Abstract A quantitative description of diversity in population-based search algorithms is put forward by comparing distribution entropy with variance. The problem of mode classification in individual space is presented for multimodal cases in optimization computation, and a classification method is proposed. On the basis of clustering analysis, the class distribution of individuals in search space is acquired. Furthermore, the diversity index described by distribution entropy is obtained. Then, diversity control is implemented by aggregation and dilation among individuals according to diversity. As an example, a first-order aggregation and dilation (A&D) algorithm for diversity control is presented and the setting of its parameters is analyzed. Simulation results demonstrate that the proposed algorithm performs better than the canonical genetic algorithm, the particle swarm optimization and the A&D search algorithm without classification.
[1] Holland J H. Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence. Michigan, USA: University of Michigan Press, 1975 [2] Kennedy J, Eberhart R. Particle Swarm Optimization // Proc of the IEEE International Conference on Neural Networks. Perth, Australia, 1995: 1942-1948 [3] Colorni A, Dorigo M, Maniezzo V. Distributed Optimization by Ant Colonies // Proc of the 1st European Conference on Artificial Life. Paris, France, 1992: 134-142 [4] Chen Jie, Xin Bin, Dou Lihua. Centralization and Decentralization of Intelligent Optimization. CAAI Trans on Intelligent Systems, 2007, 2(2): 48-56 (in Chinese) (陈 杰,辛 斌,窦丽华.关于智能优化方法的集聚性与弥散性问题.智能系统学报, 2007, 2(2): 48-56) [5] Deb K, Pratap A, Agarwal S, et al. A Fast and Elitist Multiobjective Genetic Algorithm: NSGA-II. IEEE Trans on Evolutionary Computation, 2002, 6(2): 182-197 [6] Mengshoel O J, Goldberg D E. Probabilistic Crowding: Deterministic Crowding with Probabilistic Replacement // Proc of the Conference on Genetic and Evolutionary Computation. Orlando, USA, 1999: 173-179 [7] Greenwood G W, Fogel G B, Ciobanu M. Emphasizing Extinction in Evolutionary Programming // Proc of the Congress on Evolutionary Computation. Washington, USA, 1999, Ⅰ: 666-671 [8] Riget J, Vesterstroem J S. A Diversity-Guided Particle Swarm Optimizer — The ARPSO. Technical Report, 2002-02, Aarhus, Germany: University of Aarhus. Department of Computer Science, 2002 [9] Blackwell T, Branke J. Multiswarms, Exclusion, and Anti-Convergence in Dynamic Environments. IEEE Trans on Evolutionary Computation, 2006, 10(4): 459-472 [10] Ursem R K. Diversity-Guided Evolutionary Algorithms // Proc of the 7th International Conference on Parallel Problem Solving from Nature. Granada, Spain, 2002: 462-471 [11] Cover T M, Thomas J A. Element of Information Theory. New York, USA: John Wiley &Sons, 2001 [12] Clerc M, Kennedy J. The Particle Swarm — Explosion, Stability and Convergence in a Multi-Dimensional Complex Space. IEEE Trans on Evolutionary Computation, 2002, 6(1): 58-73
2009, Vol. 22 
