97 research outputs found

    High-Quality Hypergraph Partitioning

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    This dissertation focuses on computing high-quality solutions for the NP-hard balanced hypergraph partitioning problem: Given a hypergraph and an integer kk, partition its vertex set into kk disjoint blocks of bounded size, while minimizing an objective function over the hyperedges. Here, we consider the two most commonly used objectives: the cut-net metric and the connectivity metric. Since the problem is computationally intractable, heuristics are used in practice - the most prominent being the three-phase multi-level paradigm: During coarsening, the hypergraph is successively contracted to obtain a hierarchy of smaller instances. After applying an initial partitioning algorithm to the smallest hypergraph, contraction is undone and, at each level, refinement algorithms try to improve the current solution. With this work, we give a brief overview of the field and present several algorithmic improvements to the multi-level paradigm. Instead of using a logarithmic number of levels like traditional algorithms, we present two coarsening algorithms that create a hierarchy of (nearly) nn levels, where nn is the number of vertices. This makes consecutive levels as similar as possible and provides many opportunities for refinement algorithms to improve the partition. This approach is made feasible in practice by tailoring all algorithms and data structures to the nn-level paradigm, and developing lazy-evaluation techniques, caching mechanisms and early stopping criteria to speed up the partitioning process. Furthermore, we propose a sparsification algorithm based on locality-sensitive hashing that improves the running time for hypergraphs with large hyperedges, and show that incorporating global information about the community structure into the coarsening process improves quality. Moreover, we present a portfolio-based initial partitioning approach, and propose three refinement algorithms. Two are based on the Fiduccia-Mattheyses (FM) heuristic, but perform a highly localized search at each level. While one is designed for two-way partitioning, the other is the first FM-style algorithm that can be efficiently employed in the multi-level setting to directly improve kk-way partitions. The third algorithm uses max-flow computations on pairs of blocks to refine kk-way partitions. Finally, we present the first memetic multi-level hypergraph partitioning algorithm for an extensive exploration of the global solution space. All contributions are made available through our open-source framework KaHyPar. In a comprehensive experimental study, we compare KaHyPar with hMETIS, PaToH, Mondriaan, Zoltan-AlgD, and HYPE on a wide range of hypergraphs from several application areas. Our results indicate that KaHyPar, already without the memetic component, computes better solutions than all competing algorithms for both the cut-net and the connectivity metric, while being faster than Zoltan-AlgD and equally fast as hMETIS. Moreover, KaHyPar compares favorably with the current best graph partitioning system KaFFPa - both in terms of solution quality and running time

    VLSI Design

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    This book provides some recent advances in design nanometer VLSI chips. The selected topics try to present some open problems and challenges with important topics ranging from design tools, new post-silicon devices, GPU-based parallel computing, emerging 3D integration, and antenna design. The book consists of two parts, with chapters such as: VLSI design for multi-sensor smart systems on a chip, Three-dimensional integrated circuits design for thousand-core processors, Parallel symbolic analysis of large analog circuits on GPU platforms, Algorithms for CAD tools VLSI design, A multilevel memetic algorithm for large SAT-encoded problems, etc

    On the Computational Cost and Complexity of Stochastic Inverse Solvers

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    The goal of this paper is to provide a starting point for investigations into a mainly underdeveloped area of research regarding the computational cost analysis of complex stochastic strategies for solving parametric inverse problems. This area has two main components: solving global optimization problems and solving forward problems (to evaluate the misfit function that we try to minimize). For the first component, we pay particular attention to genetic algorithms with heuristics and to multi-deme algorithms that can be modeled as ergodic Markov chains. We recall a simple method for evaluating the first hitting time for the single-deme algorithm and we extend it to the case of HGS, a multi-deme hierarchic strategy. We focus on the case in which at least the demes in the leaves are well tuned. Finally, we also express the problems of finding local and global optima in terms of a classic complexity theory. We formulate the natural result that finding a local optimum of a function is an NP-complete task, and we argue that finding a global optimum is a much harder, DP-complete, task. Furthermore, we argue that finding all global optima is, possibly, even harder (#P-hard) task. Regarding the second component of solving parametric inverse problems (i.e., regarding the forward problem solvers), we discuss the computational cost of hp-adaptive Finite Element solvers and their rates of convergence with respect to the increasing number of degrees of freedom. The presented results provide a useful taxonomy of problems and methods of studying the computational cost and complexity of various strategies for solving inverse parametric problems. Yet, we stress that our goal was not to deliver detailed evaluations for particular algorithms applied to particular inverse problems, but rather to try to identify possible ways of obtaining such results

    Advances in Evolutionary Algorithms

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    With the recent trends towards massive data sets and significant computational power, combined with evolutionary algorithmic advances evolutionary computation is becoming much more relevant to practice. Aim of the book is to present recent improvements, innovative ideas and concepts in a part of a huge EA field

