Abstract A global function optimization algorithm based on Newtons law of universal gravitation is proposed, namely maximal gravitation optimization algorithm (MGOA). The search agents are updated through the processes of gravitational clustering and gravitational elimination, which are two main strategies in MGOA. Four lemmas are provided to describe the mathematical foundation, and the convergence of MGOA is strictly proved. Furthermore, the proposed algorithm is improved. The experimental result shows MGOA has good performance in solving continuous function optimization problems, compared with some well-known heuristic search methods such as Particle Swarm Optimization, Differential Evolution, and Guo Tao algorithm.
[1] Holland J H. Adaptation in Natural and Artificial Systems. Ann Arbor, USA: University of Michigan Press, 1975 [2] Kirkpatrick S, Gelatt C D, Vecchi M P. Optimization by Simulated Annealing. Science, 1983, 220(4598): 671-680 [3] Mori K, Tsukiyama M, Fukuda T. Immune Algorithm with Searching Diversity and Its Application to Resource Allocation Problem. Trans of IEE Japan, 1993, 113(10): 872-878 [4] Dorigo M, Maniezzo V, Colorni A. Ant System: Optimization by a Colony of Cooperating Agents. IEEE Trans on Systems, Man and Cybernetics, 1996, 26(1): 29-41 [5] Kennedy J, Eberhart R. Particle Swarm Optimization // Proc of the IEEE International Conference on Neural Networks. Perth, Australia, 1995, Ⅳ: 1942-1948 [6] Storn R, Priee K. Minimizing the Real Functions of the ICEC96 Contest by Differential Evolution // Proc of the IEEE International Conference on Evolutionary Computation. Nagoya, Japan, 1996: 842-844 [7] Voudouris C, Edward T. Guided Local Search. Technical Report, CSM-247, Colchester, UK: University of Essex. Department of Computer Science, 1995 [8] Webster B L. Solving Combinatorial Optimization Problems Using a New Algorithm Based on Gravitational Attraction. Melbourne, USA: Florida Institute of Technology, 2004 [9] Balachandar S R, Kannan K. Randomized Gravitational Emulation Search Algorithm for Symmetric Traveling Salesman Problem. Applied Mathematics and Computation, 2007, 192(2): 413-421 [10] Hsiao Y T, Chuang C L, Jiang J A, et al. A Novel Optimization Algorithm: Space Gravitational Optimization // Proc of the IEEE International Conference on Systems, Man and Cybernetics. Hawaii, USA, 2005, Ⅲ: 2323-2328 [11] Chuang C L, Jiang J A. Integrated Radiation Optimization: Inspired by the Gravitational Radiation in the Curvature of Space-Time // Proc of the IEEE Congress on Evolutionary Computation. Singapore, Singapore, 2007: 3157-3164 [12] Rashedi E. Gravitational Search Algorithm. Kerman, Iran: Shahid Bahonar University of Kerman, 2007 [13] Rashedi E, Nezamabadi-Pour H, Saryazdi S. GSA: A Gravitational Search Algorithm. Information Sciences: An International Journal, 2009, 179(13): 2232-2248 [14] Rashedi E, Nezamabadi-Pour H, Saryazdi S. BGSA: Binary Gravitational Search Algorithm. Natural Computing, 2010, 9: 727-745 [15] Kang Qi, Wang Lei, Wu Qidi. A Novel Self-Organizing Particle Swarm Optimization Based on Gravitation Field Model // Proc of the American Control Conference. New York, USA, 2007: 528-533 [16] Guo Tao. Evolutionary Computation and Optimization. Ph.D Dissertation. Wuhan, China: Wuhan University. School of Computer, 1999 (in Chinese) (郭 涛.演化计算与优化.博士学位论文.武汉:武汉大学.计算机学院, 1999) [17] Xu Zongben. Computational Intelligence- Simulated Evolutionary Computation. Beijing, China: Higher Education Press, 2003 (in Chinese) (徐宗本.计算智能──模拟进化计算.北京:高等教育出版社, 2003) [18] Yang Zhenyu, Tang Ke, Yao Xin. Self-Adaptive Differential Evolution with Neighborhood Search // Proc of the IEEE Congress on Evolutionary Computation. Washington, USA, 2008: 1110-1116
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