代码 | 自适应大邻域搜索系列之(6) - 判断接受准则SimulatedAnnealing的代码解析

前言

前面三篇文章对大家来说应该很简单吧?不过轻松了这么久,今天再来看点刺激的。关于判断接受准则的代码。其实,判断接受准则有很多种,效果也因代码而异。今天介绍的是模拟退火的判断接受准则。那么,相关的原理之前的推文有讲过,不懂的同学回去翻翻这个文章 复习一下哈,小编也回去看看,咳咳~。好了,废话不多说,开始干活。

01 总体概述

其实这个ALNS的代码库提供了很多的判断接受准则,有最简单的直接根据目标值来判断,也有各种复杂的模拟退火降温冷却等过程来判断。不过,今天挑一个最具代表性的来讲吧,就是模拟退火的判断接受准则。其代码实现是由两个类IAcceptanceModule、SimulatedAnnealing来实现的。它们的关系依旧如下:

其中IAcceptanceModule依旧是抽象类,只提供接口。下面对这两货进行解析。

02 IAcceptanceModule

这个抽象类也很简单,只提供了一个接口transitionAccepted,以用来判断是否要接受新的解,为纯虚函数,需要在后续的代码中重写的。

class IAcceptanceModule
{
public:
	//! Indicate if the new created solution have to be accepted or not
	//! \param bestSolutionManager a reference to the best solution manager.
	//! \param currentSolution current solution.
	//! \param newSolution new solution.
	//! \param status the status of the current alns iteration.
	//! \return true if the transition is accepted, false otherwise.
	virtual bool transitionAccepted(IBestSolutionManager& bestSolutionManager, ISolution& currentSolution, ISolution& newSolution, ALNS_Iteration_Status& status) = 0;

	//! Some Acceptance modules needs to initialize some variable
	//! only when the solver actualy starts working. In this case
	//! you should override this method.
	virtual void startSignal(){};
};

03 SimulatedAnnealing

SimulatedAnnealing继承于上面的接口类IAcceptanceModule,它利用模拟退火的判断接受准则实现了transitionAccepted的功能。值得注意的是,该类成员变量里面是一个CoolingSchedule,用来获取当前温度。该表有另一个抽象类ICoolingSchedule定义,下面会详细说道。

class SimulatedAnnealing: public IAcceptanceModule {
private:
	//! The cooling schedule to be use to compute the temperature each time it
	//! is needed.
	ICoolingSchedule* coolingSchedule;
public:
	//! Constructor.
	//! \param cs the cooling schedule to be used by the simulated annealing.
	SimulatedAnnealing(ICoolingSchedule& cs);

	//! Destructor.
	virtual ~SimulatedAnnealing();

	//! Compute if the newly created solution have to be accepted or not
	bool transitionAccepted(IBestSolutionManager& bestSolutionManager, ISolution& currentSolution, ISolution& newSolution, ALNS_Iteration_Status& status);

	virtual void startSignal();

};

其成员函数的实现也非常的简单,不过多说两句。先利用CoolingSchedule获取当前冷却过程的温度。如果新解目标值<当前解的,那么直接接受就行了。如果>,那么按照一定的概率接受。具体公式解释嘛,小编截个图过来吧,因为在以前的文章已经讲过了:

不过这里的能量差计算用的是解的目标惩罚值算的,不是目标值。

bool SimulatedAnnealing::transitionAccepted(IBestSolutionManager& bestSolutionManager, ISolution& currentSolution, ISolution& newSolution, ALNS_Iteration_Status& status)
{
	double temperature = coolingSchedule->getCurrentTemperature();
	if(newSolution < currentSolution)
	{
		return true;
	}
	else
	{
		double difference = newSolution.getPenalizedObjectiveValue() - currentSolution.getPenalizedObjectiveValue();
		double randomVal = static_cast<double>(rand())/static_cast<double>(RAND_MAX);
		return (exp(-1*difference/temperature)>randomVal);
	}
}

void SimulatedAnnealing::startSignal()
{
	coolingSchedule->startSignal();
}

04 ICoolingSchedule

4.1 ICoolingSchedule

这货是一个抽象类,CoolingSchedule有很多种类型,根据不同需要由这个类可以派生出下面类型的CoolingSchedule:

