python DEAP PSO 算法的学习

待我称王封你为后i 2022-06-06 09:21 173阅读 0赞

翻译自：[http://deap.readthedocs.io/en/master/examples/pso\_basic.html][http_deap.readthedocs.io_en_master_examples_pso_basic.html]

## 粒子群优化基础 ##

这里的实现是基本PSO算法的实现。wikipedia的PSO的定义如下：  
PSO通过拥有一个种群规模的候选解决方案来优化一个问题，这里的候选解决方案指的是粒子，在解空间中根据简单的数学公式移动这些粒子。粒子的移动被解空间的最优位置引导着，如果粒子发现更好的位置就会更新最优位置。

## 模块 ##

在写函数和算法之前，需要从标准库和DEAP中导入一些模块。

import operator
    import random
    
    import numpy
    
    from deap import base
    from deap import benchmarks
    from deap import creator
    from deap import tools

## 实现 ##

粒子的目标是在当前位置最大化函数的返回值。  
PSO算法中的粒子实质上被描述为D维搜索空间上的一个位置。每一个粒子用一个向量来表示粒子在每一维的速度。最终，每个粒子参照目前为止最好的状态进行移动。  
在DEAP中转化为如下两行代码：

creator.create("FitnessMax", base.Fitness, weights=(1.0,))
    creator.create("Particle", list, fitness=creator.FitnessMax, speed=list, 
        smin=None, smax=None, best=None)

在creator创建了两个新的对象。首先，创建一个FitnessMax对象，指定weights为（1.0，）,这意味着我们想要最大化粒子的fitness的值（因为是正数）。第二个对象表示粒子，我们定义这个例子为一个list，并添加5个属性。第一个属性是粒子的fitness适应度，第二个是粒子的速度，也是一个list，第三个和第四个是速度的临界值，第五个是粒子迄今为止最佳状态的副本的引用。因为粒子直到被评估之前都没有最终的状态，所以引用值初始设置为None。速度的临界值也被设置为None，可以通过函数generate()设置这个值，下一部分将会介绍。

## operators 算子 ##

PSO基本算法只用三个算子：初始化，更新，评估。初始化是为每一个粒子产生一个随机的位置和随机的速度。接下来这个函数创建一个粒子并初始化属性，除了属性best，这个需要在评估以后才能设置。

def generate(size, pmin, pmax, smin, smax):
        part = creator.Particle(random.uniform(pmin, pmax) for _ in range(size)) 
        part.speed = [random.uniform(smin, smax) for _ in range(size)]
        part.smin = smin
        part.smax = smax
        return part

函数updateParticle()先计算速度，然后限制速度在smin和smax之间，最后计算新的粒子位置。

def updateParticle(part, best, phi1, phi2):
        u1 = (random.uniform(0, phi1) for _ in range(len(part)))
        u2 = (random.uniform(0, phi2) for _ in range(len(part)))
        v_u1 = map(operator.mul, u1, map(operator.sub, part.best, part))
        v_u2 = map(operator.mul, u2, map(operator.sub, best, part))
        part.speed = list(map(operator.add, part.speed, map(operator.add, v_u1, v_u2)))
        for i, speed in enumerate(part.speed):
            if speed < part.smin:
                part.speed[i] = part.smin
            elif speed > part.smax:
                part.speed[i] = part.smax
        part[:] = list(map(operator.add, part, part.speed))
    The operators are registered in the toolbox with their parameters. The par

这些算子使用参数在toolbox注册。粒子值定义在范围 \[-100, 100\] (pmin 和pmax)，速度限制在范围 \[-50, 50\] 。评估函数 h1() 来自 \[Knoek2003\]论文。这个函数已经在benchmarks模块中定义了，所以可以直接注册并使用。

toolbox = base.Toolbox()
    toolbox.register("particle", generate, size=2, pmin=-6, pmax=6, smin=-3, smax=3)
    toolbox.register("population", tools.initRepeat, list, toolbox.particle)
    toolbox.register("update", updateParticle, phi1=2.0, phi2=2.0)
    toolbox.register("evaluate", benchmarks.h1)

## 算法 ##

一旦算子在toolbox中注册以后，我们就可以使用算法来创建一个新的种群，然后应用原始PSO算法。变量best包含迄今为止发现的最优的粒子（在原始算法中表示gbest全局最优解）。

def main():
        pop = toolbox.population(n=5)
        stats = tools.Statistics(lambda ind: ind.fitness.values)
        stats.register("avg", numpy.mean)
        stats.register("std", numpy.std)
        stats.register("min", numpy.min)
        stats.register("max", numpy.max)
    
        logbook = tools.Logbook()
        logbook.header = ["gen", "evals"] + stats.fields
    
