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Article

On the runtime analysis of the 1-ANT ACO algorithm

Authors:

Benjamin Doerr,

Carsten WittAuthors Info & Claims

GECCO '07: Proceedings of the 9th annual conference on Genetic and evolutionary computation

Pages 33 - 40

https://doi.org/10.1145/1276958.1276964

Published: 07 July 2007 Publication History

Abstract

The runtime analysis of randomized search heuristics is a growing field where, in the last two decades, many rigorous results have been obtained. These results, however, apply particularly to classical search heuristics such as Evolutionary Algorithms (EAs) and Simulated Annealing. First runtime analyses of modern search heuristics have been conducted only recently w.r.t a simple Ant Colony Optimization (ACO) algorithm called 1-ANT. In particular, the influence of the evaporation factor in the pheromone update mechanism and the robustness of this parameter w.r.t the runtime behavior have been determined for the example function OneMax.This paper puts forward the rigorous runtime analysis of the 1-ANT on example functions, namely on the functions LeadingOnes and BinVal. With respect to EAs, such analyses have been essential to develop methods for the analysis on more complicated problems. The proof techniques required for the 1-ANT, unfortunately, differ significantly from those for EAs, which means that a new reservoir of methods has to be built up. Again, the influence of the evaporation factor is analyzed rigorously, and it is proved that its choice can be very crucial to allow efficient runtimes. Moreover, the analyses provide insight into the working principles of ACO algorithms and, in terms of their robustness, describe essential differences to other randomized search heuristics.

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Cited By

Kergaßner MKeszocze OWanka RLi XHandl J(2024)Markov Chain-based Optimization Time Analysis of Bivalent Ant Colony Optimization for Sorting and LeadingOnesProceedings of the Genetic and Evolutionary Computation Conference10.1145/3638529.3654022(1488-1496)Online publication date: 14-Jul-2024
https://dl.acm.org/doi/10.1145/3638529.3654022
Mühlenthaler MRaß ASchmitt MWanka R(2021)Exact Markov chain-based runtime analysis of a discrete particle swarm optimization algorithm on sorting and OneMaxNatural Computing10.1007/s11047-021-09856-021:4(651-677)Online publication date: 13-Jun-2021
https://doi.org/10.1007/s11047-021-09856-0
Elbes MAlzubi SKanan TAl-Fuqaha AHawashin B(2019)A survey on particle swarm optimization with emphasis on engineering and network applicationsEvolutionary Intelligence10.1007/s12065-019-00210-zOnline publication date: 21-Feb-2019
https://doi.org/10.1007/s12065-019-00210-z
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Index Terms

On the runtime analysis of the 1-ANT ACO algorithm
1. Theory of computation
  1. Design and analysis of algorithms

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cover image ACM Conferences

GECCO '07: Proceedings of the 9th annual conference on Genetic and evolutionary computation

July 2007

2313 pages

ISBN:9781595936974

DOI:10.1145/1276958

General Chair:
Hod Lipson
Cornell University, USA

Copyright © 2007 ACM.

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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Publication History

Published: 07 July 2007

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GECCO07

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GECCO07: Genetic and Evolutionary Computation Conference

July 7 - 11, 2007

London, England

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GECCO '07 Paper Acceptance Rate 266 of 577 submissions, 46%;

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

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Cited By

Kergaßner MKeszocze OWanka RLi XHandl J(2024)Markov Chain-based Optimization Time Analysis of Bivalent Ant Colony Optimization for Sorting and LeadingOnesProceedings of the Genetic and Evolutionary Computation Conference10.1145/3638529.3654022(1488-1496)Online publication date: 14-Jul-2024
https://dl.acm.org/doi/10.1145/3638529.3654022
Mühlenthaler MRaß ASchmitt MWanka R(2021)Exact Markov chain-based runtime analysis of a discrete particle swarm optimization algorithm on sorting and OneMaxNatural Computing10.1007/s11047-021-09856-021:4(651-677)Online publication date: 13-Jun-2021
https://doi.org/10.1007/s11047-021-09856-0
Elbes MAlzubi SKanan TAl-Fuqaha AHawashin B(2019)A survey on particle swarm optimization with emphasis on engineering and network applicationsEvolutionary Intelligence10.1007/s12065-019-00210-zOnline publication date: 21-Feb-2019
https://doi.org/10.1007/s12065-019-00210-z
Raß ASchreiner JWanka R(2019)Runtime Analysis of Discrete Particle Swarm Optimization Applied to Shortest Paths ComputationEvolutionary Computation in Combinatorial Optimization10.1007/978-3-030-16711-0_8(115-130)Online publication date: 24-Apr-2019
https://dl.acm.org/doi/10.1007/978-3-030-16711-0_8
Doerr BKrejca MTakadama K(2018)Significance-based estimation-of-distribution algorithmsProceedings of the Genetic and Evolutionary Computation Conference10.1145/3205455.3205553(1483-1490)Online publication date: 2-Jul-2018
https://dl.acm.org/doi/10.1145/3205455.3205553
Friedrich TKötzing TMelnichenko A(2017)Analyzing search heuristics with differential equationsProceedings of the Genetic and Evolutionary Computation Conference Companion10.1145/3067695.3075607(313-314)Online publication date: 15-Jul-2017
https://dl.acm.org/doi/10.1145/3067695.3075607
Mühlenthaler MRaß ASchmitt MSiegling AWanka RIgel CSudholt DWitt C(2017)Runtime Analysis of a Discrete Particle Swarm Optimization Algorithm on Sorting and OneMaxProceedings of the 14th ACM/SIGEVO Conference on Foundations of Genetic Algorithms10.1145/3040718.3040721(13-24)Online publication date: 12-Jan-2017
https://dl.acm.org/doi/10.1145/3040718.3040721
Cleghorn CEngelbrecht A(2017)Firefly optimization: A study on frame invariance2017 IEEE Symposium Series on Computational Intelligence (SSCI)10.1109/SSCI.2017.8285251(1-6)Online publication date: Nov-2017
https://doi.org/10.1109/SSCI.2017.8285251
Hongyue WHan HShuling YYushan Z(2017)Running-Time Analysis of Particle Swarm Optimization with a Single Particle Based on Average GainSimulated Evolution and Learning10.1007/978-3-319-68759-9_42(515-527)Online publication date: 14-Oct-2017
https://doi.org/10.1007/978-3-319-68759-9_42
Pat A(2014)Ant Colony Optimization and hypergraph covering problems2014 IEEE Congress on Evolutionary Computation (CEC)10.1109/CEC.2014.6900294(1714-1720)Online publication date: Jul-2014
https://doi.org/10.1109/CEC.2014.6900294
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