Using dual relaxations in multiobjective mixed-integer convex quadratic programming

Marianna Santis (), Gabriele Eichfelder (), Daniele Patria () and Leo Warnow ()
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Marianna Santis: Università degli Studi di Firenze
Gabriele Eichfelder: Technische Universität Ilmenau
Daniele Patria: Sapienza Università di Roma
Leo Warnow: Technische Universität Ilmenau

Journal of Global Optimization, 2025, vol. 92, issue 1, No 7, 159-186

Abstract: Abstract We present a branch-and-bound method for multiobjective mixed-integer convex quadratic programs that computes a superset of efficient integer assignments and a coverage of the nondominated set. The method relies on outer approximations of the upper image set of continuous relaxations. These outer approximations are obtained addressing the dual formulations of specific subproblems where the values of certain integer variables are fixed. The devised pruning conditions and a tailored preprocessing phase allow a fast enumeration of the nodes. Despite we do not require any boundedness of the feasible set, we are able to prove that the method stops after having explored a finite number of nodes. Numerical experiments on a broad set of instances with two, three, and four objectives are presented.

Keywords: Multiobjective optimization; Convex quadratic optimization; Mixed-integer quadratic programming; Branch-and-bound algorithm; 90C11; 90C25; 90C29; 90C57 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10898-024-01440-x

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