Abstract
At present particle swarm optimizers (PSO) designed for multi-objective optimization have undergone no form of theoretical stability analysis. This paper derives the sufficient and necessary conditions for order-1 and order-2 stability of the recently proposed multi-guided PSO (MGPSO), which was designed specifically for multi-objective optimization. The paper utilizes a recently published theorem for performing stability analysis on PSO variants, which requires minimal modeling assumptions. It is vital for PSO practitioners to know the actual criteria for particle stability of the given PSO variant being used, as it been shown that particle stability has a considerable impact on PSO’s performance. This paper empirically validates its theoretical findings by comparing the derived stability criteria against those of an assumption free MGPSO algorithm. It was found that the derived criteria for order-1 and order-2 stability are an accurate predictor of the unsimplified MGPSO’s particle behavior.
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Notes
- 1.
\(\rho (\mathbf {M})\) denotes the spectral radius of the matrix \(\mathbf {M}\).
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Cleghorn, C.W., Scheepers, C., Engelbrecht, A.P. (2018). Stability Analysis of the Multi-objective Multi-guided Particle Swarm Optimizer. In: Dorigo, M., Birattari, M., Blum, C., Christensen, A., Reina, A., Trianni, V. (eds) Swarm Intelligence. ANTS 2018. Lecture Notes in Computer Science(), vol 11172. Springer, Cham. https://doi.org/10.1007/978-3-030-00533-7_16
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