research-article

Analysing the Robustness of NSGA-II under Noise

Authors:

Duc-Cuong Dang,

Dirk SudholtAuthors Info & Claims

GECCO '23: Proceedings of the Genetic and Evolutionary Computation Conference

Pages 642 - 651

https://doi.org/10.1145/3583131.3590421

Published: 12 July 2023 Publication History

Abstract

Runtime analysis has produced many results on the efficiency of simple evolutionary algorithms like the (1+1) EA, and its analogue called GSEMO in evolutionary multiobjective optimisation (EMO). Recently, the first runtime analyses of the famous and highly cited EMO algorithm NSGA-II have emerged, demonstrating that practical algorithms with thousands of applications can be rigorously analysed. However, these results only show that NSGA-II has the same performance guarantees as GSEMO and it is unclear how and when NSGA-II can outperform GSEMO.

We study this question in noisy optimisation and consider a noise model that adds large amounts of posterior noise to all objectives with some constant probability p per evaluation. We show that GSEMO fails badly on every noisy fitness function as it tends to remove large parts of the population indiscriminately. In contrast, NSGA-II is able to handle the noise efficiently on LeadingOnes-TrailingZeroes when p < 1/2, as the algorithm is able to preserve useful search points. We identify a phase transition at p = 1/2 where the expected time to cover the Pareto front changes from polynomial to exponential. This is the first proof that NSGA-II can outperform GSEMO and the first runtime analysis of NSGA-II in noisy optimisation.

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Cited By

Zheng WDoerr BWooldridge MDy JNatarajan S(2024)Runtime analysis of the SMS-EMOA for many-objective optimizationProceedings of the Thirty-Eighth AAAI Conference on Artificial Intelligence and Thirty-Sixth Conference on Innovative Applications of Artificial Intelligence and Fourteenth Symposium on Educational Advances in Artificial Intelligence10.1609/aaai.v38i18.30077(20874-20882)Online publication date: 20-Feb-2024
https://dl.acm.org/doi/10.1609/aaai.v38i18.30077
Dinot MDoerr BHennebelle UWill SLi XHandl J(2024)Hot off the Press: Runtime Analyses of Multi-Objective Evolutionary Algorithms in the Presence of NoiseProceedings of the Genetic and Evolutionary Computation Conference Companion10.1145/3638530.3664070(33-34)Online publication date: 14-Jul-2024
https://dl.acm.org/doi/10.1145/3638530.3664070
Zheng WDoerr BLi XHandl J(2024)Hot off the Press: Runtime Analysis of the SMS-EMOA for Many-Objective OptimizationProceedings of the Genetic and Evolutionary Computation Conference Companion10.1145/3638530.3664064(69-70)Online publication date: 14-Jul-2024
https://dl.acm.org/doi/10.1145/3638530.3664064
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Index Terms

Analysing the Robustness of NSGA-II under Noise
1. Applied computing
  1. Operations research
    1. Decision analysis
      1. Multi-criterion optimization and decision-making
2. Theory of computation
  1. Theory and algorithms for application domains
    1. Theory of randomized search heuristics

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cover image ACM Conferences

GECCO '23: Proceedings of the Genetic and Evolutionary Computation Conference

July 2023

1667 pages

ISBN:9798400701191

DOI:10.1145/3583131

Chair:
Sara Silva,
Program Chair:
Luís Paquete

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Published: 12 July 2023

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Cited By

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https://dl.acm.org/doi/10.1609/aaai.v38i18.30077
Dinot MDoerr BHennebelle UWill SLi XHandl J(2024)Hot off the Press: Runtime Analyses of Multi-Objective Evolutionary Algorithms in the Presence of NoiseProceedings of the Genetic and Evolutionary Computation Conference Companion10.1145/3638530.3664070(33-34)Online publication date: 14-Jul-2024
https://dl.acm.org/doi/10.1145/3638530.3664070
Zheng WDoerr BLi XHandl J(2024)Hot off the Press: Runtime Analysis of the SMS-EMOA for Many-Objective OptimizationProceedings of the Genetic and Evolutionary Computation Conference Companion10.1145/3638530.3664064(69-70)Online publication date: 14-Jul-2024
https://dl.acm.org/doi/10.1145/3638530.3664064
Wietheger SDoerr BLi XHandl J(2024)A Mathematical Runtime Analysis of the Non-dominated Sorting Genetic Algorithm III (NSGA-III)Proceedings of the Genetic and Evolutionary Computation Conference Companion10.1145/3638530.3664062(63-64)Online publication date: 14-Jul-2024
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Knowles JZheng WLi XHandl J(2024)Evolutionary Multiobjective Optimization (EMO)Proceedings of the Genetic and Evolutionary Computation Conference Companion10.1145/3638530.3648415(1432-1459)Online publication date: 14-Jul-2024
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Opris ADang DNeumann FSudholt DLi XHandl J(2024)Runtime Analyses of NSGA-III on Many-Objective ProblemsProceedings of the Genetic and Evolutionary Computation Conference10.1145/3638529.3654218(1596-1604)Online publication date: 14-Jul-2024
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Antipov DDoerr BIvanova ALi XHandl J(2024)Already Moderate Population Sizes Provably Yield Strong Robustness to NoiseProceedings of the Genetic and Evolutionary Computation Conference10.1145/3638529.3654196(1524-1532)Online publication date: 14-Jul-2024
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Dang DOpris ASudholt DLi XHandl J(2024)Illustrating the Efficiency of Popular Evolutionary Multi-Objective Algorithms Using Runtime AnalysisProceedings of the Genetic and Evolutionary Computation Conference10.1145/3638529.3654177(484-492)Online publication date: 14-Jul-2024
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