A Statistical Analysis of Particle Swarm Optimization With and Without Digital Pheromones

*† Particle Swarm Optimization (PSO) is a population based heuristic search method for finding global optimal values in multi-disciplinary design optimization problems. PSO is based on simple social behavior exhibited by birds and insects. Due to its simplicity in implementation, PSO has been increasingly gaining popularity in the optimization community. Previous work by the authors demonstrated superior design space search capabilities of particle swarm through implementing digital pheromones in a regular PSO. Although preliminary results showed substantial performance gains, a quantitative assessment has not yet been made to prove the claim. Through a formal statistical hypothesis testing, this paper attempts to evaluate the performance characteristics of PSO with digital pheromones. Specifically, the authors’ claim that the use of digital pheromones improves the solution quality and solution times are tested using various multi-dimensional unconstrained optimization test problems. Conclusions are drawn based on the results from statistical analysis of these test problems and presented in the paper.

[1]  Russell C. Eberhart,et al.  A new optimizer using particle swarm theory , 1995, MHS'95. Proceedings of the Sixth International Symposium on Micro Machine and Human Science.

[2]  Jaco F. Schutte,et al.  Particle swarms in sizing and global optimization , 2002 .

[3]  Russell C. Eberhart,et al.  Solving Constrained Nonlinear Optimization Problems with Particle Swarm Optimization , 2002 .

[4]  Eliot Winer,et al.  Digital Pheromone Implementation of PSO with Velocity Vector Accelerated by Commodity Graphics Hardware , 2006 .

[5]  R. H. Myers,et al.  Probability and Statistics for Engineers and Scientists , 1978 .

[6]  Russell C. Eberhart,et al.  Parameter Selection in Particle Swarm Optimization , 1998, Evolutionary Programming.

[7]  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).

[8]  E. Bonabeau,et al.  Swarm Intelligence: A New C2 Paradigm with an Application to Control Swarms of UAVs , 2003 .

[9]  B J Fregly,et al.  Parallel global optimization with the particle swarm algorithm , 2004, International journal for numerical methods in engineering.

[10]  Marco Dorigo,et al.  Distributed Optimization by Ant Colonies , 1992 .

[11]  H. Van Dyke Parunak,et al.  DIGITAL PHEROMONES FOR AUTONOMOUS COORDINATION OF SWARMING UAV'S , 2002 .

[12]  James Kennedy,et al.  Particle swarm optimization , 2002, Proceedings of ICNN'95 - International Conference on Neural Networks.

[13]  Raymond H. Myers,et al.  Probability and Statistics for Engineers and Scientists (2nd ed.). , 1979 .

[14]  Tim Urdan,et al.  Statistics in Plain English , 2001 .

[15]  Yuhui Shi,et al.  Particle swarm optimization: developments, applications and resources , 2001, Proceedings of the 2001 Congress on Evolutionary Computation (IEEE Cat. No.01TH8546).

[16]  Sheldon M. Ross,et al.  Introduction to Probability and Statistics for Engineers and Scientists , 1987 .

[17]  Russell C. Eberhart,et al.  Particle swarm with extended memory for multiobjective optimization , 2003, Proceedings of the 2003 IEEE Swarm Intelligence Symposium. SIS'03 (Cat. No.03EX706).

[18]  Hitoshi Iba,et al.  Particle swarm optimization with Gaussian mutation , 2003, Proceedings of the 2003 IEEE Swarm Intelligence Symposium. SIS'03 (Cat. No.03EX706).

[19]  Richard L. Scheaffer,et al.  Probability and statistics for engineers , 1986 .

[20]  Marco Dorigo,et al.  Ant system: optimization by a colony of cooperating agents , 1996, IEEE Trans. Syst. Man Cybern. Part B.

[21]  Tony White,et al.  Towards multi-swarm problem solving in networks , 1998, Proceedings International Conference on Multi Agent Systems (Cat. No.98EX160).

[22]  Eliot Winer,et al.  A parallel implementation of particle swarm optimization using digital pheromones , 2006 .

[23]  Russell C. Eberhart,et al.  Swarm intelligence for permutation optimization: a case study of n-queens problem , 2003, Proceedings of the 2003 IEEE Swarm Intelligence Symposium. SIS'03 (Cat. No.03EX706).

[24]  Jaroslaw Sobieszczanski-Sobieski,et al.  Multidisciplinary optimization of a transport aircraft wing using particle swarm optimization , 2002 .

[25]  B. P. Wang,et al.  Particle Swarm Optimization for Mixed Discrete, Integer and Continuous Variables , 2004 .

[26]  A Kaveh,et al.  ENGINEERING OPTIMIZATION WITH HYBRID PARTICLE SWARM AND ANT COLONY OPTIMIZATION , 2009 .

[27]  James H. Oliver,et al.  UAV Swarm Control: Calculating Digital Pheromone Fields with the GPU , 2006 .

[28]  Stephen B. Vardeman,et al.  Probability and Statistics for Engineers and Scientists.@@@Probability and Statistics for Engineers. , 1986 .

[29]  Byung-Il Koh,et al.  Parallel asynchronous particle swarm optimization , 2006, International journal for numerical methods in engineering.