| 元胞蚂蚁算法的收敛性分析 |
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| 引用本文： | 朱刚,马良,高岩. 元胞蚂蚁算法的收敛性分析[J]. 系统仿真学报, 2007, 19(7): 1442-1444,1459 |
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| 作者姓名： | 朱刚 马良 高岩 |
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| 作者单位： | 1. 上海理工大学管理学院,上海,200093;上海第二工业大学电子电气工程学院,上海,201209
2. 上海理工大学管理学院,上海,200093 |
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| 基金项目： | 国家自然科学基金;上海市重点学科建设项目 |
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| 摘 要： | 提出一种新的优化算法，元胞蚂蚁算法，该算法将元胞自动机的邻居和规则引入传统的蚂蚁算法，实验结果证明该算法可行且有效，有良好的全局优化能力。定义元胞蚂蚁算法的求解迭代过程为一个概率测度空间中的随机算子，利用随机不动点理论，证明了该算子为连续压缩算子，存在唯一的随机不动点，从而给出了元胞蚂蚁算法的收敛性的论证，为算法奠定了相应的理论基础。
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| 关 键 词： | 蚂蚁算法 元胞自动机 随机不动点理论 收敛性 |
| 文章编号： | 1004-731X（2007）07-1442-03 |
| 收稿时间： | 2006-02-22 |
| 修稿时间： | 2006-02-222007-01-10 |
Convergence Analysis of Cellular Ant Algorithm |
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| ZHU Gang,MA Liang,GAO Yan. Convergence Analysis of Cellular Ant Algorithm[J]. Journal of System Simulation, 2007, 19(7): 1442-1444,1459 |
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| Authors: | ZHU Gang MA Liang GAO Yan |
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| Affiliation: | 1. College of Management, University of Shanghai for Science and Technology, Shanghai 200093, China; 2. College of Electronic and Electric Engineering, Shanghai Second Polytechnic University, Shanghai 201209, China |
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| Abstract: | A new optimization algorithm-cellular ant algorithm was proposed. The proposed algorithm introduces the concept of neighborhood and the rule of cellular automata into the conventional ant algorithm. Experimental results of numerical simulation show the robustness and efficiency of the algorithm. The process of iterative problem solving of cellular ant algorithm was defined as a random operator of probability measure space. The proof of the operator was a continuous and compress operator and has only random fixed point by the theory of random fixed point. So the convergence proof of cellular ant algorithm was given, which makes the relevant theoretical foundation of the convergence property of the algorithm. |
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| Keywords: | ant algorithm cellular automata random fixed point convergence |
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