In multi-objective optimization, set-based quality indicators are a cornerstone of benchmarking and performance assessment. They capture the quality of a set of trade-off solutions by reducing it to a scalar number. One of the most commonly used set-based metrics is the R2 indicator, which describes the expected utility of a solution set to a decision-maker under a distribution of utility functions. Typically, this indicator is applied by discretizing this distribution of utility functions, yielding a weakly Pareto-compliant indicator. In consequence, adding a nondominated or dominating solution to a solution set may – but does not have to – improve the indicator’s value. In this paper, we reinvestigate the R2 indicator under the premise that we have a continuous, uniform distribution of (Tchebycheff) utility functions. We analyze its properties in detail, demonstrating that this continuous variant is indeed Pareto-compliant – that is, any beneficial solution will improve the metric’s value. Additionally, we provide an efficient computational procedure to compute this metric for bi-objective problems in O(NlogN). As a result, this work contributes to the state-of-the-art Pareto-compliant unary performance metrics, such as the hypervolume indicator, offering an efficient and promising alternative.
%0 Conference Paper
%1 e4cb2139d97b417b8e5e0e68a26eb4f8
%A Schäpermeier, Lennart
%A Kerschke, Pascal
%B Parallel Problem Solving from Nature – PPSN XVIII
%D 2024
%E Affenzeller, Michael
%E Winkler, Stephan M.
%E Kononova, Anna V.
%E Bäck, Thomas
%E Trautmann, Heike
%E Tusar, Tea
%E Machado, Penousal
%I Springer, Berlin u. a.
%K topic_engineering Benchmarking, FIS_scads Multi-objective Pareto Performance R2 Utility assessment, compliance, functions indicator, optimization,
%P 202--216
%R 10.1007/978-3-031-70085-9_13
%T Reinvestigating the R2 Indicator: Achieving Pareto Compliance by Integration
%X In multi-objective optimization, set-based quality indicators are a cornerstone of benchmarking and performance assessment. They capture the quality of a set of trade-off solutions by reducing it to a scalar number. One of the most commonly used set-based metrics is the R2 indicator, which describes the expected utility of a solution set to a decision-maker under a distribution of utility functions. Typically, this indicator is applied by discretizing this distribution of utility functions, yielding a weakly Pareto-compliant indicator. In consequence, adding a nondominated or dominating solution to a solution set may – but does not have to – improve the indicator’s value. In this paper, we reinvestigate the R2 indicator under the premise that we have a continuous, uniform distribution of (Tchebycheff) utility functions. We analyze its properties in detail, demonstrating that this continuous variant is indeed Pareto-compliant – that is, any beneficial solution will improve the metric’s value. Additionally, we provide an efficient computational procedure to compute this metric for bi-objective problems in O(NlogN). As a result, this work contributes to the state-of-the-art Pareto-compliant unary performance metrics, such as the hypervolume indicator, offering an efficient and promising alternative.
%@ 978-3-031-70084-2
@inproceedings{e4cb2139d97b417b8e5e0e68a26eb4f8,
abstract = {In multi-objective optimization, set-based quality indicators are a cornerstone of benchmarking and performance assessment. They capture the quality of a set of trade-off solutions by reducing it to a scalar number. One of the most commonly used set-based metrics is the R2 indicator, which describes the expected utility of a solution set to a decision-maker under a distribution of utility functions. Typically, this indicator is applied by discretizing this distribution of utility functions, yielding a weakly Pareto-compliant indicator. In consequence, adding a nondominated or dominating solution to a solution set may – but does not have to – improve the indicator{\textquoteright}s value. In this paper, we reinvestigate the R2 indicator under the premise that we have a continuous, uniform distribution of (Tchebycheff) utility functions. We analyze its properties in detail, demonstrating that this continuous variant is indeed Pareto-compliant – that is, any beneficial solution will improve the metric{\textquoteright}s value. Additionally, we provide an efficient computational procedure to compute this metric for bi-objective problems in O(NlogN). As a result, this work contributes to the state-of-the-art Pareto-compliant unary performance metrics, such as the hypervolume indicator, offering an efficient and promising alternative.},
added-at = {2024-11-28T16:27:18.000+0100},
author = {Sch{\"a}permeier, Lennart and Kerschke, Pascal},
biburl = {https://puma.scadsai.uni-leipzig.de/bibtex/2e69f2e3b652e238b160c53a1625beba1/scadsfct},
booktitle = {Parallel Problem Solving from Nature – PPSN XVIII},
day = 7,
doi = {10.1007/978-3-031-70085-9_13},
editor = {Affenzeller, Michael and Winkler, {Stephan M.} and Kononova, {Anna V.} and B{\"a}ck, Thomas and Trautmann, Heike and Tu{\v s}ar, Tea and Machado, Penousal},
interhash = {440f90b5e7e2d6da960dff7df32304d3},
intrahash = {e69f2e3b652e238b160c53a1625beba1},
isbn = {978-3-031-70084-2},
keywords = {topic_engineering Benchmarking, FIS_scads Multi-objective Pareto Performance R2 Utility assessment, compliance, functions indicator, optimization,},
language = {English},
month = sep,
note = {Publisher Copyright: {\textcopyright} The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.},
pages = {202--216},
publisher = {Springer, Berlin [u. a.]},
series = {Lecture Notes in Computer Science},
timestamp = {2024-11-28T17:41:02.000+0100},
title = {Reinvestigating the R2 Indicator: Achieving Pareto Compliance by Integration},
year = 2024
}
