Measuring Diversity in the Cooperative Particle Swarm Optimizer

Diversity is an important aspect of population-based search algorithms such as particle swarm optimizers (PSO) since it influences their performance. Diversity is closely linked to the exploration-exploitation tradeoff. High diversity facilitates exploration, which is usually required during the initial iterations of the optimization algorithm. A low diversity is indicative of exploitation of a small area of the search space, desired during the latter part of the optimization process. The success of the Cooperative Particle Swarm Optimizer (CPSO), a variant of PSO which has outperformed the basic PSO on numerous multi-modal functions, has been ascribed to its increased diversity. Although numerous population diversity measures have been proposed for the basic PSO, not all can be readily applied to the CPSO. This paper proposes a measurement of diversity for the CPSO which is compared with three other diversity measures to establish the most appropriate diversity measure for CPSO. The proposed diversity measure is applied to the CPSO on a few well known test functions and compared with the diversity of the basic global best PSO with the objective to justify the claim that the CPSO increases diversity. The paper also investigates whether diversity increases with an increase in the number of subswarms of the CPSO.

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

[2]  Andries Petrus Engelbrecht,et al.  A Cooperative approach to particle swarm optimization , 2004, IEEE Transactions on Evolutionary Computation.

[3]  Russell C. Eberhart,et al.  Population diversity of particle swarms , 2008, 2008 IEEE Congress on Evolutionary Computation (IEEE World Congress on Computational Intelligence).

[4]  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.

[5]  Andries Petrus Engelbrecht,et al.  Measuring exploration/exploitation in particle swarms using swarm diversity , 2008, 2008 IEEE Congress on Evolutionary Computation (IEEE World Congress on Computational Intelligence).

[6]  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).

[7]  Yuhui Shi,et al.  Diversity control in particle swarm optimization , 2011, 2011 IEEE Symposium on Swarm Intelligence.

[8]  Chongzhao Han,et al.  Knowledge-based cooperative particle swarm optimization , 2008, Appl. Math. Comput..

[9]  Millie Pant,et al.  A Simple Diversity Guided Particle Swarm Optimization , 2007, 2007 IEEE Congress on Evolutionary Computation.

[10]  Yu Cui,et al.  A diversity guided PSO combined with BP for feedforward neural networks , 2010, 2010 3rd International Congress on Image and Signal Processing.

[11]  James Kennedy,et al.  Particle swarm optimization , 1995, Proceedings of ICNN'95 - International Conference on Neural Networks.

[12]  R. Thangaraj,et al.  A New Particle Swarm Optimization with Quadratic Crossover , 2007, 15th International Conference on Advanced Computing and Communications (ADCOM 2007).

[13]  Jing J. Liang,et al.  Comprehensive learning particle swarm optimizer for global optimization of multimodal functions , 2006, IEEE Transactions on Evolutionary Computation.

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

[15]  R. Salomon.  Re-evaluating genetic algorithm performance under coordinate rotation of benchmark functions. A survey of some theoretical and practical aspects of genetic algorithms. , 1996, Bio Systems.