Runtime analysis of the (1+1) evolutionary algorithm for the chance-constrained knapsack problem

Frank Neumann; Andrew M. Sutton

doi:10.1145/3299904.3340315

Runtime analysis of the (1+1) evolutionary algorithm for the chance-constrained knapsack problem

Frank Neumann, Andrew M. Sutton

Computer Science (Duluth)

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

12 Scopus citations

Abstract

The area of runtime analysis has made important contributions to the theoretical understanding of evolutionary algoirthms for stochastic problems in recent years. Important real-world applications involve chance constraints where the goal is to optimize a function under the condition that constraints are only violated with a small probability. We rigorously analyze the runtime of the (1+1) EA for the chance-constrained knapsack problem. In this setting, the weights are stochastic, and the objective is to maximize a linear profit function while minimizing the probability of a constraint violation in the total weight. We investigate a number of special cases for this problem, paying attention to how the structure of the chance constraint influences the runtime behavior of the (1+1) EA. Our results reveal that small changes to the profit value can result in hard-to-escape local optima.

Original language	English (US)
Title of host publication	FOGA 2019 - Proceedings of the 15th ACM/SIGEVO Conference on Foundations of Genetic Algorithms
Publisher	Association for Computing Machinery, Inc
Pages	147-153
Number of pages	7
ISBN (Electronic)	9781450362542
DOIs	https://doi.org/10.1145/3299904.3340315
State	Published - Aug 27 2019
Event	15th ACM/SIGEVO Conference on Foundations of Genetic Algorithms, FOGA 2019 - Potsdam, Germany Duration: Aug 27 2019 → Aug 29 2019

Publication series

Name	FOGA 2019 - Proceedings of the 15th ACM/SIGEVO Conference on Foundations of Genetic Algorithms

Conference

Conference	15th ACM/SIGEVO Conference on Foundations of Genetic Algorithms, FOGA 2019
Country/Territory	Germany
City	Potsdam
Period	8/27/19 → 8/29/19

Bibliographical note

Funding Information:
This work has been supported by the Australian Research Council through grant DP160102401 and by the South Australian Government through the Research Consortium "Unlocking Complex Resources through Lean Processing".

Publisher Copyright:
© 2019 Copyright held by the owner/author(s).

Keywords

Chance-constrained optimization
Evolutionary algorithms
Knapsack problem

Access

10.1145/3299904.3340315

OpenUrl availability

Full text

Cite this

Neumann, F., & Sutton, A. M. (2019). Runtime analysis of the (1+1) evolutionary algorithm for the chance-constrained knapsack problem. In FOGA 2019 - Proceedings of the 15th ACM/SIGEVO Conference on Foundations of Genetic Algorithms (pp. 147-153). (FOGA 2019 - Proceedings of the 15th ACM/SIGEVO Conference on Foundations of Genetic Algorithms). Association for Computing Machinery, Inc. https://doi.org/10.1145/3299904.3340315

Runtime analysis of the (1+1) evolutionary algorithm for the chance-constrained knapsack problem. / Neumann, Frank; Sutton, Andrew M.
FOGA 2019 - Proceedings of the 15th ACM/SIGEVO Conference on Foundations of Genetic Algorithms. Association for Computing Machinery, Inc, 2019. p. 147-153 (FOGA 2019 - Proceedings of the 15th ACM/SIGEVO Conference on Foundations of Genetic Algorithms).

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

Neumann, F & Sutton, AM 2019, Runtime analysis of the (1+1) evolutionary algorithm for the chance-constrained knapsack problem. in FOGA 2019 - Proceedings of the 15th ACM/SIGEVO Conference on Foundations of Genetic Algorithms. FOGA 2019 - Proceedings of the 15th ACM/SIGEVO Conference on Foundations of Genetic Algorithms, Association for Computing Machinery, Inc, pp. 147-153, 15th ACM/SIGEVO Conference on Foundations of Genetic Algorithms, FOGA 2019, Potsdam, Germany, 8/27/19. https://doi.org/10.1145/3299904.3340315

Neumann F, Sutton AM. Runtime analysis of the (1+1) evolutionary algorithm for the chance-constrained knapsack problem. In FOGA 2019 - Proceedings of the 15th ACM/SIGEVO Conference on Foundations of Genetic Algorithms. Association for Computing Machinery, Inc. 2019. p. 147-153. (FOGA 2019 - Proceedings of the 15th ACM/SIGEVO Conference on Foundations of Genetic Algorithms). doi: 10.1145/3299904.3340315

Neumann, Frank ; Sutton, Andrew M. / Runtime analysis of the (1+1) evolutionary algorithm for the chance-constrained knapsack problem. FOGA 2019 - Proceedings of the 15th ACM/SIGEVO Conference on Foundations of Genetic Algorithms. Association for Computing Machinery, Inc, 2019. pp. 147-153 (FOGA 2019 - Proceedings of the 15th ACM/SIGEVO Conference on Foundations of Genetic Algorithms).

