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 ba...

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Vydáno v:Computational optimization and applications Ročník 62; číslo 2; s. 565 - 588
Hlavní autoři: Gago-Vargas, J., Hartillo, I., Puerto, J., Ucha, J. M.
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York Springer US 01.11.2015
Springer Nature B.V
Témata:
Algorithms
Computation
Convex and Discrete Geometry
Costs
Design engineering
Engineering
Engineering design
Integer programming
Integers
Linear programming
Management Science
Mathematical analysis
Mathematical models
Mathematics
Mathematics and Statistics
Nonlinearity
Operations Research
Operations Research/Decision Theory
Optimization
Optimization techniques
Statistics
Studies
Test sets
Non-linear integer programming
Gröbner basis
Test set
Chance constrained programming
ISSN:0926-6003, 1573-2894
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Popis
Shrnutí: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 optimality.
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ISSN:0926-6003
1573-2894
DOI:10.1007/s10589-015-9739-3