Addressing the envelope reduction of sparse matrices using a genetic programming system
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- @Article{Koohestani:2014:COA,
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author = "Behrooz Koohestani and Riccardo Poli",
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title = "Addressing the envelope reduction of sparse matrices
using a genetic programming system",
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journal = "Computational Optimization and Applications",
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year = "2015",
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volume = "60",
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number = "3",
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pages = "789--814",
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month = apr,
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keywords = "genetic algorithms, genetic programming, Envelope
reduction problem, Sparse matrices, Graph labelling,
Combinatorial optimisation",
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ISSN = "0926-6003",
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publisher = "Springer US",
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URL = "http://link.springer.com/article/10.1007/s10589-014-9688-2",
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URL = "http://dx.doi.org/10.1007/s10589-014-9688-2",
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DOI = "doi:10.1007/s10589-014-9688-2",
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size = "26 pages",
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abstract = "Large sparse symmetric matrix problems arise in a
number of scientific and engineering fields such as
fluid mechanics, structural engineering, finite element
analysis and network analysis. In all such problems,
the performance of solvers depends critically on the
sum of the row bandwidths of the matrix, a quantity
known as envelope size. This can be reduced by
appropriately reordering the rows and columns of the
matrix, but for an N by N matrix, there are N! such
permutations, and it is difficult to predict how each
permutation affects the envelope size without actually
performing the reordering of rows and columns. These
two facts compounded with the large values of N used in
practical applications, make the problem of minimising
the envelope size of a matrix an exceptionally hard
one. Several methods have been developed to reduce the
envelope size. These methods are mainly heuristic in
nature and based on graph-theoretic concepts. While
metaheuristic approaches are popular alternatives to
classical optimisation techniques in a variety of
domains, in the case of the envelope reduction problem,
there has been a very limited exploration of such
methods. In this paper, a Genetic Programming system
capable of reducing the envelope size of sparse
matrices is presented and evaluated against four of the
best-known and broadly used envelope reduction
algorithms. The results obtained on a wide-ranging set
of standard benchmarks from the Harwell-Boeing sparse
matrix collection show that the proposed method
compares very favourably with these algorithms.",
- }
Genetic Programming entries for
Behrooz Koohestani
Riccardo Poli
Citations