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A rigorous runtime analysis of the 2-MMAS_ib on jump functions: ant colony optimizers can cope well with local optima

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Benjamin DoerrAuthors Info & Claims

GECCO '21: Proceedings of the Genetic and Evolutionary Computation Conference

Pages 4 - 13

https://doi.org/10.1145/3449639.3459350

Published: 26 June 2021 Publication History

Abstract

Ant colony optimizers have been successfully used as general-purpose optimization heuristics. Due to the complicated nature of the random processes that describe the runs of ACO algorithms, the mathematical understanding of these algorithms is much less developed than that of other nature-inspired heuristics. In this first runtime analysis of a basic ACO algorithm on a classic multimodal benchmark, we analyze the runtime of the 2-MMAS_ib on jump functions. For moderate jump sizes k ≤ α₀ ln n, α₀ > 0 a constant, we prove a runtime of order O(√n/ρ), when the evaporation factor ρ satisfies ρ ≤ Cn^-1/2 ln(n)^-1 for a sufficiently small constant C. For ρ = Θ(n^-1/2 ln(n)^-1), we thus obtain a runtime of O(n ln(n)). This result shows that simple ACO algorithms can cope much better with local optima than many evolutionary algorithms, which need Ω(n^k) time.

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Cited By

Adak SWitt C(2024)Runtime Analysis of a Multi-valued Compact Genetic Algorithm on Generalized OneMaxParallel Problem Solving from Nature – PPSN XVIII10.1007/978-3-031-70071-2_4(53-69)Online publication date: 7-Sep-2024
https://doi.org/10.1007/978-3-031-70071-2_4
Doerr BQu ZWilliams BChen YNeville J(2023)Runtime analysis for the NSGA-IIProceedings of the Thirty-Seventh AAAI Conference on Artificial Intelligence and Thirty-Fifth Conference on Innovative Applications of Artificial Intelligence and Thirteenth Symposium on Educational Advances in Artificial Intelligence10.1609/aaai.v37i10.26461(12399-12407)Online publication date: 7-Feb-2023
https://dl.acm.org/doi/10.1609/aaai.v37i10.26461
Zheng WDoerr B(2023)Theoretical Analyses of Multiobjective Evolutionary Algorithms on Multimodal Objectives*Evolutionary Computation10.1162/evco_a_0032831:4(337-373)Online publication date: 1-Dec-2023
https://doi.org/10.1162/evco_a_00328
Show More Cited By

Index Terms

A rigorous runtime analysis of the 2-MMAS_ib on jump functions: ant colony optimizers can cope well with local optima
1. Theory of computation
  1. Randomness, geometry and discrete structures
    1. Random search heuristics

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cover image ACM Conferences

GECCO '21: Proceedings of the Genetic and Evolutionary Computation Conference

June 2021

1219 pages

ISBN:9781450383509

DOI:10.1145/3449639

Editor:
Francisco Chicano
University of Malaga
,
General Chair:
Krzysztof Krawiec
Poznan University of Technology

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Published: 26 June 2021

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July 10 - 14, 2021

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Cited By

Adak SWitt C(2024)Runtime Analysis of a Multi-valued Compact Genetic Algorithm on Generalized OneMaxParallel Problem Solving from Nature – PPSN XVIII10.1007/978-3-031-70071-2_4(53-69)Online publication date: 7-Sep-2024
https://doi.org/10.1007/978-3-031-70071-2_4
Doerr BQu ZWilliams BChen YNeville J(2023)Runtime analysis for the NSGA-IIProceedings of the Thirty-Seventh AAAI Conference on Artificial Intelligence and Thirty-Fifth Conference on Innovative Applications of Artificial Intelligence and Thirteenth Symposium on Educational Advances in Artificial Intelligence10.1609/aaai.v37i10.26461(12399-12407)Online publication date: 7-Feb-2023
https://dl.acm.org/doi/10.1609/aaai.v37i10.26461
Zheng WDoerr B(2023)Theoretical Analyses of Multiobjective Evolutionary Algorithms on Multimodal Objectives*Evolutionary Computation10.1162/evco_a_0032831:4(337-373)Online publication date: 1-Dec-2023
https://doi.org/10.1162/evco_a_00328
Ivanova AAntipov DDoerr BSilva SPaquete L(2023)Larger Offspring Populations Help the (1 + (λ, λ)) Genetic Algorithm to Overcome the NoiseProceedings of the Genetic and Evolutionary Computation Conference10.1145/3583131.3590514(919-928)Online publication date: 15-Jul-2023
https://dl.acm.org/doi/10.1145/3583131.3590514
Doerr BDremaux ALutzeyer JStumpf ASilva SPaquete L(2023)How the Move Acceptance Hyper-Heuristic Copes With Local Optima: Drastic Differences Between Jumps and CliffsProceedings of the Genetic and Evolutionary Computation Conference10.1145/3583131.3590509(990-999)Online publication date: 15-Jul-2023
https://dl.acm.org/doi/10.1145/3583131.3590509
Doerr BGhannane YIbn Brahim M(2023)Runtime Analysis for Permutation-based Evolutionary AlgorithmsAlgorithmica10.1007/s00453-023-01146-886:1(90-129)Online publication date: 26-Jul-2023
https://doi.org/10.1007/s00453-023-01146-8
Antipov DBuzdalov MDoerr B(2023)Lazy Parameter Tuning and Control: Choosing All Parameters Randomly from a Power-Law DistributionAlgorithmica10.1007/s00453-023-01098-z86:2(442-484)Online publication date: 22-Feb-2023
https://doi.org/10.1007/s00453-023-01098-z
Bambury HBultel ADoerr B(2022)An Extended Jump Functions Benchmark for the Analysis of Randomized Search HeuristicsAlgorithmica10.1007/s00453-022-00977-186:1(1-32)Online publication date: 23-May-2022
https://doi.org/10.1007/s00453-022-00977-1
Antipov DDoerr BKaravaev V(2022)A Rigorous Runtime Analysis of the $$(1 + (\lambda , \lambda ))$$ GA on Jump FunctionsAlgorithmica10.1007/s00453-021-00907-784:6(1573-1602)Online publication date: 15-Jan-2022
https://doi.org/10.1007/s00453-021-00907-7

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