    A hybrid genetic pattern search augmented Lagrangian method for constrained global optimization

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    Hybridization of genetic algorithms with local search approaches can enhance their performance in global optimization. Genetic algorithms, as most population based algorithms, require a considerable number of function evaluations. This may be an important drawback when the functions involved in the problem are computationally expensive as it occurs in most real world problems. Thus, in order to reduce the total number of function evaluations, local and global techniques may be combined. Moreover, the hybridization may provide a more effective trade-off between exploitation and exploration of the search space. In this study, we propose a new hybrid genetic algorithm based on a local pattern search that relies on an augmented Lagrangian function for constraint-handling. The local search strategy is used to improve the best approximation found by the genetic algorithm. Convergence to an ε\varepsilon-global minimizer is proved. Numerical results and comparisons with other stochastic algorithms using a set of benchmark constrained problems are provided.FEDER COMPETEFundação para a Ciência e a Tecnologia (FCT

    Crossover control in selection hyper-heuristics: case studies using MKP and HyFlex

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    Hyper-heuristics are a class of high-level search methodologies which operate over a search space of heuristics rather than a search space of solutions. Hyper-heuristic research has set out to develop methods which are more general than traditional search and optimisation techniques. In recent years, focus has shifted considerably towards cross-domain heuristic search. The intention is to develop methods which are able to deliver an acceptable level of performance over a variety of different problem domains, given a set of low-level heuristics to work with. This thesis presents a body of work investigating the use of selection hyper-heuristics in a number of different problem domains. Specifically the use of crossover operators, prevalent in many evolutionary algorithms, is explored within the context of single-point search hyper-heuristics. A number of traditional selection hyper-heuristics are applied to instances of a well-known NP-hard combinatorial optimisation problem, the multidimensional knapsack problem. This domain is chosen as a benchmark for the variety of existing problem instances and solution methods available. The results suggest that selection hyper-heuristics are a viable method to solve some instances of this problem domain. Following this, a framework is defined to describe the conceptual level at which crossover low-level heuristics are managed in single-point selection hyper-heuristics. HyFlex is an existing software framework which supports the design of heuristic search methods over multiple problem domains, i.e. cross-domain optimisation. A traditional heuristic selection mechanism is modified in order to improve results in the context of cross-domain optimisation. Finally the effect of crossover use in cross-domain optimisation is explored

    A review of population-based metaheuristics for large-scale black-box global optimization: Part A

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    Scalability of optimization algorithms is a major challenge in coping with the ever growing size of optimization problems in a wide range of application areas from high-dimensional machine learning to complex large-scale engineering problems. The field of large-scale global optimization is concerned with improving the scalability of global optimization algorithms, particularly population-based metaheuristics. Such metaheuristics have been successfully applied to continuous, discrete, or combinatorial problems ranging from several thousand dimensions to billions of decision variables. In this two-part survey, we review recent studies in the field of large-scale black-box global optimization to help researchers and practitioners gain a bird’s-eye view of the field, learn about its major trends, and the state-of-the-art algorithms. Part of the series covers two major algorithmic approaches to large-scale global optimization: problem decomposition and memetic algorithms. Part of the series covers a range of other algorithmic approaches to large-scale global optimization, describes a wide range of problem areas, and finally touches upon the pitfalls and challenges of current research and identifies several potential areas for future research

    Crossover control in selection hyper-heuristics: case studies using MKP and HyFlex

    Get PDF
    Hyper-heuristics are a class of high-level search methodologies which operate over a search space of heuristics rather than a search space of solutions. Hyper-heuristic research has set out to develop methods which are more general than traditional search and optimisation techniques. In recent years, focus has shifted considerably towards cross-domain heuristic search. The intention is to develop methods which are able to deliver an acceptable level of performance over a variety of different problem domains, given a set of low-level heuristics to work with. This thesis presents a body of work investigating the use of selection hyper-heuristics in a number of different problem domains. Specifically the use of crossover operators, prevalent in many evolutionary algorithms, is explored within the context of single-point search hyper-heuristics. A number of traditional selection hyper-heuristics are applied to instances of a well-known NP-hard combinatorial optimisation problem, the multidimensional knapsack problem. This domain is chosen as a benchmark for the variety of existing problem instances and solution methods available. The results suggest that selection hyper-heuristics are a viable method to solve some instances of this problem domain. Following this, a framework is defined to describe the conceptual level at which crossover low-level heuristics are managed in single-point selection hyper-heuristics. HyFlex is an existing software framework which supports the design of heuristic search methods over multiple problem domains, i.e. cross-domain optimisation. A traditional heuristic selection mechanism is modified in order to improve results in the context of cross-domain optimisation. Finally the effect of crossover use in cross-domain optimisation is explored
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