ICoolingSchedule只提供了两个接口,其中getCurrentTemperature是纯虚函数,用以获取当前的退火温度,需要重写。

class ICoolingSchedule
{
public:
	//! \return the current temperature.
	virtual double getCurrentTemperature()=0;

	//! This method should be called when the optimization
	//! process start. The cooling schedules that actually need
	//! this should override this method.
	virtual void startSignal(){};
};

4.2 LinearCoolingSchedule

由于CoolingSchedule有很多类型,小编挑一个LinearCoolingSchedule给大家讲解吧。LinearCoolingSchedule主要的根据是迭代的次数来工作的。成员函数getCurrentTemperature是核心,用以获取当前的温度,便于上面的判断接受准则计算概率。

class LinearCoolingSchedule: public ICoolingSchedule {
private:
	//! The current temperature.
	double currentTemperature;

	//! The amount to remove at each temperature recomputation.
	double amountRemove;
public:
	//! Constructor.
	//! \param initSol the initial solution.
	//! \param csParam the cooling schedule parameters.
	//! \param nbIterations the number of iterations to be performed.
	LinearCoolingSchedule(ISolution& initSol, CoolingSchedule_Parameters& csParam, size_t nbIterations);

	//! Constructor.
	//! \param startingTemperature the initial temperature.
	//! \param nbIterations the number of iterations to be performed.
	LinearCoolingSchedule(double startingTemperature, size_t nbIterations);

	//! Destructor.
	virtual ~LinearCoolingSchedule();

	//! Compute and return the current temperature.
	//! \return the current temperature.
	double getCurrentTemperature();

	void startSignal(){};
};

然后现在来看看其具体方法是怎么实现的吧。其实也很简单,没有那么复杂。每次获取currentTemperature的时候呢,先让currentTemperature降降温,再返回。降温的幅度是利用currentTemperature 减去 amountRemove实现的。那么amountRemove又是怎么得出来的呢?LinearCoolingSchedule提供了两个构造函数,对应不同的计算方法:

currentTemperature = (csParam.setupPercentage*initSol.getPenalizedObjectiveValue())/(-log(0.5));
    amountRemove = currentTemperature/static_cast<double>(nbIterations);
其中,setupPercentage为参数,nbIterations为总的迭代次数。LinearCoolingSchedule::LinearCoolingSchedule(ISolution& initSol, CoolingSchedule_Parameters& csParam, size_t nbIterations) {
	currentTemperature = (csParam.setupPercentage*initSol.getPenalizedObjectiveValue())/(-log(0.5));
	amountRemove = currentTemperature/static_cast<double>(nbIterations);

}

LinearCoolingSchedule::LinearCoolingSchedule(double startingTemperature, size_t nbIterations) {
	assert(nbIterations>0);
	assert(startingTemperature>=0);
	currentTemperature = startingTemperature;
	amountRemove = startingTemperature/static_cast<double>(nbIterations);

}

LinearCoolingSchedule::~LinearCoolingSchedule() {
	// Nothing to be done.
}

double LinearCoolingSchedule::getCurrentTemperature()
{
	currentTemperature-= amountRemove;
	if(currentTemperature < 0)
	{
		currentTemperature = 0;
	}
	assert(currentTemperature>=0);
	return currentTemperature;
}
amountRemove = startingTemperature/static_cast<double>(nbIterations);
其中,startingTemperature为传入参数。

05 小结

今天讲的总体也不是很难,相信之前模拟退火学得好的小伙伴一眼就能看懂了,如果其他小伙伴还不是很理解的话,回去看看之前的文章,看看模拟退火的判断接受准则再多加理解,相信对大家不是什么问题。

至此,代码已经讲得差不多了,估摸着还能再做几篇文章,依然感谢大家一路过来的支持。谢谢!咱们下期再见。

原创声明,本文系作者授权云+社区发表,未经许可,不得转载。

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