An Analysis of Control Parameter Importance in the Particle Swarm Optimization Algorithm

Particle swarm optimization (PSO) is a stochastic search algorithm based on the social dynamics of a flock of birds. The performance of the PSO algorithm is known to be sensitive to the values assigned to its control parameters, and appropriate tuning of these control parameters can greatly improve performance. This paper employs function analysis of variance (fANOVA) to quantify the importance of each of the three conventional PSO control parameters, namely the inertia weight (\(\omega \)), the cognitive acceleration coefficient (\(c_1\)), and the social acceleration coefficient (\(c_2\)), according to their respective variances associated with the fitness. Results indicate that the inertia value, \(\omega \), has the greatest sensitivity to its assigned value and thus is the most important parameter to tune when optimizing PSO performance for low dimensional problems.

[1]  Andries Petrus Engelbrecht,et al.  Comparison of self-adaptive particle swarm optimizers , 2014, 2014 IEEE Symposium on Swarm Intelligence.

[2]  Fernando J. Von Zuben,et al.  Necessary and Sufficient Conditions for Surrogate Functions of Pareto Frontiers and Their Synthesis Using Gaussian Processes , 2017, IEEE Transactions on Evolutionary Computation.

[3]  Kevin Leyton-Brown,et al.  An Efficient Approach for Assessing Hyperparameter Importance , 2014, ICML.

[4]  Narasimhan Sundararajan,et al.  Self regulating particle swarm optimization algorithm , 2015, Inf. Sci..

[5]  Riccardo Poli,et al.  Particle swarm optimization , 1995, Swarm Intelligence.

[6]  Ilya M. Sobol,et al.  Sensitivity Estimates for Nonlinear Mathematical Models , 1993 .

[7]  R. Eberhart,et al.  Comparing inertia weights and constriction factors in particle swarm optimization , 2000, Proceedings of the 2000 Congress on Evolutionary Computation. CEC00 (Cat. No.00TH8512).

[8]  M. Jiang,et al.  Particle Swarm Optimization - Stochastic Trajectory Analysis and Parameter Selection , 2007 .

[9]  Thomas Stützle,et al.  F-Race and Iterated F-Race: An Overview , 2010, Experimental Methods for the Analysis of Optimization Algorithms.

[10]  Andries Petrus Engelbrecht,et al.  Particle swarm optimizer: The impact of unstable particles on performance , 2016, 2016 IEEE Symposium Series on Computational Intelligence (SSCI).

[11]  Harold J. Kushner,et al.  A New Method of Locating the Maximum Point of an Arbitrary Multipeak Curve in the Presence of Noise , 1964 .

[12]  Andries Petrus Engelbrecht,et al.  Particle swarm optimization: Velocity initialization , 2012, 2012 IEEE Congress on Evolutionary Computation.

[13]  James Kennedy,et al.  Defining a Standard for Particle Swarm Optimization , 2007, 2007 IEEE Swarm Intelligence Symposium.

[14]  Yue Shi,et al.  A modified particle swarm optimizer , 1998, 1998 IEEE International Conference on Evolutionary Computation Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98TH8360).

[15]  Wei Zhang,et al.  A parameter selection strategy for particle swarm optimization based on particle positions , 2014, Expert Syst. Appl..

[16]  Gang Xu,et al.  An adaptive parameter tuning of particle swarm optimization algorithm , 2013, Appl. Math. Comput..

[17]  Andries Petrus Engelbrecht,et al.  Particle swarm stability: a theoretical extension using the non-stagnate distribution assumption , 2018, Swarm Intelligence.

[18]  Qunfeng Liu,et al.  Order-2 Stability Analysis of Particle Swarm Optimization , 2015, Evolutionary Computation.

[19]  Andries Petrus Engelbrecht,et al.  The sad state of self-adaptive particle swarm optimizers , 2016, 2016 IEEE Congress on Evolutionary Computation (CEC).

[20]  Shiyuan Yang,et al.  Stochastic convergence analysis and parameter selection of the standard particle swarm optimization algorithm , 2007, Inf. Process. Lett..

[21]  Ioan Cristian Trelea,et al.  The particle swarm optimization algorithm: convergence analysis and parameter selection , 2003, Inf. Process. Lett..

[22]  Frans van den Bergh,et al.  An analysis of particle swarm optimizers , 2002 .

[23]  Saman K. Halgamuge,et al.  Self-organizing hierarchical particle swarm optimizer with time-varying acceleration coefficients , 2004, IEEE Transactions on Evolutionary Computation.

[24]  Zbigniew Michalewicz,et al.  Impacts of Coefficients on Movement Patterns in the Particle Swarm Optimization Algorithm , 2017, IEEE Transactions on Evolutionary Computation.

[25]  Andries Petrus Engelbrecht,et al.  Optimal parameter regions and the time-dependence of control parameter values for the particle swarm optimization algorithm , 2018, Swarm Evol. Comput..

[26]  Andries Petrus Engelbrecht,et al.  Self-adaptive particle swarm optimization: a review and analysis of convergence , 2017, Swarm Intelligence.

[27]  Michael N. Vrahatis,et al.  Tuning PSO Parameters Through Sensitivity Analysis , 2002 .

[28]  Andries Petrus Engelbrecht,et al.  A study of particle swarm optimization particle trajectories , 2006, Inf. Sci..

[29]  Holger H. Hoos,et al.  Algorithm Configuration Landscapes: - More Benign Than Expected? , 2018, PPSN.

[30]  Andries Petrus Engelbrecht,et al.  Inertia weight control strategies for particle swarm optimization , 2016, Swarm Intelligence.

[31]  Jun Zhang,et al.  Adaptive Particle Swarm Optimization , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[32]  J. Kennedy,et al.  Population structure and particle swarm performance , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).