Adaptive piecewise linear relaxations for enclosure computations for nonconvex multiobjective mixed-integer quadratically constrained programs

In this paper, a new method for computing an enclosure of the nondominated set of multiobjective mixed-integer quadratically constrained programs without any convexity requirements is presented. In fact, our criterion space method makes use of piecewise linear relaxations in order to bypass the nonc...

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Bibliographic Details
Published in:Journal of global optimization Vol. 87; no. 1; pp. 97 - 132
Main Authors: Link, Moritz, Volkwein, Stefan
Format: Journal Article
Language:English
Published: New York, NY Springer US 01.09.2023
Springer Nature B.V
Subjects:
Adaptive piecewise linear relaxation
Approximation
Box enclosure
Computer Science
Convexity
Enclosures
Energy supply networks
Linear programming
Mathematics
Mathematics and Statistics
Mixed integer
Mixed-integer nonlinear programming
Multiobjective optimization
Network management systems
Operations Research/Decision Theory
Optimization
Real Functions
Variables
Adaptive piecewise linear relaxation
65K05
Mixed-integer nonlinear programming
90C35
Multiobjective optimization
Energy supply networks
90C11
90C29
Box enclosure
90C26
ISSN:1573-2916, 0925-5001, 1573-2916
Online Access:Get full text
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Summary:In this paper, a new method for computing an enclosure of the nondominated set of multiobjective mixed-integer quadratically constrained programs without any convexity requirements is presented. In fact, our criterion space method makes use of piecewise linear relaxations in order to bypass the nonconvexity of the original problem. The method chooses adaptively which level of relaxation is needed in which parts of the image space. Furthermore, it is guaranteed that after finitely many iterations, an enclosure of the nondominated set of prescribed quality is returned. We demonstrate the advantages of this approach by applying it to multiobjective energy supply network problems.
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ISSN:1573-2916
0925-5001
1573-2916
DOI:10.1007/s10898-023-01309-5