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Edges of mutually non-dominating sets

Authors:

Richard M. Everson,

David J. Walker,

Jonathan E. FieldsendAuthors Info & Claims

GECCO '13: Proceedings of the 15th annual conference on Genetic and evolutionary computation

Pages 607 - 614

https://doi.org/10.1145/2463372.2463452

Published: 06 July 2013 Publication History

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Abstract

Multi-objective optimisation yields an estimated Pareto front of mutually non-dominating solutions, but with more than three objectives understanding the relationships between solutions is challenging. Natural solutions to use as landmarks are those lying near to the edges of the mutually non-dominating set. We propose four definitions of edge points for many-objective mutually non-dominating sets and examine the relations between them.

The first defines edge points to be those that extend the range of the attainment surface. This is shown to be equivalent to finding points which are not dominated on projection onto subsets of the objectives. If the objectives are to be minimised, a further definition considers points which are not dominated under maximisation when projected onto objective subsets. A final definition looks for edges via alternative projections of the set.

We examine the relations between these definitions and their efficacy for synthetic concave- and convex-shaped sets, and on solutions to a prototypical many-objective optimisation problem, showing how they can reveal information about the structure of the estimated Pareto front.

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Cited By

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Everson RWalker DFieldsend J(2014)Life on the Edge: Characterising the Edges of Mutually Non-dominating SetsEvolutionary Computation10.1162/EVCO_a_0012422:3(479-501)Online publication date: Sep-2014
https://doi.org/10.1162/EVCO_a_00124
Li MYang SLiu X(2014)A test problem for visual investigation of high-dimensional multi-objective search2014 IEEE Congress on Evolutionary Computation (CEC)10.1109/CEC.2014.6900306(2140-2147)Online publication date: Jul-2014
https://doi.org/10.1109/CEC.2014.6900306

Index Terms

Edges of mutually non-dominating sets
1. Mathematics of computing
  1. Mathematical analysis
    1. Mathematical optimization
2. Theory of computation
  1. Design and analysis of algorithms
    1. Mathematical optimization

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Published In

GECCO '13: Proceedings of the 15th annual conference on Genetic and evolutionary computation

July 2013

1672 pages

ISBN:9781450319638

DOI:10.1145/2463372

Editor:
Christian Blum
IKERBASQUE and University of the Basque Country UPV/EHU, Spain
,
General Chair:
Enrique Alba
University of Malaga, Spain

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 06 July 2013

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GECCO '13

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SIGEVO

GECCO '13: Genetic and Evolutionary Computation Conference

July 6 - 10, 2013

Amsterdam, The Netherlands

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GECCO '13 Paper Acceptance Rate 204 of 570 submissions, 36%;

Overall Acceptance Rate 1,669 of 4,410 submissions, 38%

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Everson RWalker DFieldsend J(2014)Life on the Edge: Characterising the Edges of Mutually Non-dominating SetsEvolutionary Computation10.1162/EVCO_a_0012422:3(479-501)Online publication date: Sep-2014
https://doi.org/10.1162/EVCO_a_00124
Li MYang SLiu X(2014)A test problem for visual investigation of high-dimensional multi-objective search2014 IEEE Congress on Evolutionary Computation (CEC)10.1109/CEC.2014.6900306(2140-2147)Online publication date: Jul-2014
https://doi.org/10.1109/CEC.2014.6900306

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