Quadratic Assignment Problems

Burkard, Rainer E.

doi:10.1007/978-1-4419-7997-1_22

Cited by 41 publications

(9 citation statements)

References 164 publications

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“…Many outstanding NP-hard problems like LAP (Linear Arrangement Problem), MCP (Maximum Clique Problem) and TSP (Travelling Salesman Problem) are just particular QAP instances [3]. In fact:…”

Section: Combinatorial Optimization Problems Formulated As Qapsmentioning

confidence: 99%

Combinatorial optimization np-hard problem solved by using the quadratic assignment problem (QAP) solution through a parallel genetic algorithm on GPU

Gómez¹,

Chaves²,

Hurtado³

2018

Vis. Electron.

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In this article, some instances of well known combinatorial optimization NP-Hard problems are solved by using Koopmans and Beckmann formulation of the quadratic assignment problem (QAP). These instances are solved by using an Embarrassingly Parallel Genetic Algorithm or by using an Island Parallel Genetic Algorithm; in both cases, the implementation is carried out on Graphics Processing Units (GPUs).

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“…Many outstanding NP-hard problems like LAP (Linear Arrangement Problem), MCP (Maximum Clique Problem) and TSP (Travelling Salesman Problem) are just particular QAP instances [3]. In fact:…”

Section: Combinatorial Optimization Problems Formulated As Qapsmentioning

confidence: 99%

Combinatorial optimization np-hard problem solved by using the quadratic assignment problem (QAP) solution through a parallel genetic algorithm on GPU

Gómez¹,

Chaves²,

Hurtado³

2018

Vis. Electron.

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“…In general, instances with n > 30 are difficult to solve by exact methods in reasonable time [1,5]. This fact has motivated the use of the problem as a benchmark to test solution methodologies.…”

Section: Introductionmentioning

confidence: 99%

ASIMD tabu searchimplementation for solving the quadratic assignment problem with GPU acceleration

Novoa¹,

Qasem²,

Chaparala³

2015

Proceedings of the 2015 XSEDE Conference on Scientific Advancements Enabled by Enhanced Cyberinfrastructure - XSEDE '15

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In the Quadratic Assignment Problem (QAP), n units (usually departments , machines, or electronic components) must be assigned to n locations given the distance between the locations and the flow between the units. The goal is to find the assignment that minimizes the sum of the products of distance traveled and flow between units. The QAP is a combinatorial problem difficult to solve to optimality even for problems where n is relatively small (e.g., n = 30). In this paper, we develop a parallel tabu search algorithm to solve the QAP and leverage the compute capabilities of current GPUs. The single instruction multiple data (SIMD) algorithm is implemented on the Stampede cluster hosted by the Texas Advanced Computing Center (TACC) at the University of Texas at Austin. We enhance our implementation by exploiting the dynamic parallelism made available in the Nvidia Kepler high performance computing architecture. On a series of experiments on the well-known QAPLIB data sets, our algorithm produces solutions that are as good as the best known ones posted in QAPLIB. The worst case percentage of accuracy we obtained was 0.83%. Given the applicability of QAP, our algorithm has very good potential to accelerate scholarly research in Engineering, in the fields of Operations Research and design of electronic devices. To the best of our knowledge, this work is the first to successfully parallelize the tabu search metaheuristic to solve the QAP with the recency-based feature, implemented serially in [10]. Our work is also the first to exploit GPU dynamic parallelism in a tabu search metaheuristic to solve the QAP.

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“…Related Work. Permutation optimization is a long standing problem arising in operations research, graph matching among other applications [3,8]. Well-known examples are linear and quadratic assignment problems [18].…”

Section: Introductionmentioning

confidence: 99%

AutoShuffleNet: Learning Permutation Matrices via an Exact Lipschitz Continuous Penalty in Deep Convolutional Neural Networks

Lyu

Zhang

et al. 2020

Proceedings of the 26th ACM SIGKDD International Conference on Knowledge Discovery &Amp; Data Mining

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ShuffleNet is a state-of-the-art light weight convolutional neural network architecture. Its basic operations include group, channelwise convolution and channel shuffling. However, channel shuffling is manually designed on empirical grounds. Mathematically, shuffling is a multiplication by a permutation matrix. In this paper, we propose to automate channel shuffling by learning permutation matrices in network training. We introduce an exact Lipschitz continuous non-convex penalty so that it can be incorporated in the stochastic gradient descent to approximate permutation at high precision. Exact permutations are obtained by simple rounding at the end of training and are used in inference. The resulting network, referred to as AutoShuffleNet, achieved improved classification accuracies on data from CIFAR-10, CIFAR-100 and ImageNet while preserving the inference costs of ShuffleNet. In addition, we found experimentally that the standard convex relaxation of permutation matrices into stochastic matrices leads to poor performance. We prove theoretically the exactness (error bounds) in recovering permutation matrices when our penalty function is zero (very small). We present examples of permutation optimization through graph matching and two-layer neural network models where the loss functions are calculated in closed analytical form. In the examples, convex relaxation failed to capture permutations whereas our penalty succeeded.

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Quadratic Assignment Problems

Cited by 41 publications

References 164 publications

Combinatorial optimization np-hard problem solved by using the quadratic assignment problem (QAP) solution through a parallel genetic algorithm on GPU

Combinatorial optimization np-hard problem solved by using the quadratic assignment problem (QAP) solution through a parallel genetic algorithm on GPU

ASIMD tabu searchimplementation for solving the quadratic assignment problem with GPU acceleration

AutoShuffleNet: Learning Permutation Matrices via an Exact Lipschitz Continuous Penalty in Deep Convolutional Neural Networks

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