TY - GEN

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

AU - Neumann, Frank

AU - Sutton, Andrew M.

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 -