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

Moritz Link () and Stefan Volkwein ()
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Moritz Link: University of Konstanz
Stefan Volkwein: University of Konstanz

Journal of Global Optimization, 2023, vol. 87, issue 1, No 4, 97-132

Abstract: Abstract 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.

Keywords: Mixed-integer nonlinear programming; Multiobjective optimization; Box enclosure; Adaptive piecewise linear relaxation; Energy supply networks; 65K05; 90C11; 90C26; 90C29; 90C35 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10898-023-01309-5

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