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Solving Multiobjective Mixed Integer Convex Optimization Problems

Marianna De Santis(mdesantis***at***diag.uniroma1.it)
Gabriele Eichfelder(gabriele.eichfelder***at***tu-ilmenau.de)
Julia Niebling(julia.niebling***at***tu-ilmenau.de)
Stefan Rocktäschel(stefan.rocktaeschel***at***tu-ilmenau.de)

Abstract: Multiobjective mixed integer convex optimization refers to mathematical programming problems where more than one convex objective function needs to be optimized simultaneously and some of the variables are constrained to take integer values. We present a branch-and-bound method based on the use of properly defined lower bounds. We do not simply rely on convex relaxations, but we built linear outer approximations of the image set in an adaptive way. We are able to guarantee correctness in terms of detecting both the efficient and the nondominated set of multiobjective mixed integer convex problems according to a prescribed precision. As far as we know, the procedure we present is the first deterministic algorithm devised to handle this class of problems. Our numerical experiments show results on biobjective and triobjective mixed integer convex instances.

Keywords: Multiobjective Optimization, Mixed Integer Convex Programming, Outer Approximations

Category 1: Integer Programming ((Mixed) Integer Nonlinear Programming )

Category 2: Other Topics (Multi-Criteria Optimization )

Category 3: Global Optimization


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Entry Submitted: 05/28/2019
Entry Accepted: 05/28/2019
Entry Last Modified: 05/28/2019

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