch of optimization in applied mathematics and computer science, related to operational research, algorithm theory and computational complexity theory. It sits at the intersection of several fields, including artificial intelligence, mathematics and software engineering. Its increasing interest arises for the fact that a large number of scientific and industrial problems can be formulated as abstract combinatorial optimization problems, through graphs and/or (integer) linear programs. Some of these problems have polynomial-time (“efficient”) algorithms, while most of them are NP-hard, i.e. it is not proved that they can be solved in polynomial-time. Mainly, it means that it is not possible to guarantee that an exact solution to the problem can be found and one has to settle for an approximate solution with known performance guarantees. Indeed, the goal of approximate methods is to find “quickly” (reasonable run-times), with “high” probability, provable “good” solutions (low error from the real optimal solution). In the last 20 years, a new kind of algorithm commonly called metaheuristics have emerged in this class, which basically try to combine heuristics in high level frameworks aimed at efficiently and effectively exploring the search space. This report briefly outlines the components, concepts, advantages and disadvantages of different metaheuristic approaches from a conceptual point of view, in order to analyze their similarities and differences. The two very significant forces of intensification and diversification, that mainly determine the behavior of a metaheuristic, will be pointed out. The report concludes by exploring the importance of hybridization and integration methods
Parallel local search for solving Constraint Problems on the Cell Broadband Engine (Preliminary Results)
We explore the use of the Cell Broadband Engine (Cell/BE for short) for
combinatorial optimization applications: we present a parallel version of a
constraint-based local search algorithm that has been implemented on a
multiprocessor BladeCenter machine with twin Cell/BE processors (total of 16
SPUs per blade). This algorithm was chosen because it fits very well the
Cell/BE architecture and requires neither shared memory nor communication
between processors, while retaining a compact memory footprint. We study the
performance on several large optimization benchmarks and show that this
achieves mostly linear time speedups, even sometimes super-linear. This is
possible because the parallel implementation might explore simultaneously
different parts of the search space and therefore converge faster towards the
best sub-space and thus towards a solution. Besides getting speedups, the
resulting times exhibit a much smaller variance, which benefits applications
where a timely reply is critical
An ADMM Based Framework for AutoML Pipeline Configuration
We study the AutoML problem of automatically configuring machine learning
pipelines by jointly selecting algorithms and their appropriate
hyper-parameters for all steps in supervised learning pipelines. This black-box
(gradient-free) optimization with mixed integer & continuous variables is a
challenging problem. We propose a novel AutoML scheme by leveraging the
alternating direction method of multipliers (ADMM). The proposed framework is
able to (i) decompose the optimization problem into easier sub-problems that
have a reduced number of variables and circumvent the challenge of mixed
variable categories, and (ii) incorporate black-box constraints along-side the
black-box optimization objective. We empirically evaluate the flexibility (in
utilizing existing AutoML techniques), effectiveness (against open source
AutoML toolkits),and unique capability (of executing AutoML with practically
motivated black-box constraints) of our proposed scheme on a collection of
binary classification data sets from UCI ML& OpenML repositories. We observe
that on an average our framework provides significant gains in comparison to
other AutoML frameworks (Auto-sklearn & TPOT), highlighting the practical
advantages of this framework
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