Approximate solution of mp-MILP problems using piecewise affine relaxation of bilinear terms

•A two-stage method for multi-parametric mixed integer linear programming problems is proposed.•Sub-optimal solutions are computed.•Overestimators of bilinear terms over an ab initio partitioning of the domain are employed.•Linear and logarithmic partitioning scheme based approximate models are stud...

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Bibliographic Details
Published in:Computers & chemical engineering Vol. 61; pp. 136 - 155
Main Authors: Wittmann-Hohlbein, Martina, Pistikopoulos, Efstratios N.
Format: Journal Article
Language:English
Published: Kidlington Elsevier Ltd 11.02.2014
Elsevier
Subjects:
Applied sciences
Bilinear programming
Exact sciences and technology
Mathematical programming
Mathematics
Mixed-integer programming
Multi-parametric programming
Operational research and scientific management
Operational research. Management science
Parametric inference
Probability and statistics
Sciences and techniques of general use
Statistics
Multi-parametric programming
Mixed-integer programming
Bilinear programming
Partition
Bilinear system
Conservatism
Logarithmic function
Parametric programming
Algorithmics
Mixed integer programming
Modeling
Linear model
Partitioning
Relaxation method
Metamodel
Piecewise linearization
ISSN:0098-1354, 1873-4375
Online Access:Get full text
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Summary:•A two-stage method for multi-parametric mixed integer linear programming problems is proposed.•Sub-optimal solutions are computed.•Overestimators of bilinear terms over an ab initio partitioning of the domain are employed.•Linear and logarithmic partitioning scheme based approximate models are studied.•Approximate models are tunable by the number of partitions. We propose an approximate solution strategy for multi-parametric mixed integer linear programming (mp-MILP) problems with parameter dependency at multiple locations in the model. A two-stage solution strategy, consisting of an approximation stage and a multi-parametric programming stage, is introduced. At the approximation stage, surrogate mp-MILP models are derived by overestimating bilinear terms in the constraints over an ab initio partitioning of the domain. We then incorporate piecewise affine relaxation based models using a linear partitioning scheme and a logarithmic partitioning scheme, respectively. The models are tuned by the number of partitions chosen. Problem sizes of the varied models, and computational requirements for the algorithmic procedure are compared. The conservatism of the suboptimal solution of the mp-MILP problem for the piecewise affine relaxation based two-stage method is discussed.
ISSN:0098-1354
1873-4375
DOI:10.1016/j.compchemeng.2013.10.009