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。 - amountRemove = startingTemperature/static_cast<double>(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;
}
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。
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