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 …
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
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 …
efficient computation of upper and lower bound sets. These bound sets are used as a …
Set optimization—a rather short introduction
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 …
relations as well as fundamental constructions of a convex analysis for set-and vector …
Primal and dual approximation algorithms for convex vector optimization problems
Two approximation algorithms for solving convex vector optimization problems (CVOPs) are
provided. Both algorithms solve the CVOP and its geometric dual problem simultaneously …
provided. Both algorithms solve the CVOP and its geometric dual problem simultaneously …
A multi-objective constraint-based approach for modeling genome-scale microbial ecosystems
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 …
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
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 …
integer linear programming problems. In the recent literature, competitive frameworks has …
Set-valued average value at risk and its computation
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 …
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 …
problems. The algorithm provides both an outer and an inner polyhedral approximation of …
A linear risk-return model for enhanced indexation in portfolio optimization
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 …
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
This paper is concerned with solution algorithms for general convex vector optimization
problems (CVOPs). So far, solution concepts and approximation algorithms for solving …
problems (CVOPs). So far, solution concepts and approximation algorithms for solving …