A Benson-Type Algorithm for Bounded Convex Vector Optimization Problems with Vertex Selection

TL;DR

This paper introduces a modified Benson-type algorithm with a new vertex selection rule for bounded convex vector optimization, improving efficiency by reducing the number of scalar problems needed for approximation.

Contribution

It proposes a novel vertex selection strategy in Benson-type algorithms, enhancing computational efficiency in solving convex vector optimization problems.

Findings

Fewer scalar problems are needed for the same approximation quality.

The new method can be faster than previous algorithms.

Numerical examples demonstrate improved efficiency.

Abstract

We present an algorithm for approximately solving bounded convex vector optimization problems. The algorithm provides both an outer and an inner polyhedral approximation of the upper image. It is a modification of the primal algorithm presented by L\"ohne, Rudloff, and Ulus in 2014. There, vertices of an already known outer approximation are successively cut off to improve the approximation error. We propose a new and efficient selection rule for deciding which vertex to cut off. Numerical examples are provided which illustrate that this method may solve fewer scalar problems overall and therefore may be faster while achieving the same approximation quality.