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38. Using Dual Relaxations in Multiobjective Mixed-Integer Convex Quadratic Programming
Invited abstract in session TC-37: Multiobjective Mixed-Integer Nonlinear Optimization, stream Multiobjective Optimization.
Tuesday, 12:30-14:00Room: 33 (building: 306)
Authors (first author is the speaker)
| 1. | Gabriele Eichfelder
|
| Institute of Mathematics, Technische Universität Ilmenau | |
| 2. | Marianna De Santis
|
| DIAG, Sapienza, University of Rome | |
| 3. | Daniele Patria
|
| DIAG, Sapienza, University of Rome | |
| 4. | Leo Warnow
|
| Institute of Mathematics, Technische Universität Ilmenau |
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
- Programming, Multi-Objective
- Programming, Mixed-Integer
- Programming, Quadratic
Status: accepted
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