A locally convergent rotationally invariant particle swarm optimization algorithm

Bonyadi, Mohammad Reza and Michalewicz, Zbigniew (2014) A locally convergent rotationally invariant particle swarm optimization algorithm. Swarm Intelligence, 8 3: 159-198. doi:10.1007/s11721-014-0095-1


Author Bonyadi, Mohammad Reza
Michalewicz, Zbigniew
Title A locally convergent rotationally invariant particle swarm optimization algorithm
Journal name Swarm Intelligence   Check publisher's open access policy
ISSN 1935-3820
1935-3812
Publication date 2014-09-01
Year available 2014
Sub-type Article (original research)
DOI 10.1007/s11721-014-0095-1
Open Access Status Not yet assessed
Volume 8
Issue 3
Start page 159
End page 198
Total pages 40
Place of publication New York, NY, United States
Publisher Springer New York LLC
Language eng
Formatted abstract
Several well-studied issues in the particle swarm optimization algorithm are outlined and some earlier methods that address these issues are investigated from the theoretical and experimental points of view. These issues are the: stagnation of particles in some points in the search space, inability to change the value of one or more decision variables, poor performance when the swarm size is small, lack of guarantee to converge even to a local optimum (local optimizer), poor performance when the number of dimensions grows, and sensitivity of the algorithm to the rotation of the search space. The significance of each of these issues is discussed and it is argued that none of the particle swarm optimizers we are aware of can address all of these issues at the same time. To address all of these issues at the same time, a new general form of velocity update rule for the particle swarm optimization algorithm that contains a user-definable function f is proposed. It is proven that the proposed velocity update rule guarantees to address all of these issues if the function f satisfies the following two conditions: (i) the function f is designed in such a way that for any input vector (y→) in the search space, there exists a region A which contains (y) and f(y) can be located anywhere in A, and (ii) f is invariant under any affine transformation. An example of function f is provided that satisfies these conditions and its performance is examined through some experiments. The experiments confirm that the proposed algorithm (with an appropriate function f) can effectively address all of these issues at the same time. Also, comparisons with earlier methods show that the overall ability of the proposed method for solving benchmark functions is significantly better.
Keyword Local convergence
Particle swarm optimizer
Rotation invariance
Stagnation
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Non-UQ

Document type: Journal Article
Sub-type: Article (original research)
Collection: School of Information Technology and Electrical Engineering Publications
 
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Citation counts: TR Web of Science Citation Count  Cited 7 times in Thomson Reuters Web of Science Article | Citations
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