        GEN = 1000
        best = None
    
        for g in range(GEN):
            for part in pop:
                part.fitness.values = toolbox.evaluate(part)
                if not part.best or part.best.fitness < part.fitness:
                    part.best = creator.Particle(part)
                    part.best.fitness.values = part.fitness.values
                if not best or best.fitness < part.fitness:
                    best = creator.Particle(part)
                    best.fitness.values = part.fitness.values
            for part in pop:
                toolbox.update(part, best)
    
            # Gather all the fitnesses in one list and print the stats
            logbook.record(gen=g, evals=len(pop), **stats.compile(pop))
            print(logbook.stream)
    
        return pop, logbook, best

## 结论 ##

完整的PSO例子在这里：[https://github.com/DEAP/deap/blob/09b2562aad70c6f171ebca2bdac0c30387f5e8f5/examples/pso/basic.py][https_github.com_DEAP_deap_blob_09b2562aad70c6f171ebca2bdac0c30387f5e8f5_examples_pso_basic.py]  
链接的代码如下：

# This file is part of DEAP.
    #
    # DEAP is free software: you can redistribute it and/or modify
    # it under the terms of the GNU Lesser General Public License as
    # published by the Free Software Foundation, either version 3 of
    # the License, or (at your option) any later version.
    #
    # DEAP is distributed in the hope that it will be useful,
    # but WITHOUT ANY WARRANTY; without even the implied warranty of
    # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
    # GNU Lesser General Public License for more details.
    #
    # You should have received a copy of the GNU Lesser General Public
    # License along with DEAP. If not, see <http://www.gnu.org/licenses/>.
    
    import operator
    import random
    
    import numpy
    
    from deap import base
    from deap import benchmarks
    from deap import creator
    from deap import tools
    
    creator.create("FitnessMax", base.Fitness, weights=(1.0,))
    creator.create("Particle", list, fitness=creator.FitnessMax, speed=list, 
        smin=None, smax=None, best=None)
    
    def generate(size, pmin, pmax, smin, smax):
        part = creator.Particle(random.uniform(pmin, pmax) for _ in range(size)) 
        part.speed = [random.uniform(smin, smax) for _ in range(size)]
        part.smin = smin
        part.smax = smax
        return part
    
    def updateParticle(part, best, phi1, phi2):
        u1 = (random.uniform(0, phi1) for _ in range(len(part)))
        u2 = (random.uniform(0, phi2) for _ in range(len(part)))
        v_u1 = map(operator.mul, u1, map(operator.sub, part.best, part))
        v_u2 = map(operator.mul, u2, map(operator.sub, best, part))
        part.speed = list(map(operator.add, part.speed, map(operator.add, v_u1, v_u2)))
        for i, speed in enumerate(part.speed):
            if speed < part.smin:
                part.speed[i] = part.smin
            elif speed > part.smax:
                part.speed[i] = part.smax
        part[:] = list(map(operator.add, part, part.speed))
    
    toolbox = base.Toolbox()
    toolbox.register("particle", generate, size=2, pmin=-6, pmax=6, smin=-3, smax=3)
    toolbox.register("population", tools.initRepeat, list, toolbox.particle)
    toolbox.register("update", updateParticle, phi1=2.0, phi2=2.0)
    toolbox.register("evaluate", benchmarks.h1)
    
    def main():
        pop = toolbox.population(n=5)
        stats = tools.Statistics(lambda ind: ind.fitness.values)
        stats.register("avg", numpy.mean)
        stats.register("std", numpy.std)
        stats.register("min", numpy.min)
        stats.register("max", numpy.max)
    
        logbook = tools.Logbook()
        logbook.header = ["gen", "evals"] + stats.fields
    
        GEN = 1000
        best = None
    
        for g in range(GEN):
            for part in pop:
                part.fitness.values = toolbox.evaluate(part)
                if not part.best or part.best.fitness < part.fitness:
                    part.best = creator.Particle(part)
                    part.best.fitness.values = part.fitness.values
                if not best or best.fitness < part.fitness:
                    best = creator.Particle(part)
                    best.fitness.values = part.fitness.values
            for part in pop:
                toolbox.update(part, best)
    
            # Gather all the fitnesses in one list and print the stats
            logbook.record(gen=g, evals=len(pop), **stats.compile(pop))
            print(logbook.stream)
    
        return pop, logbook, best
    
    if __name__ == "__main__":
        main()

[http_deap.readthedocs.io_en_master_examples_pso_basic.html]: http://deap.readthedocs.io/en/master/examples/pso_basic.html
[https_github.com_DEAP_deap_blob_09b2562aad70c6f171ebca2bdac0c30387f5e8f5_examples_pso_basic.py]: https://github.com/DEAP/deap/blob/09b2562aad70c6f171ebca2bdac0c30387f5e8f5/examples/pso/basic.py