Class CauchyMutation<T extends RealValued>

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

    public class CauchyMutation<T extends RealValued>
    extends Object
    implements MutationOperator<T>, RealValued, Copyable<CauchyMutation<T>>

    This class implements Cauchy mutation. 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 RealValuedCauchyMutation<T> createCauchyMutation()
        Creates a Cauchy mutation operator with scale parameter equal to 1.
        Type Parameters:
        T - The specific RealValued type.
        Returns:
        A Cauchy mutation operator.
      • createCauchyMutation

        public static <T extends RealValuedCauchyMutation<T> createCauchyMutation​(double scale)
        Creates a Cauchy mutation operator.
        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 RealValuedCauchyMutation<T> createCauchyMutation​(double scale,
                                                                                    int k)
        Create a Cauchy mutation operator.
        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 RealValuedCauchyMutation<T> createCauchyMutation​(double scale,
                                                                                    double p)
        Create a Cauchy mutation operator.
        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>
        Parameters:
        c - The candidate solution subject to the mutation. This method changes the state of c.
      • split

        public CauchyMutation<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>
        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.
      • equals

        public boolean equals​(Object other)
        Indicates whether some other object is equal to this one. The objects are equal if they are the same type of operator with the same parameters.
        Overrides:
        equals in class Object
        Parameters:
        other - the object with which to compare
        Returns:
        true if and only if the objects are equal
      • hashCode

        public int hashCode()
        Returns a hash code value for the object. This method is supported for the benefit of hash tables such as those provided by HashMap.
        Overrides:
        hashCode in class Object
        Returns:
        a hash code value for this object
      • length

        public final int length()
        Description copied from interface: RealValued
        Gets the number of parameters.
        Specified by:
        length in interface RealValued
        Returns:
        The number of parameters for this function.
      • get

        public final double get​(int i)
        Accesses the current value of scale.
        Specified by:
        get in interface RealValued
        Parameters:
        i - Ignored.
        Returns:
        The current value of scale.
      • toArray

        public final double[] toArray​(double[] values)
        Accesses the current value of scale as an array. This method implemented strictly to meet implementation requirements of RealValued interface.
        Specified by:
        toArray in interface RealValued
        Parameters:
        values - An array to hold the result. If values is null or if values.length is not equal 1, then a new array is constructed for the result.
        Returns:
        An array containing the current value of scale.
      • set

        public final void set​(int i,
                              double value)
        Sets scale to a specified value.
        Specified by:
        set in interface RealValued
        Parameters:
        i - Ignored.
        value - The new value for scale.