Improving the run time of the (1 + 1) evolutionary algorithm with luby sequences

Tobias Friedrich; Francesco Quinzan; Timo Kötzing; Andrew M. Sutton

doi:10.1145/3205455.3205525

Improving the run time of the (1 + 1) evolutionary algorithm with luby sequences

Tobias Friedrich, Francesco Quinzan, Timo Kötzing, Andrew M. Sutton

Computer Science (Duluth)

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

1 Scopus citations

Abstract

In the context of black box optimization, one of the most common ways to handle deceptive attractors is to periodically restart the algorithm. In this paper, we explore the benefits of combining the simple (1+1) Evolutionary Algorithm (EA) with the Luby Universal Strategy - the (1 + 1) EA_U , a meta-heuristic that does not require parameter tuning. We first consider two artificial pseudo-Boolean landscapes, on which the (1 + 1) EA exhibits exponential run time. We prove that the (1 + 1) EA_U has polynomial run time on both instances. We then consider the Minimum Vertex Cover on two classes of graphs. Again, the (1 + 1) EA yields exponential run time on those instances, and the (1 + 1) EA_U finds the global optimum in polynomial time. We conclude by studying the Makespan Scheduling. We consider an instance on which the (1 + 1) EA does not find a (4/3 − )- approximation in polynomial time, and we show that the (1 + 1) EA_U reaches a (4/3 −)-approximation in polynomial time. We then prove that the (1 + 1) EA_U serves as an Efficient Polynomial-time Approximation Scheme (EPTAS) for the Partition Problem, for a (1 +)-approximation with > 4/n.

Original language	English (US)
Title of host publication	GECCO 2018 - Proceedings of the 2018 Genetic and Evolutionary Computation Conference
Publisher	Association for Computing Machinery, Inc
Pages	301-308
Number of pages	8
ISBN (Electronic)	9781450356183
DOIs	https://doi.org/10.1145/3205455.3205525
State	Published - Jul 2 2018
Event	2018 Genetic and Evolutionary Computation Conference, GECCO 2018 - Kyoto, Japan Duration: Jul 15 2018 → Jul 19 2018

Publication series

Name	GECCO 2018 - Proceedings of the 2018 Genetic and Evolutionary Computation Conference

Other

Other	2018 Genetic and Evolutionary Computation Conference, GECCO 2018
Country/Territory	Japan
City	Kyoto
Period	7/15/18 → 7/19/18

Bibliographical note

Funding Information:
The research leading to these results has received funding from the German Science Foundation (DFG) under grant agreement FR 2988 (TOSU).

Publisher Copyright:
© 2018 Copyright held by the owner/author(s).

Keywords

Combinatorial optimization
Deceptive attractors
Restart strategy

Publisher link

10.1145/3205455.3205525

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Cite this

Friedrich, T., Quinzan, F., Kötzing, T., & Sutton, A. M. (2018). Improving the run time of the (1 + 1) evolutionary algorithm with luby sequences. In GECCO 2018 - Proceedings of the 2018 Genetic and Evolutionary Computation Conference (pp. 301-308). (GECCO 2018 - Proceedings of the 2018 Genetic and Evolutionary Computation Conference). Association for Computing Machinery, Inc. https://doi.org/10.1145/3205455.3205525

Improving the run time of the (1 + 1) evolutionary algorithm with luby sequences. / Friedrich, Tobias; Quinzan, Francesco; Kötzing, Timo et al.
GECCO 2018 - Proceedings of the 2018 Genetic and Evolutionary Computation Conference. Association for Computing Machinery, Inc, 2018. p. 301-308 (GECCO 2018 - Proceedings of the 2018 Genetic and Evolutionary Computation Conference).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Friedrich, T, Quinzan, F, Kötzing, T & Sutton, AM 2018, Improving the run time of the (1 + 1) evolutionary algorithm with luby sequences. in GECCO 2018 - Proceedings of the 2018 Genetic and Evolutionary Computation Conference. GECCO 2018 - Proceedings of the 2018 Genetic and Evolutionary Computation Conference, Association for Computing Machinery, Inc, pp. 301-308, 2018 Genetic and Evolutionary Computation Conference, GECCO 2018, Kyoto, Japan, 7/15/18. https://doi.org/10.1145/3205455.3205525

