In this paper selection of fast algorithm portfolios for 2SP packing problem is considered. The 2SP problem consists in placing rectangles on a strip of the given width for minimum strip length. The 2SP packing has ap...
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In this paper selection of fast algorithm portfolios for 2SP packing problem is considered. The 2SP problem consists in placing rectangles on a strip of the given width for minimum strip length. The 2SP packing has application in many industries, but suitability of the related algorithms is limited by their runtimes. While solving combinatorial optimization problems, longer runtimes increase chances of obtaining higher quality solutions. This means that runtime vs solution quality trade-off is important in solving problems such as strip packing. Given some limited runtime, a method is needed to provide the best solution possible. However, a single algorithm outperforming all other methods under all possible conditions usually does not exist. Therefore, algorithm portfolios can reliably provide high quality solutions in the limited runtime. We propose a method choosing algorithm portfolios on the basis of the algorithm performance on a set of training instances. A portfolio covers the instances with the best solutions which could be obtained in the given runtime, subject to the minimum computational cost of the selected algorithms. The portfolios are evaluated in extensive experiments carried out on designed and literature datasets. We demonstrate that our method is capable of carrying over solution quality from the training datasets to the testing datasets. In other words, our algorithmselection method can learn from the training instances. We also compare performance of our portfolio selection method with some other more straightforward approaches to the portfolio selection.
The choice of which objective functions, or benchmark problems, should be used to test an optimization algorithm is a crucial part of the algorithmselection framework. Benchmark suites that are often used in the lite...
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The choice of which objective functions, or benchmark problems, should be used to test an optimization algorithm is a crucial part of the algorithmselection framework. Benchmark suites that are often used in the literature have been shown to exhibit poor coverage of the problem space. Exploratory landscape analysis can be used to quantify characteristics of objective functions. However, exploratory landscape analysis measures are based on samples of the objective function, and there is a lack of work on the appropriate choice of sample size needed to produce reliable measures. This study presents an approach to determine the minimum sample size needed to obtain robust exploratory landscape analysis measures. Based on reliable exploratory landscape analysis measures, a self-organizing feature map is used to cluster a comprehensive set of benchmark functions. From this, a benchmark suite that has better coverage of the single-objective, boundary-constrained problem space is proposed.
In online three-dimensional packing problems (3D-PPs), unlike offline problems, items arrive sequentially and require immediate packing decisions without any information about the quantities and sizes of the items to ...
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In online three-dimensional packing problems (3D-PPs), unlike offline problems, items arrive sequentially and require immediate packing decisions without any information about the quantities and sizes of the items to come. Heuristic methods are of great importance in solving online problems to find good solutions in a reasonable amount of time. However, the literature on heuristics for online problems is sparse. As our first contribution, we developed a pool of heuristics applicable to online 3D-PPs with complementary performance on different sets of instances. Computational results showed that in terms of the number of used bins, in all problem instances, at least one of our heuristics had a better or equal performance compared to existing heuristics in the literature. The developed heuristics are also fully applicable to an intermediate class between offline and online problems, referred to in this paper as a specific type of "semi-online with full look-ahead", which has several practical applications. In this class, as in offline problems, complete information about all items is known in advance (i.e., full look-ahead);however, due to time or space constraints, as in online problems, items should be packed immediately in the order of their arrival. As our second contribution, we presented an algorithmselection framework, building on developed heuristics and utilizing prior information about items in this specific class of problems. We used supervised machine learning techniques to find the relationship between the features of problem instances and the performance of heuristics and to build a prediction model. The results indicate an 88% accuracy in predicting (identifying) the most promising heuristic(s) for solving any new instance from this class of problems.
Many scientific applications consist of large and computationally intensive loops. Dynamic loop self-scheduling (DLS) techniques are used to parallelize and to balance the load of such applications during execution. L...
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Many scientific applications consist of large and computationally intensive loops. Dynamic loop self-scheduling (DLS) techniques are used to parallelize and to balance the load of such applications during execution. Load imbalance arises from variations in the loop iteration (or tasks) execution times, caused by problem, algorithmic, or systemic characteristics. Variations in systemic characteristics are referred to as perturbations. Our hypothesis is that no single DLS technique can achieve the absolute best performance under various perturbations on heterogeneous high-performance computing (HPC) systems. Therefore, the selection of the most efficient DLS technique is critical to achieve the best application performance. The goal of this work is to solve the algorithm selection problem for the scheduling of computationally intensive applications under perturbations. Existing work only considers perturbations caused by variations in the delivered computational speed of the HPC systems. However, perturbations in available network bandwidth or latency are inevitable on production HPC systems. A simulation-assisted scheduling algorithmselection (SimAS) approach is introduced herein as a novel control-theoretic-inspired approach to select DLS techniques dynamically that improve the performance of applications executing on heterogeneous HPC systems under perturbations. The present work examines the performance of seven applications on a heterogeneous HPC system under all the above system perturbations. SimAS is evaluated using native and simulative experiments. The performance results confirm the original hypothesis that motivates this work. The experimental evaluation shows that the SimAS-based DLS selection identifies the most efficient technique and improves application performance in most cases.
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