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A new particle swarm optimization algorithm for noisy optimization problems

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Abstract

We propose a new particle swarm optimization algorithm for problems where objective functions are subject to zero-mean, independent, and identically distributed stochastic noise. While particle swarm optimization has been successfully applied to solve many complex deterministic nonlinear optimization problems, straightforward applications of particle swarm optimization to noisy optimization problems are subject to failure because the noise in objective function values can lead the algorithm to incorrectly identify positions as the global/personal best positions. Instead of having the entire swarm follow a global best position based on the sample average of objective function values, the proposed new algorithm works with a set of statistically global best positions that include one or more positions with objective function values that are statistically equivalent, which is achieved using a combination of statistical subset selection and clustering analysis. The new PSO algorithm can be seamlessly integrated with adaptive resampling procedures to enhance the capability of PSO to cope with noisy objective functions. Numerical experiments demonstrate that the new algorithm is able to consistently find better solutions than the canonical particle swarm optimization algorithm in the presence of stochastic noise in objective function values with different resampling procedures.

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  1. Department of Systems Engineering and Operations Research, George Mason University, Fairfax, VA, 22030, USA

    Sajjad Taghiyeh & Jie Xu

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  1. Sajjad Taghiyeh
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  2. Jie Xu
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Correspondence to Jie Xu.

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This work was supported in part by the National Science Foundation under Grant CMMI-1233376.

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Taghiyeh, S., Xu, J. A new particle swarm optimization algorithm for noisy optimization problems. Swarm Intell 10, 161–192 (2016). https://doi.org/10.1007/s11721-016-0125-2

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