The vector linear program solver Bensolve–notes on theoretical background

A Löhne, B Weißing - European Journal of Operational Research, 2017 - Elsevier
Bensolve is an open source implementation of Benson's algorithm and its dual variant. Both
algorithms compute primal and dual solutions of vector linear programs (VLP), which include …

[HTML][HTML] Branch-and-bound and objective branching with three or more objectives

N Forget, SL Gadegaard, K Klamroth… - Computers & Operations …, 2022 - Elsevier
The recent success of bi-objective Branch-and-Bound (B&B) algorithms heavily relies on the
efficient computation of upper and lower bound sets. These bound sets are used as a …

Set optimization—a rather short introduction

AH Hamel, F Heyde, A Löhne, B Rudloff… - … The State of the Art: From …, 2015 - Springer
Recent developments in set optimization are surveyed and extended including various set
relations as well as fundamental constructions of a convex analysis for set-and vector …

Primal and dual approximation algorithms for convex vector optimization problems

A Löhne, B Rudloff, F Ulus - Journal of Global Optimization, 2014 - Springer
Two approximation algorithms for solving convex vector optimization problems (CVOPs) are
provided. Both algorithms solve the CVOP and its geometric dual problem simultaneously …

A multi-objective constraint-based approach for modeling genome-scale microbial ecosystems

M Budinich, J Bourdon, A Larhlimi, D Eveillard - PloS one, 2017 - journals.plos.org
Interplay within microbial communities impacts ecosystems on several scales, and
elucidation of the consequent effects is a difficult task in ecology. In particular, the integration …

[HTML][HTML] Warm-starting lower bound set computations for branch-and-bound algorithms for multi objective integer linear programs

N Forget, SL Gadegaard, LR Nielsen - European Journal of Operational …, 2022 - Elsevier
In this paper we propose a generic branch-and-bound algorithm for solving multi-objective
integer linear programming problems. In the recent literature, competitive frameworks has …

Set-valued average value at risk and its computation

AH Hamel, B Rudloff, M Yankova - Mathematics and Financial Economics, 2013 - Springer
New versions of the set-valued average value at risk for multivariate risks are introduced by
generalizing the well-known certainty equivalent representation to the set-valued case. The …

A Benson-type algorithm for bounded convex vector optimization problems with vertex selection

D Dörfler, A Löhne, C Schneider… - … Methods and Software, 2022 - Taylor & Francis
We present an algorithm for approximately solving bounded convex vector optimization
problems. The algorithm provides both an outer and an inner polyhedral approximation of …

A linear risk-return model for enhanced indexation in portfolio optimization

R Bruni, F Cesarone, A Scozzari, F Tardella - OR spectrum, 2015 - Springer
Enhanced indexation (EI) is the problem of selecting a portfolio that should produce excess
return with respect to a given benchmark index. In this work, we propose a linear bi-objective …

Algorithms to solve unbounded convex vector optimization problems

A Wagner, F Ulus, B Rudloff, G Kováčová… - SIAM Journal on …, 2023 - SIAM
This paper is concerned with solution algorithms for general convex vector optimization
problems (CVOPs). So far, solution concepts and approximation algorithms for solving …