Test Function Generators for Assessing the Performance of PSO Algorithms in Multimodal Optimization

The particle swarm optimization (PSO) algorithm has gained increasing popularity in the last few years mainly because of its relative simplicity and its good overall performance, particularly in continuous optimization problems. As PSO is adopted in more types of application domains, it becomes more important to have well-established methodologies to assess its performance. For that purpose, several test problems have been proposed. In this chapter, we review several state-of-the-art test function generators that have been used for assessing the performance of PSO variants. As we will see, such test problems sometimes have regularities which can be easily exploited by PSO (or any other algorithm for that sake) resulting in an outstanding performance. In order to avoid such regularities, we describe here several basic design principles that should be followed when creating a test function generator for single-objective continuous optimization.

[1]  Steven Harrington,et al.  Computer graphics: a programming approach, 2nd ed. , 1987 .

[2]  Thomas Stützle,et al.  Frankenstein's PSO: A Composite Particle Swarm Optimization Algorithm , 2009, IEEE Transactions on Evolutionary Computation.

[3]  Andries Petrus Engelbrecht,et al.  Fundamentals of Computational Swarm Intelligence , 2005 .

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

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

[6]  Antonina Starita,et al.  Particle swarm optimization for multimodal functions: a clustering approach , 2008 .

[7]  Xiaodong Li,et al.  Enhancing the robustness of a speciation-based PSO , 2006, 2006 IEEE International Conference on Evolutionary Computation.

[8]  Xiaodong Li,et al.  A Generator for Multimodal Test Functions with Multiple Global Optima , 2008, SEAL.

[9]  Marcus Gallagher,et al.  A general-purpose tunable landscape generator , 2006, IEEE Transactions on Evolutionary Computation.

[10]  James E. Vastyan,et al.  Computer graphics: A programming approach , 1983 .

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

[12]  Kalyanmoy Deb,et al.  Comparison of multi-modal optimization algorithms based on evolutionary algorithms , 2006, GECCO.

[13]  Maurice Clerc,et al.  The particle swarm - explosion, stability, and convergence in a multidimensional complex space , 2002, IEEE Trans. Evol. Comput..

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

[15]  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.

[16]  Jing J. Liang,et al.  Novel composition test functions for numerical global optimization , 2005, Proceedings 2005 IEEE Swarm Intelligence Symposium, 2005. SIS 2005..

[17]  James Kennedy,et al.  Proceedings of the 1998 IEEE International Conference on Evolutionary Computation [Book Review] , 1999, IEEE Transactions on Evolutionary Computation.

[18]  R.W. Morrison,et al.  A test problem generator for non-stationary environments , 1999, Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406).

[19]  Kalyanmoy Deb,et al.  An Investigation of Niche and Species Formation in Genetic Function Optimization , 1989, ICGA.

[20]  R. Eberhart,et al.  Empirical study of particle swarm optimization , 1999, Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406).

[21]  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.

[22]  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).

[23]  James Kennedy,et al.  Small worlds and mega-minds: effects of neighborhood topology on particle swarm performance , 1999, Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406).