Enhanced linear reformulation for engineering optimization models with discrete and bounded continuous variables

•Establish a new linearization method for treating general nonlinear discrete terms.•Extend ELDP to handle representable programming problems with engineering application.•Reduce a half order of linear equations in ELDP reformulation for fast computation.•Conduct numerical tests to highlight power o...

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Bibliographic Details
Published in:Applied Mathematical Modelling 2018-06, Vol.58, p.140-157
Main Authors: An, Qi, Fang, Shu-Cherng, Li, Han-Lin, Nie, Tiantian
Format: Article
Language:English
Subjects:
Computing time
Continuity (mathematics)
Design engineering
Discrete element method
Linear reformulation
Linearization
Mathematical models
Mathematical programming
Nonlinear discrete optimization
Nonlinear equations
Optimization
Optimization models
Polynomial programming
Polynomials
Signomial programming
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Summary:•Establish a new linearization method for treating general nonlinear discrete terms.•Extend ELDP to handle representable programming problems with engineering application.•Reduce a half order of linear equations in ELDP reformulation for fast computation.•Conduct numerical tests to highlight power of treating large-size engineering problem. In this paper, we significantly extend the applicability of state-of-the-art ELDP (equations for linearizing discrete product terms) method by providing a new linearization to handle more complicated non-linear terms involving both of discrete and bounded continuous variables. A general class of “representable programming problems” is formally proposed for a much wider range of engineering applications. Moreover, by exploiting the logarithmic feature embedded in the discrete structure, we present an enhanced linear reformulation model which requires half an order fewer equations than the original ELDP. Computational experiments on various engineering design problems support the superior computational efficiency of the proposed linearization reformulation in solving engineering optimization problems with discrete and bounded continuous variables.
ISSN:0307-904X
1088-8691
0307-904X
DOI:10.1016/j.apm.2017.09.047