Approximating Biobjective Minimization Problems Using General Ordering Cones

09/21/2021
by   Arne Herzel, et al.
0

This article investigates the approximation quality achievable for biobjective minimization problems with respect to the Pareto cone by solutions that are (approximately) optimal with respect to larger ordering cones. When simultaneously considering α-approximations for all closed convex ordering cones of a fixed inner angle γ∈ [π/2, π], an approximation guarantee between α and 2 α is achieved, which depends continuously on γ. The analysis is best-possible for any inner angle and it generalizes and unifies the known results that the set of supported solutions is a 2-approximation and that the efficient set itself is a 1-approximation. Moreover, it is shown that, for maximization problems, no approximation guarantee is achievable by considering larger ordering cones in the described fashion, which again generalizes a known result about the set of supported solutions.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 1

page 2

page 3

page 4

08/03/2019

The Power of the Weighted Sum Scalarization for Approximating Multiobjective Optimization Problems

We determine the power of the weighted sum scalarization with respect to...
04/13/2020

A General Framework for Approximating Min Sum Ordering Problems

We consider a large family of problems in which an ordering of a finite ...
04/25/2022

A Structural Investigation of the Approximability of Polynomial-Time Problems

We initiate the systematic study of a recently introduced polynomial-tim...
08/27/2012

New results of ant algorithms for the Linear Ordering Problem

Ant-based algorithms are successful tools for solving complex problems. ...
04/14/2022

Exact and approximate determination of the Pareto set using minimal correction subsets

Recently, it has been shown that the enumeration of Minimal Correction S...
06/28/2018

Quit When You Can: Efficient Evaluation of Ensembles with Ordering Optimization

Given a classifier ensemble and a set of examples to be classified, many...
10/16/2012

Multi-objective Influence Diagrams

We describe multi-objective influence diagrams, based on a set of p obje...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.