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Solving the Quadratic Assignment Problem on heterogeneous environment (CPUs and GPUs) with the application of Level 2 Reformulation and Linearization Technique

Alexandre Domingues Goncalves, Artur Alves Pessoa, Lucia Maria de Assumpcao Drummond, Cristiana Bentes, Ricardo Farias
Campus Sao Goncalo, Instituto Federal do Rio de Janeiro, IFRJ
arXiv:1510.02065 [cs.DC], (7 Oct 2015)

@article{goncalves2015solving,

   title={Solving the Quadratic Assignment Problem on heterogeneous environment (CPUs and GPUs) with the application of Level 2 Reformulation and Linearization Technique},

   author={Goncalves, Alexandre Domingues and Pessoa, Artur Alves and Drummond, Lucia Maria de Assumpcao and Bentes, Cristiana and Farias, Ricardo},

   year={2015},

   month={oct},

   archivePrefix={"arXiv"},

   primaryClass={cs.DC}

}

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The Quadratic Assignment Problem, QAP, is a classic combinatorial optimization problem, classified as NP-hard and widely studied. This problem consists in assigning N facilities to N locations obeying the relation of 1 to 1, aiming to minimize costs of the displacement between the facilities. The application of Reformulation and Linearization Technique, RLT, to the QAP leads to a tight linear relaxation but large and difficult to solve. Previous works based on level 3 RLT needed about 700GB of working memory to process one large instances (N = 30 facilities). We present a modified version of the algorithm proposed by Adams et al. which executes on heterogeneous systems (CPUs and GPUs), based on level 2 RLT. For some instances, our algorithm is up to 140 times faster and occupy 97% less memory than the level 3 RLT version. The proposed algorithm was able to solve by first time two instances: tai35b and tai40b.
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