现代智能优化算法-粒子群算法 华北电力大学输配电系统研究所 刘自发 2008年3月 1/18/2019 Ladies and Gentlemen: I am from Tsinghua University in China. The topic of my presentation is “A Dissipative Particle Swarm Optimization”. Since the student, Xiao-Feng Xie, which is the first author, is refused by the visa officer with some unfair reasons, if some details are not be presented clearly, please contact him by this address&.

背景 粒子群算法原理 粒子群算法模型流程 粒子群算法的应用 1/18/2019 Ladies and Gentlemen: I am from Tsinghua University in China. The topic of my presentation is “A Dissipative Particle Swarm Optimization”. Since the student, Xiao-Feng Xie, which is the first author, is refused by the visa officer with some unfair reasons, if some details are not be presented clearly, please contact him by this address&.

粒子群算法---背景 起源： 生物社会学家对鸟群捕食行为研究 1/18/2019 Ladies and Gentlemen: I am from Tsinghua University in China. The topic of my presentation is “A Dissipative Particle Swarm Optimization”. Since the student, Xiao-Feng Xie, which is the first author, is refused by the visa officer with some unfair reasons, if some details are not be presented clearly, please contact him by this address&.

粒子群算法---背景 1/18/2019 我们可以设想这样的一个场景，一群鳥在随机搜寻食物。这个区域裡只有一块食物。所有的鸟都不知道食物在哪里，那么找到食物的最佳策略是什么？最简单的方法就是找尋距离食物最近的鸟的周围区域及根据自己本身飞行的经验判断食物的所在。 Ladies and Gentlemen: I am from Tsinghua University in China. The topic of my presentation is “A Dissipative Particle Swarm Optimization”. Since the student, Xiao-Feng Xie, which is the first author, is refused by the visa officer with some unfair reasons, if some details are not be presented clearly, please contact him by this address&.

鸟群觅食行为 Food Global Best Solution Past Best Solution

Particle Swarm Optimization (PSO)为James Kennedy 于1995年提出。 1/18/2019 Particle Swarm Optimization (PSO)为James Kennedy 于1995年提出。 Ladies and Gentlemen: I am from Tsinghua University in China. The topic of my presentation is “A Dissipative Particle Swarm Optimization”. Since the student, Xiao-Feng Xie, which is the first author, is refused by the visa officer with some unfair reasons, if some details are not be presented clearly, please contact him by this address&.

1/18/2019 PSO特点： PSO is a robust stochastic optimization technique based on the movement and intelligence of swarms. PSO applies the concept of social interaction to problem solving. It was developed in 1995 by James Kennedy (social-psychologist) and Russell Eberhart (electrical engineer). Ladies and Gentlemen: I am from Tsinghua University in China. The topic of my presentation is “A Dissipative Particle Swarm Optimization”. Since the student, Xiao-Feng Xie, which is the first author, is refused by the visa officer with some unfair reasons, if some details are not be presented clearly, please contact him by this address&.

1/18/2019 PSO特点： It uses a number of agents (particles) that constitute a swarm moving around in the search space looking for the best solution. Each particle is treated as a point in a N-dimensional space which adjusts its “flying” according to its own flying experience as well as the flying experience of other particles. Ladies and Gentlemen: I am from Tsinghua University in China. The topic of my presentation is “A Dissipative Particle Swarm Optimization”. Since the student, Xiao-Feng Xie, which is the first author, is refused by the visa officer with some unfair reasons, if some details are not be presented clearly, please contact him by this address&.

