The vector linear program solver Bensolve -- notes on theoretical background

TL;DR

Bensolve is an open source solver for vector linear programs based on Benson's algorithm, with a focus on its theoretical foundations and duality principles, supporting arbitrary VLPs without lines in the upper image.

Contribution

This paper surveys the theoretical background of Bensolve, highlighting its implementation of Benson's algorithm and duality in solving vector linear programs.

Findings

Supports arbitrary VLPs without lines in the upper image

Provides numerical examples demonstrating solver capabilities

Emphasizes the role of duality in the implementation

Abstract

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 the subclass of multiple objective linear programs (MOLP). The recent version of Bensolve can treat arbitrary vector linear programs whose upper image does not contain lines. This article surveys the theoretical background of the implementation. In particular, the role of VLP duality for the implementation is pointed out. Some numerical examples are provided.