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

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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：
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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 notbool 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：
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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：
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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(nbIterations);
其中，setupPercentage为参数，nbIterations为总的迭代次数。
amountRemove = startingTemperature/static_cast(nbIterations);
其中，startingTemperature为传入参数。

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;
}