5,410 research outputs found
Exact cost minimization of a series-parallel reliable system with multiple component choices using an algebraic method
The redundancy allocation problem is formulated minimizing the design cost for a series-parallel system with multiple component choices while ensuring a given system reliability level. The obtained model is a nonlinear integer programming problem with a nonlinear, nonseparable constraint. We propose a method based on the construction of a test set of an integer linear problem, which allows us to obtain an exact solution of the problem. It is compared to other approaches in the literature and standard nonlinear solvers.FQM-5849, MTM2010-19336, MTM2010-19576 and FEDE
Finding Multiple Solutions in Nonlinear Integer Programming with Algebraic Test-Sets
We explain how to compute all the solutions of a nonlinear
integer problem using the algebraic test-sets associated to a suitable
linear subproblem. These test-sets are obtained using Gröbner bases. The
main advantage of this method, compared to other available alternatives,
is its exactness within a quite good efficiency.Ministerio de Economía y Competitividad MTM2016-75024-PMinisterio de Economía y Competitividad MTM2016-74983-C2- 1-RJunta de Andalucía P12-FQM-269
An improved test set approach to nonlinear integer problems with applications to engineering design
Many problems in engineering design involve the use of nonlinearities
and some integer variables. Methods based on test sets have been
proposed to solve some particular problems with integer variables, but they
have not been frequently applied because of computation costs. The walk-back
procedure based on a test set gives an exact method to obtain an optimal point
of an integer programming problem with linear and nonlinear constraints, but
the calculation of this test set and the identification of an optimal solution
using the test set directions are usually computationally intensive.
In problems for which obtaining the test set is reasonably fast, we show
how the effectiveness can still be substantially improved. This methodology
is presented in its full generality and illustrated on two specific problems: (1)
minimizing cost in the problem of scheduling jobs on parallel machines given
restrictions on demands and capacity, and (2) minimizing cost in the series
parallel redundancy allocation problem, given a target reliability. Our computational
results are promising and suggest the applicability of this approach
to deal with other problems with similar characteristics or to combine it with
mainstream solvers to certify optimalityJunta de Andalucía FQM- 5849Ministerio de Ciencia e Innovación MTM2010-19336Ministerio de Ciencia e Innovación MTM2010-19576Ministerio de Ciencia e Innovación MTM2013-46962- C2-1-PFEDE
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