ABSTRACT
At present the fitness-distance-ratio particle swarm optimizer (FDR-PSO) has undergone no form of theoretical stability analysis. This paper theoretically derives the conditions necessary for order-1 and order-2 stability under the well known stagnation assumption. Since it has been shown that particle stability has a meaningful impact on PSO's performance, it is important for PSO practitioners to know the actual criteria for particle stability. This paper validates its theoretical findings against an assumption free FDR-PSO algorithm. This empirical validation is necessary for a truly accurate representation of FDR-PSO's stability criteria.
Supplemental Material
Available for Download
Supplemental material.
- K. Atkinson and W. Han. 2009. Theoretical Numerical Analysis: A Functional Analysis Framework. Springer, Heidelberg, Berlin.Google Scholar
- A. Banks, J. Vincent, and C. Anyakoha. 2007. A review of particle swarm optimization, part i: background and development. Natural Computing 6, 4 (2007), 467--484. Google ScholarDigital Library
- A. Banks, J. Vincent, and C. Anyakoha. 2008. review of particle swarm optimization, part ii: hybridisation, combinatorial, multicriteria and constrained optimization, and indicative applications. Natural Computing 7, 1 (2008), 109--124. Google ScholarDigital Library
- T. Blackwell. 2012. A Study of Collapse in Bare Bones Particle Swarm Optimzation. IEEE Transactions on Evolutionary Computation 16, 3 (2012), 354--372. Google ScholarDigital Library
- M.R. Bonyadi and Z. Michalewicz. 2016. Particle swarm optimization for single objective continuous space problems: a review. Evolutionary Computation (2016), 1--54. Google ScholarDigital Library
- M.R. Bonyadi and Z. Michalewicz. 2016. Stability analysis of the particle swarm optimization without stagnation assumption. IEEE Transactions on Evolutionary Computation 20, 5 (2016), 814--819.Google ScholarCross Ref
- C.W. Cleghorn and A.P. Engelbrecht. 2014. A generalized theoretical deterministic particle swarm model. Swarm Intelligence 8, 1 (2014), 35--59.Google ScholarCross Ref
- C.W. Cleghorn and A.P. Engelbrecht. 2014. Particle Swarm Convergence: Standardized Analysis and Topological Influence. In Proceedings of International Swarm Intelligence Conference (ANTS), Swarm Intelligence. Springer International Publishing, Switzerland, 134--145.Google Scholar
- C.W. Cleghorn and A.P. Engelbrecht. 2015. Fully informed particle swarm optimizer: Convergence analysis. In Proceedings of the IEEE Congress on Evolutionary Computation. IEEE Press, Piscataway, NJ, 164--170.Google Scholar
- C.W. Cleghorn and A.P. Engelbrecht. 2015. Particle Swarm Variants: Standardized Convergence Analysis. Swarm Intelligence 9, 2--3 (2015), 177--203.Google ScholarCross Ref
- C.W. Cleghorn and A.P. Engelbrecht. 2016. Particle Swarm Optimizer: The Impact of Unstable Particles on Performance. In Proceedings of the IEEE Symposium Series on Swarm Intelligence. IEEE Press, Piscataway, NJ, 1--7.Google Scholar
- C.W. Cleghorn and A.P. Engelbrecht. 2016. Unified Particle Swarm Optimizer: Convergence Analysis. In Proceedings of the IEEE Congress on Evolutionary Computation. IEEE Press, Piscataway, NJ, 448--454.Google Scholar
- M. Clerc. 1999. The Swarm and the Queen: Towards a Deterministic and Adaptive Particle Swarm Optimization. In Proceedings of the IEEE Congress on Evolutionary Computation, Vol. 3. IEEE Press, Piscataway, NJ, USA, 1951--1957.Google ScholarCross Ref
- M. Clerc and J. Kennedy. 2002. The Particle Swarm-Explosion, Stability, and Convergence in a Multidimensional Complex Space. IEEE Transactions on Evolutionary Computation 6, 1 (2002), 58--73. Google ScholarDigital Library
- A.P. Engelbrecht. 2013. Particle Swarm Optimization: Global Best or Local Best?. In Proceedings of the 1st BRICS Countries Congress on Computational Intelligence. IEEE Press, Piscataway, NJ, 124--135. Google ScholarDigital Library
- A.P. Engelbrecht. 2013. Roaming Behavior of Unconstrained Particles. In Proceedings of the 1st BRICS Countries Congress on Computational Intelligence. IEEE Press, Piscataway, NJ, 104--111. Google ScholarDigital Library
- E. García-Gonzalo and J.L. Fernández-Martinez. 2014. Convergence and stochastic stability analysis of particle swarm optimization variants with generic parameter distributions. Appl. Math. Comput. 249 (2014), 286--302. Google ScholarDigital Library
- V. Gazi. 2012. Stochastic Stability Analysis of the Particle Dynamics in the PSO Algorithm. In Proceedings of the IEEE International Symposium on Intelligent Control. IEEE Press, Piscataway, 708--713.Google ScholarCross Ref
