Package org.uma.jmetal.operator.mutation.impl

Class LevyFlightMutation

java.lang.Object

org.uma.jmetal.operator.mutation.impl.LevyFlightMutation

All Implemented Interfaces:

Serializable, MutationOperator<DoubleSolution>, Operator<DoubleSolution,DoubleSolution>

public class LevyFlightMutation
extends Object
implements MutationOperator<DoubleSolution>

This class implements a Lévy flight mutation operator for real-valued solutions. Lévy flights are characterized by heavy-tailed distributions with infinite variance, producing mostly small steps with occasional very large jumps. This behavior is beneficial for global optimization as it provides both local search capabilities and the ability to escape local optima through large jumps.

The implementation uses the Mantegna algorithm to generate Lévy-distributed steps: 1. Generate u ~ Normal(0, σ_u²) where σ_u = [Γ(1+β)sin(πβ/2)/Γ((1+β)/2)β2^((β-1)/2)]^(1/β) 2. Generate v ~ Normal(0, 1) 3. Lévy step = u / |v|^(1/β)

Parameters:

• mutationProbability: The probability of mutating each variable. Must be in [0, 1].
• beta: The Lévy index parameter. Must be in (1, 2]. Controls the tail heaviness:
  • Values closer to 1.0 produce heavier tails with more frequent large jumps
  • Values around 1.5 provide balanced exploration with moderate large jumps (typical choice)
  • Values closer to 2.0 approach Gaussian behavior with fewer large jumps
• stepSize: The scaling factor for Lévy steps. Must be positive (> 0). Typical values range from 0.001 to 0.1:
  • Smaller values (0.001-0.01) provide fine-grained local search
  • Medium values (0.01-0.05) balance local and global search
  • Larger values (0.05-0.1) emphasize global exploration

Author:

Antonio J. Nebro

Code generated by Claude Sonnet 4

See Also:

• Serialized Form

Constructor Summary

Constructors

Constructor	Description
LevyFlightMutation()	Constructor with default parameters Default: beta = 1.5 (typical for Lévy flights), stepSize = 0.01
LevyFlightMutation(double mutationProbability, double beta, double stepSize)	Constructor
LevyFlightMutation(double mutationProbability, double beta, double stepSize, RepairDoubleSolution solutionRepair)	Constructor
LevyFlightMutation(double mutationProbability, double beta, double stepSize, RepairDoubleSolution solutionRepair, RandomGenerator<Double> randomGenerator)	Constructor

Method Summary

Modifier and Type	Method	Description
double	beta()	Get the beta parameter
void	beta(double beta)	Set the beta parameter
DoubleSolution	execute(DoubleSolution solution)	Execute the mutation operation
double	mutationProbability()	Get the mutation probability
void	mutationProbability(double mutationProbability)	Set the mutation probability
RepairDoubleSolution	solutionRepair()	Get the solution repair strategy
void	solutionRepair(RepairDoubleSolution solutionRepair)	Set the solution repair strategy
double	stepSize()	Get the step size parameter
void	stepSize(double stepSize)	Set the step size parameter
String	toString()	Get string representation of the operator

Methods inherited from class java.lang.Object

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

Constructor Details

LevyFlightMutation

public LevyFlightMutation()

Constructor with default parameters Default: beta = 1.5 (typical for Lévy flights), stepSize = 0.01

LevyFlightMutation

public LevyFlightMutation(double mutationProbability,
 double beta,
 double stepSize)

Constructor

Parameters:

mutationProbability - The probability of mutating each variable

beta - The Lévy index parameter

stepSize - The scaling factor for Lévy steps

LevyFlightMutation

public LevyFlightMutation(double mutationProbability,
 double beta,
 double stepSize,
 RepairDoubleSolution solutionRepair)

Constructor

Parameters:

mutationProbability - The probability of mutating each variable

beta - The Lévy index parameter

stepSize - The scaling factor for Lévy steps

solutionRepair - The repair strategy for out-of-bounds values

LevyFlightMutation

public LevyFlightMutation(double mutationProbability,
 double beta,
 double stepSize,
 RepairDoubleSolution solutionRepair,
 RandomGenerator<Double> randomGenerator)

Constructor

Parameters:

mutationProbability - The probability of mutating each variable

beta - The Lévy index parameter

stepSize - The scaling factor for Lévy steps

solutionRepair - The repair strategy for out-of-bounds values

randomGenerator - The random number generator

Method Details

execute

public DoubleSolution execute(DoubleSolution solution)

Execute the mutation operation

Specified by:

execute in interface MutationOperator<DoubleSolution>

Specified by:

execute in interface Operator<DoubleSolution,DoubleSolution>

Parameters:

solution - The solution to be mutated

Returns:

The mutated solution

mutationProbability

public double mutationProbability()

Get the mutation probability

Specified by:

mutationProbability in interface MutationOperator<DoubleSolution>

Returns:

The mutation probability

mutationProbability

public void mutationProbability(double mutationProbability)

Set the mutation probability

Parameters:

mutationProbability - The new mutation probability

beta

public double beta()

Get the beta parameter

Returns:

The beta parameter

beta

public void beta(double beta)

Set the beta parameter

Parameters:

beta - The new beta parameter

stepSize

public double stepSize()

Get the step size parameter

Returns:

The step size parameter

stepSize

public void stepSize(double stepSize)

Set the step size parameter

Parameters:

stepSize - The new step size parameter

solutionRepair

public RepairDoubleSolution solutionRepair()

Get the solution repair strategy

Returns:

The solution repair strategy

solutionRepair

public void solutionRepair(RepairDoubleSolution solutionRepair)

Set the solution repair strategy

Parameters:

solutionRepair - The new solution repair strategy

toString

public String toString()

Get string representation of the operator

Overrides:

toString in class Object

Returns:

String representation