Class UndoableCauchyMutation<T extends RealValued>

  • Type Parameters:
    T - The specific RealValued type.
    All Implemented Interfaces:
    Splittable<MutationOperator<T>>, MutationOperator<T>, UndoableMutationOperator<T>, RealValued, Copyable<CauchyMutation<T>>

    public class UndoableCauchyMutation<T extends RealValued>
    extends CauchyMutation<T>
    implements UndoableMutationOperator<T>

    This class implements Cauchy mutation with support for the undo(T) method. Cauchy mutation is for mutating floating-point values. This class can be used to mutate objects of any of the classes that implement the RealValued interface, including both univariate and multivariate function input objects.

    In a Cauchy mutation, a value v is mutated by adding a randomly generated m such that m is drawn from a Cauchy distribution with location parameter 0 (i.e., median 0) and scale parameter, scale. It is commonly employed in evolutionary computation when mutating real valued parameters. It is an alternative to the slightly more common Gaussian mutation (see the GaussianMutation class). Gaussian mutation has better convergence properties, however, due to the heavy-tailed nature of the Cauchy distribution, Cauchy mutation can sometimes escape local optima better than Gaussian mutation (i.e., Cauchy mutation is more likely than Gaussian mutation to make large jumps).

    This mutation operator also implements the RealValued interface to enable implementation of metaheuristics that mutate their own mutation parameters. That is, you can pass a CauchyMutation object to the mutate(T) method of a CauchyMutation object.

    To construct a CauchyMutation, you must use one of the factory methods. See the various createCauchyMutation() methods.

    Cauchy mutation was introduced in the following article:
    H.H. Szu and R.L. Hartley. Nonconvex optimization by fast simulated annealing. Proceedings of the IEEE, 75(11): 1538–1540, November 1987.

    • Method Detail

      • createCauchyMutation

        public static <T extends RealValuedUndoableCauchyMutation<T> createCauchyMutation()
        Creates a Cauchy mutation operator with scale parameter equal to 1 that supports the undo operation.
        Type Parameters:
        T - The specific RealValued type.
        Returns:
        A Cauchy mutation operator.
      • createCauchyMutation

        public static <T extends RealValuedUndoableCauchyMutation<T> createCauchyMutation​(double scale)
        Creates a Cauchy mutation operator that supports the undo operation.
        Type Parameters:
        T - The specific RealValued type.
        Parameters:
        scale - The scale parameter of the Cauchy.
        Returns:
        A Cauchy mutation operator.
      • createCauchyMutation

        public static <T extends RealValuedUndoableCauchyMutation<T> createCauchyMutation​(double scale,
                                                                                            int k)
        Create a Cauchy mutation operator that supports the undo operation.
        Type Parameters:
        T - The specific RealValued type.
        Parameters:
        scale - The scale parameter of the Cauchy mutation.
        k - The number of input variables that the mutate(T) method changes when called. The k input variables are chosen uniformly at random from among all subsets of size k. If there are less than k input variables, then all are mutated.
        Returns:
        A Cauchy mutation operator
        Throws:
        IllegalArgumentException - if k < 1
      • createCauchyMutation

        public static <T extends RealValuedUndoableCauchyMutation<T> createCauchyMutation​(double scale,
                                                                                            double p)
        Create a Cauchy mutation operator that supports the undo operation.
        Type Parameters:
        T - The specific RealValued type.
        Parameters:
        scale - The scale parameter of the Cauchy mutation.
        p - The probability that the mutate(T) method changes an input variable. If there are n input variables, then n*p input variables will be mutated on average during a single call to the mutate(T) method.
        Returns:
        A Cauchy mutation operator
        Throws:
        IllegalArgumentException - if p ≤ 0
      • mutate

        public void mutate​(T c)
        Description copied from interface: MutationOperator
        Mutates a candidate solution to a problem, by randomly modifying its state. The mutant that is produced is in the local neighborhood of the original candidate solution.
        Specified by:
        mutate in interface MutationOperator<T extends RealValued>
        Overrides:
        mutate in class CauchyMutation<T extends RealValued>
        Parameters:
        c - The candidate solution subject to the mutation. This method changes the state of c.
      • undo

        public void undo​(T c)
        Description copied from interface: UndoableMutationOperator

        Returns a candidate solution to its previous state prior to the most recent mutation performed.

        For example, consider the following. Let c' be the current state of c. Let c'' be the state of c after mutate(c); If we then call undo(c), the state of c should revert back to c'.

        The behavior of undo is undefined if c is altered by some other process between the calls to mutate and undo. The behavior is also undefined if a different candidate is given to undo then the last given to mutate. For example, if the following two statements are executed, mutate(c); undo(d);, the effect on d is undefined as it wasn't the most recently mutated candidate solution.

        Specified by:
        undo in interface UndoableMutationOperator<T extends RealValued>
        Parameters:
        c - The candidate solution to revert.
      • split

        public UndoableCauchyMutation<T> 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<T extends RealValued>
        Specified by:
        split in interface UndoableMutationOperator<T extends RealValued>
        Overrides:
        split in class CauchyMutation<T extends RealValued>
        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.