- K.H. Harrison, A.P. Engelbrecht, and B.M. Ombuki-Berman. 2016. The sad state of self-adaptive particle swarm optimizers. In Proceedings of the IEEE Congress on Evolutionary Computation. IEEE Press, Piscataway, NJ, 431--439.Google Scholar
- X. Hu, Y. Shi, and R. Eberhart. 2004. Recent advances in particle swarm.. In Proceedings of the IEEE Congress on Evolutionary Computation. IEEE Press, Piscataway, NJ, 90--97.Google Scholar
- M. Jiang, Y.P. Luo, and S.Y. Yang. 2007. Stochastic convergence analysis and parameter selection of the standard particle swarm optimization algorithm. Inform. Process. Lett. 102, 1 (2007), 8--16. Google ScholarDigital Library
- V. Kadirkamanathan, K. Selvarajah, and P.J. Fleming. 2006. Stability Analysis of the Particle Dynamics in Particle Swarm Optimizer. IEEE Transactions on Evolutionary Computation 10, 3 (2006), 245--255. Google ScholarDigital Library
- J. Kennedy. 1999. Small worlds and mega-minds: effects of neighborhood topology on particle swarm performance. In Proceedings of the IEEE Congress on Evolutionary Computation, Vol. 3. IEEE Press, Piscataway, NJ, 1931--1938.Google ScholarCross Ref
- J. Kennedy and R.C. Eberhart. 1995. Particle Swarm Optimization. In Proceedings of the IEEE International Joint Conference on Neural Networks. IEEE Press, Piscataway, NJ, 1942--1948.Google Scholar
- J. Kennedy and R. Mendes. 2002. Population Structure and Particle Performance. In Proceedings of the IEEE Congress on Evolutionary Computation. IEEE Press, Piscataway, NJ, 1671--1676. Google ScholarDigital Library
- Q. Liu. 2015. Order-2 Stability Analysis of Particle Swarm Optimization. Evolutionary Computation 23, 2 (2015), 187--216. Google ScholarDigital Library
- E. Ozcan and C.K. Mohan. 1998. Analysis of a simple particle swarm optimization system. Intelligent Engineering Systems through Artificial Neural Networks 8 (1998), 253--258.Google Scholar
- E. Ozcan and C.K. Mohan. 1999. Particle Swarm Optimization: Surfing the Waves. In Proceedings of the IEEE Congress on Evolutionary Computation, Vol. 3. IEEE Press, Piscataway, NJ, USA, 1939--1944.Google Scholar
- T. Peram, K. Veeramachaneni, and C.K Mohan. 2003. Fitness-Distance-Ratio Based Particle Swarm Optiniization. In Proceedings of the IEEE Swarm Intelligence Symposium. IEEE Press, Piscataway, NJ, 174--181.Google Scholar
- R. Poli. 2008. Analysis of the Publications on the Applications of Particle Swarm Optimisation. Journal of Artificial Evolution and Applications 2008 (2008), 1--10.Google Scholar
- R. Poli. 2009. Mean and variance of the sampling distribution of particle swarm optimizers during stagnation. IEEE Transactions on Evolutionary Computation 13, 4 (2009), 712--721. Google ScholarDigital Library
- R. Poli and D. Broomhead. 2007. Exact analysis of the sampling distribution for the canonical particle swarm optimiser and its convergence during stagnation. In Proceedings of the Genetic and Evolutionary Computation Conference. ACM Press, New York, NY, 134--141. Google ScholarDigital Library
- R. Poli, J. Kennedy, and T Blackwell. 2007. Particle swarm optimization. An overview. Swarm Intelligence 1, 1 (2007), 33--57.Google ScholarCross Ref
- Y. Shi and R.C. Eberhart. 1998. A Modified Particle Swarm Optimizer. In Proceedings of the IEEE Congress on Evolutionary Computation. IEEE Press, Piscataway, NJ, 69--73.Google Scholar
- I.C Trelea. 2003. The Particle Swarm Optimization Algorithm: Convergence Analysis and Parameter Selection. Inform. Process. Lett. 85, 6 (2003), 317--325. Google ScholarDigital Library
- F. Van den Bergh and A.P. Engelbrecht. 2006. A Study of Particle Swarm Optimization Particle Trajectories. Information Sciences 176, 8 (2006), 937--971. Google ScholarDigital Library
Index Terms
- Fitness-distance-ratio particle swarm optimization: stability analysis
Recommendations
An improved cooperative quantum-behaved particle swarm optimization
Particle swarm optimization (PSO) is a population-based stochastic optimization. Its parameters are easy to control, and it operates easily. But, the particle swarm optimization is a local convergence algorithm. Quantum-behaved particle swarm ...
An enhanced particle swarm optimization with levy flight for global optimization
Enhanced PSO with levy flight.Random walk of the particles.High convergence rate.Provides solution accuracy and robust. Hüseyin Haklı and Harun Uguz (2014) proposed a novel approach for global function optimization using particle swarm optimization with ...
Cellular particle swarm optimization
This paper proposes a cellular particle swarm optimization (CPSO), hybridizing cellular automata (CA) and particle swarm optimization (PSO) for function optimization. In the proposed CPSO, a mechanism of CA is integrated in the velocity update to modify ...
Comments