570 research outputs found
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
A new algebraic geometry algorithm for integer programming
"June 1998"--T.p. -- "March 1998"--Cover.Includes bibliographical references (leaf 21).by D. Bertsimas, G. Perakis, S. Tayur
An algebraic approach to Integer Portfolio problems
Integer variables allow the treatment of some portfolio optimization problems in a more realistic way and introduce the possibility of adding some natural features to the model.
We propose an algebraic approach to maximize the expected return under a given admissible level of risk measured by the covariance matrix. To reach an optimal portfolio it is an essential ingredient the computation of different test sets (via Gr\"obner basis) of linear subproblems that are used in a dual search strategy.Universidad de Sevilla P06-FQM-01366Junta de Andalucía (Plan Andaluz de Investigación) FQM-333Ministerio de Ciencia e Innovación (España) MTM2007-64509Instituto de Matemáticas de la Universidad de Sevilla MTM2007-67433-C02-0
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