1/18/2019 PSO搜索机理 Each particle keeps track of its coordinates in the solution space which are associated with the best solution (fitness) that has achieved so far by that particle. This value is called personal best , pbest. Another best value that is tracked by the PSO is the best value obtained so far by any particle in the neighborhood of that particle. This value is called gbest. The basic concept of PSO lies in accelerating each particle toward its pbest and the gbest locations, with a random weighted accelaration at each time step as shown in Fig.1 Ladies and Gentlemen: I am from Tsinghua University in China. The topic of my presentation is “A Dissipative Particle Swarm Optimization”. Since the student, Xiao-Feng Xie, which is the first author, is refused by the visa officer with some unfair reasons, if some details are not be presented clearly, please contact him by this address&.

sk : current searching point 1/18/2019 Fig.1 Concept of modification of a searching point by PSO Ladies and Gentlemen: I am from Tsinghua University in China. The topic of my presentation is “A Dissipative Particle Swarm Optimization”. Since the student, Xiao-Feng Xie, which is the first author, is refused by the visa officer with some unfair reasons, if some details are not be presented clearly, please contact him by this address&. sk : current searching point sk+1: modified searching point. vk: current velocity. vk+1: modified velocity. vpbest : velocity based on pbest，vgbest : velocity based on gbest.

1/18/2019 PSO搜索机理 Each particle tries to modify its position using the following information: the current positions, the current velocities, the distance between the current position and pbest, the distance between the current position and the gbest. Ladies and Gentlemen: I am from Tsinghua University in China. The topic of my presentation is “A Dissipative Particle Swarm Optimization”. Since the student, Xiao-Feng Xie, which is the first author, is refused by the visa officer with some unfair reasons, if some details are not be presented clearly, please contact him by this address&.

1/18/2019 PSO搜索机理 The modification of the particle’s position can be mathematically modeled according the following equation : Ladies and Gentlemen: I am from Tsinghua University in China. The topic of my presentation is “A Dissipative Particle Swarm Optimization”. Since the student, Xiao-Feng Xie, which is the first author, is refused by the visa officer with some unfair reasons, if some details are not be presented clearly, please contact him by this address&.

PSO计算步骤 Initial： 将种群做初始化，以随机的方式求出每一Particle 的初始位置与速度。 Evaluation： 1/18/2019 PSO计算步骤 Initial： 将种群做初始化，以随机的方式求出每一Particle 的初始位置与速度。 Evaluation： 依据fitness function 计算出其fitness value 以作为判断每一Particle之好坏。 Fine the Pbest： 找出每一Particle 到目前為止的搜寻过程中最佳解，這個最佳解我们称之为Pbest。 Fine the Gbest： 找出所有Particle 到目前为止所搜寻到的整体最佳解，這個最佳解我们称之为Gbest。 Update the Velocity： 依据式(1) 和(2) 更新每一Particle的速度和位置。 回到步骤2. 继续執行，直到获得一个令人满意的结果或符合终止条件。 Ladies and Gentlemen: I am from Tsinghua University in China. The topic of my presentation is “A Dissipative Particle Swarm Optimization”. Since the student, Xiao-Feng Xie, which is the first author, is refused by the visa officer with some unfair reasons, if some details are not be presented clearly, please contact him by this address&.

PSO计算流程 Loop until max iter Start 1/18/2019 PSO计算流程 Loop until max iter Loop until all particles exhaust Start Initialize particles with random position and velocity vectors. For each particle’s position (p) evaluate fitness If fitness(p) better than fitness(pbest) then pbest= p Set best of pBests as gBest Update particles velocity (eq. 1) and position (eq. 3) Stop: giving gBest, optimal solution. Ladies and Gentlemen: I am from Tsinghua University in China. The topic of my presentation is “A Dissipative Particle Swarm Optimization”. Since the student, Xiao-Feng Xie, which is the first author, is refused by the visa officer with some unfair reasons, if some details are not be presented clearly, please contact him by this address&.

PSO应用实例 1/18/2019 Ladies and Gentlemen: I am from Tsinghua University in China. The topic of my presentation is “A Dissipative Particle Swarm Optimization”. Since the student, Xiao-Feng Xie, which is the first author, is refused by the visa officer with some unfair reasons, if some details are not be presented clearly, please contact him by this address&.

搜索过程－初始状态

搜尋過程－經過5代

搜尋過程－經過10代

搜尋過程－經過15代

搜尋過程－經過20代

搜尋過程－經過25代

搜尋過程－經過100代

搜尋過程－經過500代

搜尋結果 移動次數 搜尋結果 416.245599 5 515.748796 10 759.404006 15 793.732019 20 834.813763 100 837.911535 5000 837.965771 最佳解 837.9658