Friedrich T, Quinzan F, Kötzing T, Sutton AM. Improving the run time of the (1 + 1) evolutionary algorithm with luby sequences. In GECCO 2018 - Proceedings of the 2018 Genetic and Evolutionary Computation Conference. Association for Computing Machinery, Inc. 2018. p. 301-308. (GECCO 2018 - Proceedings of the 2018 Genetic and Evolutionary Computation Conference). doi: 10.1145/3205455.3205525

Friedrich, Tobias ; Quinzan, Francesco ; Kötzing, Timo et al. / Improving the run time of the (1 + 1) evolutionary algorithm with luby sequences. GECCO 2018 - Proceedings of the 2018 Genetic and Evolutionary Computation Conference. Association for Computing Machinery, Inc, 2018. pp. 301-308 (GECCO 2018 - Proceedings of the 2018 Genetic and Evolutionary Computation Conference).

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abstract = "In the context of black box optimization, one of the most common ways to handle deceptive attractors is to periodically restart the algorithm. In this paper, we explore the benefits of combining the simple (1+1) Evolutionary Algorithm (EA) with the Luby Universal Strategy - the (1 + 1) EAU , a meta-heuristic that does not require parameter tuning. We first consider two artificial pseudo-Boolean landscapes, on which the (1 + 1) EA exhibits exponential run time. We prove that the (1 + 1) EAU has polynomial run time on both instances. We then consider the Minimum Vertex Cover on two classes of graphs. Again, the (1 + 1) EA yields exponential run time on those instances, and the (1 + 1) EAU finds the global optimum in polynomial time. We conclude by studying the Makespan Scheduling. We consider an instance on which the (1 + 1) EA does not find a (4/3 − )- approximation in polynomial time, and we show that the (1 + 1) EAU reaches a (4/3 −)-approximation in polynomial time. We then prove that the (1 + 1) EAU serves as an Efficient Polynomial-time Approximation Scheme (EPTAS) for the Partition Problem, for a (1 +)-approximation with > 4/n.",

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N2 - In the context of black box optimization, one of the most common ways to handle deceptive attractors is to periodically restart the algorithm. In this paper, we explore the benefits of combining the simple (1+1) Evolutionary Algorithm (EA) with the Luby Universal Strategy - the (1 + 1) EAU , a meta-heuristic that does not require parameter tuning. We first consider two artificial pseudo-Boolean landscapes, on which the (1 + 1) EA exhibits exponential run time. We prove that the (1 + 1) EAU has polynomial run time on both instances. We then consider the Minimum Vertex Cover on two classes of graphs. Again, the (1 + 1) EA yields exponential run time on those instances, and the (1 + 1) EAU finds the global optimum in polynomial time. We conclude by studying the Makespan Scheduling. We consider an instance on which the (1 + 1) EA does not find a (4/3 − )- approximation in polynomial time, and we show that the (1 + 1) EAU reaches a (4/3 −)-approximation in polynomial time. We then prove that the (1 + 1) EAU serves as an Efficient Polynomial-time Approximation Scheme (EPTAS) for the Partition Problem, for a (1 +)-approximation with > 4/n.

AB - In the context of black box optimization, one of the most common ways to handle deceptive attractors is to periodically restart the algorithm. In this paper, we explore the benefits of combining the simple (1+1) Evolutionary Algorithm (EA) with the Luby Universal Strategy - the (1 + 1) EAU , a meta-heuristic that does not require parameter tuning. We first consider two artificial pseudo-Boolean landscapes, on which the (1 + 1) EA exhibits exponential run time. We prove that the (1 + 1) EAU has polynomial run time on both instances. We then consider the Minimum Vertex Cover on two classes of graphs. Again, the (1 + 1) EA yields exponential run time on those instances, and the (1 + 1) EAU finds the global optimum in polynomial time. We conclude by studying the Makespan Scheduling. We consider an instance on which the (1 + 1) EA does not find a (4/3 − )- approximation in polynomial time, and we show that the (1 + 1) EAU reaches a (4/3 −)-approximation in polynomial time. We then prove that the (1 + 1) EAU serves as an Efficient Polynomial-time Approximation Scheme (EPTAS) for the Partition Problem, for a (1 +)-approximation with > 4/n.

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Improving the run time of the (1 + 1) evolutionary algorithm with luby sequences

Abstract

Publication series

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Bibliographical note

Keywords

Publisher link

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