蚁群算法原理与应用1.ppt

自然计算与群体智能 赵林亮 计算机应用技术研究所 zhaoll@ 蚁群算法 赵林亮 计算机应用技术研究所 zhaoll@ 参考文献 APPEARED IN PROCEEDINGS OF ECAL91-EUROPEAN CONFERENCE ON ARTIFICIAL LIFE, PARIS, FRANCE, ELSEVIER PUBLISHING,134–142. Distributed Optimization by Ant Colonies Alberto Colorni, Marco Dorigo, Vittorio Maniezzo Dipartimento di Elettronica, Politecnico di Milano Piazza Leonardo da Vinci 32, 20133 Milano, Italy IEEE Transactions on Systems, Man, And Cybernetics- Part B: Cybernetics,Vol.26, No.1, Feb 1996. 29-41 Ant System: Optimization by a Colony of Cooperating Agents Marco Dorigo, Member, IEEE, Vittorio Maniezzo, and Alberto Colorni http://iridia.ulb.ac.be/~mdorigo/HomePageDorigo/ Fig. 1. An example with real ants a) Ants follow a path between points A and E. b) An obstacle is interposed; ants can choose to go around it following one of the two different paths with equal probability. c) On the shorter path more pheromone is laid down. Fig. 2. An example with artificial ants a) The initial graph with distances. b) At time t=0 there is no trail on the graph edges; therefore, ants choose whether to turn right or left with equal probability. c) At time t=1 trail is stronger on shorter edges, which are therefore, in the average, preferred by ants. 双桥实验(Goss S, 1989) Naturwissenschaften 76, 579-581 (1989) Self-organized Shortcuts in the Argentine Ant S. Goss, S. Aron, J. L. Deneubourg, and J. M. Pasteels Unit of Behavioural Ecology, C.P. 231, Universit6 Libre de Bruxelles, B- 1050 Bruxelles Fig. 1. A colony of I humilis selecting the short branches on both modules of the bridge a) one module of the bridge b) and c): photos taken 4 and 8 min after placement of the bridge 双桥实验数学模型 参数h 和 k用以匹配真实实验数据 第m+1只蚂蚁首先计算 然后生成一个在区间[0,1]上均匀分布的随机数 若 ，则选择桥A，否则选择桥B 基本蚁群算法的数学模型 P、NP、NP-C、NP-hard问题 P类问题 所有可用DTM (Deterministic one-tape Turing Machine) 在多项式时间内求解的判定问题Π的集合。简记为O(p(n)) 即 P={L: 存在一个多项式时间DTM程序M，是的L=LM} , 其中LM表示程序M所识别的语言。 若存在一个多项式时间DTM程序，它在编码策略e之下求解判定问题Π，即L[Π, e]∈P,则称该判定问题属于P类问题。 P、NP、NP-C、NP-