Module org.cicirello.chips_n_salsa

Package org.cicirello.search.sa

Class ExponentialCooling

java.lang.Object

org.cicirello.search.sa.ExponentialCooling

All Implemented Interfaces:

Splittable<AnnealingSchedule>, AnnealingSchedule

public final class ExponentialCooling
extends Object
implements AnnealingSchedule

This class implements the classic and most commonly encountered cooling schedule for simulated annealing, the annealing schedule known as exponential cooling (sometimes referred to as geometric cooling). In this cooling schedule, the k-th temperature, t_k, is determined as follows: t_k = α^k * t₀, where t₀ is the initial temperature and α is the cooling rate. The new temperature is usually computed incrementally from the previous with: t_k = α * t_k-1. In some applications, the temperature update occurs with each simulated annealing evaluation, while in others it is updated periodically, such as every s steps (i.e., iterations) of simulated annealing. This class supports this periodic update approach, with a default of every step. See the parameters of the constructors for more information.

Additionally, this class stops updating the temperature once it is less than or equal to 0.001. For any foreseeable cost scale that a problem may have, a temperature value of 0.001 is sufficiently low such that all moves that are worse than the current state will be rejected, so further cooling would be superfluous.

The accept methods of this class use the classic, and most common, Boltzmann distribution for determining whether to accept a neighbor.

Constructor Summary

Constructors

Constructor	Description
ExponentialCooling(double t0, double alpha)	Constructs an exponential cooling schedule for simulated annealing.
ExponentialCooling(double t0, double alpha, int steps)	Constructs an exponential cooling schedule for simulated annealing.

Method Summary

Modifier and Type	Method	Description
boolean	accept(double neighborCost, double currentCost)	Determine whether or not to accept a neighboring solution based on its cost and the current cost, both passed as parameters.
void	init(int maxEvals)	Perform any initialization necessary for the annealing schedule at to the start of a run of simulated annealing.
ExponentialCooling	split()	Generates a functionally identical copy of this object, for use in multithreaded implementations of search algorithms.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Details

ExponentialCooling

public ExponentialCooling(double t0,
 double alpha,
 int steps)

Constructs an exponential cooling schedule for simulated annealing.

Parameters:

t0 - The initial temperature for the start of an annealing run. The value of t0 must be positive.

alpha - The cooling rate. Each time the temperature is cooled, it is cooled as follows: t = t * alpha. The value of alpha must be greater than 0 and less than 1.

steps - The number of iterations of simulated annealing between cooling events. Steps must be positive. If 0 or a negative is passed for steps, steps is set to 1.

Throws:

IllegalArgumentException - if t0 ≤ 0 or alpha ≤ 0 or alpha ≥ 1.

ExponentialCooling

public ExponentialCooling(double t0,
 double alpha)

Constructs an exponential cooling schedule for simulated annealing.

Parameters:

t0 - The initial temperature for the start of an annealing run. The value of t0 must be positive.

alpha - The cooling rate. During each iteration of simulated annealing, the temperature is cooled as follows: t = t * alpha. The value of alpha must be greater than 0 and less than 1.

Throws:

IllegalArgumentException - if t0 ≤ 0 or alpha ≤ 0 or alpha ≥ 1.

Method Details

init

public void init(int maxEvals)

Description copied from interface: AnnealingSchedule

Perform any initialization necessary for the annealing schedule at to the start of a run of simulated annealing. This includes initializing the temperature parameter. This method is called once by implementations of simulated annealing at the start of the run. Implementations of simulated annealing that perform reannealing will also call this once at the start of each reanneal.

Specified by:

init in interface AnnealingSchedule

Parameters:

maxEvals - The maximum length of the run of simulated annealing about to start. Some annealing schedules depend upon prior knowledge of run length. For those annealing schedules that don't depend upon run length, this parameter is ignored.

accept

public boolean accept(double neighborCost,
 double currentCost)

Description copied from interface: AnnealingSchedule

Determine whether or not to accept a neighboring solution based on its cost and the current cost, both passed as parameters. Lower cost indicates better solution. This method must also update the temperature and any other state data related to the annealing schedule.

Specified by:

accept in interface AnnealingSchedule

Parameters:

neighborCost - The cost of the neighboring solution under consideration.

currentCost - The cost of the current solution.

Returns:

true if simulated annealing should accept the neighbor, and false otherwise.

split

public ExponentialCooling split()

Description copied from interface: Splittable

Generates a functionally identical copy of this object, for use in multithreaded implementations of search algorithms. The state of the object that is returned may or may not be identical to that of the original. Thus, this is a distinct concept from the functionality of the Copyable interface. Classes that implement this interface must ensure that the object returned performs the same functionality, and that it does not share any state data that would be either unsafe or inefficient for concurrent access by multiple threads. The split method is allowed to simply return the this reference, provided that it is both safe and efficient for multiple threads to share a single copy of the Splittable object. The intention is to provide a multithreaded search with the capability to provide spawned threads with their own distinct search operators. Such multithreaded algorithms can call the split method for each thread it spawns to generate a functionally identical copy of the operator, but with independent state.

Specified by:

split in interface Splittable<AnnealingSchedule>

Returns:

A functionally identical copy of the object, or a reference to this if it is both safe and efficient for multiple threads to share a single instance of this Splittable object.