@inproceedings{d37a337973e849cf9da11077d23ad30f,

title = "Runtime analysis of the (1+1) evolutionary algorithm for the chance-constrained knapsack problem",

abstract = "The area of runtime analysis has made important contributions to the theoretical understanding of evolutionary algoirthms for stochastic problems in recent years. Important real-world applications involve chance constraints where the goal is to optimize a function under the condition that constraints are only violated with a small probability. We rigorously analyze the runtime of the (1+1) EA for the chance-constrained knapsack problem. In this setting, the weights are stochastic, and the objective is to maximize a linear profit function while minimizing the probability of a constraint violation in the total weight. We investigate a number of special cases for this problem, paying attention to how the structure of the chance constraint influences the runtime behavior of the (1+1) EA. Our results reveal that small changes to the profit value can result in hard-to-escape local optima.",

keywords = "Chance-constrained optimization, Evolutionary algorithms, Knapsack problem",

author = "Frank Neumann and Sutton, {Andrew M.}",

note = "Funding Information: This work has been supported by the Australian Research Council through grant DP160102401 and by the South Australian Government through the Research Consortium {"}Unlocking Complex Resources through Lean Processing{"}. Publisher Copyright: {\textcopyright} 2019 Copyright held by the owner/author(s).; 15th ACM/SIGEVO Conference on Foundations of Genetic Algorithms, FOGA 2019 ; Conference date: 27-08-2019 Through 29-08-2019",

year = "2019",

month = aug,

day = "27",

doi = "10.1145/3299904.3340315",

language = "English (US)",

series = "FOGA 2019 - Proceedings of the 15th ACM/SIGEVO Conference on Foundations of Genetic Algorithms",

publisher = "Association for Computing Machinery, Inc",

pages = "147--153",

booktitle = "FOGA 2019 - Proceedings of the 15th ACM/SIGEVO Conference on Foundations of Genetic Algorithms",

}

TY - GEN

T1 - Runtime analysis of the (1+1) evolutionary algorithm for the chance-constrained knapsack problem

AU - Neumann, Frank

AU - Sutton, Andrew M.

N1 - Funding Information: This work has been supported by the Australian Research Council through grant DP160102401 and by the South Australian Government through the Research Consortium "Unlocking Complex Resources through Lean Processing". Publisher Copyright: © 2019 Copyright held by the owner/author(s).

PY - 2019/8/27

Y1 - 2019/8/27

N2 - The area of runtime analysis has made important contributions to the theoretical understanding of evolutionary algoirthms for stochastic problems in recent years. Important real-world applications involve chance constraints where the goal is to optimize a function under the condition that constraints are only violated with a small probability. We rigorously analyze the runtime of the (1+1) EA for the chance-constrained knapsack problem. In this setting, the weights are stochastic, and the objective is to maximize a linear profit function while minimizing the probability of a constraint violation in the total weight. We investigate a number of special cases for this problem, paying attention to how the structure of the chance constraint influences the runtime behavior of the (1+1) EA. Our results reveal that small changes to the profit value can result in hard-to-escape local optima.

AB - The area of runtime analysis has made important contributions to the theoretical understanding of evolutionary algoirthms for stochastic problems in recent years. Important real-world applications involve chance constraints where the goal is to optimize a function under the condition that constraints are only violated with a small probability. We rigorously analyze the runtime of the (1+1) EA for the chance-constrained knapsack problem. In this setting, the weights are stochastic, and the objective is to maximize a linear profit function while minimizing the probability of a constraint violation in the total weight. We investigate a number of special cases for this problem, paying attention to how the structure of the chance constraint influences the runtime behavior of the (1+1) EA. Our results reveal that small changes to the profit value can result in hard-to-escape local optima.

KW - Chance-constrained optimization

KW - Evolutionary algorithms

KW - Knapsack problem

UR - http://www.scopus.com/inward/record.url?scp=85076409939&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85076409939&partnerID=8YFLogxK

U2 - 10.1145/3299904.3340315

DO - 10.1145/3299904.3340315

M3 - Conference contribution

AN - SCOPUS:85076409939

T3 - FOGA 2019 - Proceedings of the 15th ACM/SIGEVO Conference on Foundations of Genetic Algorithms

SP - 147

EP - 153

BT - FOGA 2019 - Proceedings of the 15th ACM/SIGEVO Conference on Foundations of Genetic Algorithms

PB - Association for Computing Machinery, Inc

T2 - 15th ACM/SIGEVO Conference on Foundations of Genetic Algorithms, FOGA 2019

Y2 - 27 August 2019 through 29 August 2019

ER -

Runtime analysis of the (1+1) evolutionary algorithm for the chance-constrained knapsack problem

Abstract

Publication series

Conference

Bibliographical note

Keywords

Access

OpenUrl availability

Other files and links

Fingerprint

Cite this