gh-k-dense-ai-claude-scientific-skills-scientific-skills/skills/pymoo/references/operators.md

Pymoo Genetic Operators Reference

Comprehensive reference for genetic operators in pymoo.

Sampling Operators

Sampling operators initialize populations at the start of optimization.

Random Sampling

Purpose: Generate random initial solutions Types:

• FloatRandomSampling: Continuous variables
• BinaryRandomSampling: Binary variables
• IntegerRandomSampling: Integer variables
• PermutationRandomSampling: Permutation-based problems

Usage:

from pymoo.operators.sampling.rnd import FloatRandomSampling
sampling = FloatRandomSampling()

Latin Hypercube Sampling (LHS)

Purpose: Space-filling initial population Benefit: Better coverage of search space than random Types:

• LHS: Standard Latin Hypercube

Usage:

from pymoo.operators.sampling.lhs import LHS
sampling = LHS()

Custom Sampling

Provide initial population through Population object or NumPy array

Selection Operators

Selection operators choose parents for reproduction.

Tournament Selection

Purpose: Select parents through tournament competition Mechanism: Randomly select k individuals, choose best Parameters:

• pressure: Tournament size (default: 2)
• func_comp: Comparison function

Usage:

from pymoo.operators.selection.tournament import TournamentSelection
selection = TournamentSelection(pressure=2)

Random Selection

Purpose: Uniform random parent selection Use case: Baseline or exploration-focused algorithms

Usage:

from pymoo.operators.selection.rnd import RandomSelection
selection = RandomSelection()

Crossover Operators

Crossover operators recombine parent solutions to create offspring.

For Continuous Variables

Simulated Binary Crossover (SBX)

Purpose: Primary crossover for continuous optimization Mechanism: Simulates single-point crossover of binary-encoded variables Parameters:

• prob: Crossover probability (default: 0.9)
• eta: Distribution index (default: 15)
  • Higher eta → offspring closer to parents
  • Lower eta → more exploration

Usage:

from pymoo.operators.crossover.sbx import SBX
crossover = SBX(prob=0.9, eta=15)

String shorthand: "real_sbx"

Differential Evolution Crossover

Purpose: DE-specific recombination Variants:

• DE/rand/1/bin
• DE/best/1/bin
• DE/current-to-best/1/bin

Parameters:

• CR: Crossover rate
• F: Scaling factor

For Binary Variables

Single Point Crossover

Purpose: Cut and swap at one point Usage:

from pymoo.operators.crossover.pntx import SinglePointCrossover
crossover = SinglePointCrossover()

Two Point Crossover

Purpose: Cut and swap between two points Usage:

from pymoo.operators.crossover.pntx import TwoPointCrossover
crossover = TwoPointCrossover()

K-Point Crossover

Purpose: Multiple cut points Parameters:

• n_points: Number of crossover points

Uniform Crossover

Purpose: Each gene independently from either parent Parameters:

• prob: Per-gene swap probability (default: 0.5)

Usage:

from pymoo.operators.crossover.ux import UniformCrossover
crossover = UniformCrossover(prob=0.5)

Half Uniform Crossover (HUX)

Purpose: Exchange exactly half of differing genes Benefit: Maintains genetic diversity

For Permutations

Order Crossover (OX)

Purpose: Preserve relative order from parents Use case: Traveling salesman, scheduling problems

Usage:

from pymoo.operators.crossover.ox import OrderCrossover
crossover = OrderCrossover()

Edge Recombination Crossover (ERX)

Purpose: Preserve edge information from parents Use case: Routing problems where edge connectivity matters

Partially Mapped Crossover (PMX)

Purpose: Exchange segments while maintaining permutation validity

Mutation Operators

Mutation operators introduce variation to maintain diversity.

For Continuous Variables

Polynomial Mutation (PM)

Purpose: Primary mutation for continuous optimization Mechanism: Polynomial probability distribution Parameters:

• prob: Per-variable mutation probability
• eta: Distribution index (default: 20)
  • Higher eta → smaller perturbations
  • Lower eta → larger perturbations

Usage:

from pymoo.operators.mutation.pm import PM
mutation = PM(prob=None, eta=20)  # prob=None means 1/n_var

String shorthand: "real_pm"

Probability guidelines:

• None or 1/n_var: Standard recommendation
• Higher for more exploration
• Lower for more exploitation

For Binary Variables

Bitflip Mutation

Purpose: Flip bits with specified probability Parameters:

• prob: Per-bit flip probability

Usage:

from pymoo.operators.mutation.bitflip import BitflipMutation
mutation = BitflipMutation(prob=0.05)

For Integer Variables

Integer Polynomial Mutation

Purpose: PM adapted for integers Ensures: Valid integer values after mutation

For Permutations

Inversion Mutation

Purpose: Reverse a segment of the permutation Use case: Maintains some order structure

Usage:

from pymoo.operators.mutation.inversion import InversionMutation
mutation = InversionMutation()

Scramble Mutation

Purpose: Randomly shuffle a segment

Custom Mutation

Define custom mutation by extending Mutation class

Repair Operators

Repair operators fix constraint violations or ensure solution feasibility.

Rounding Repair

Purpose: Round to nearest valid value Use case: Integer/discrete variables with bound constraints

Bounce Back Repair

Purpose: Reflect out-of-bounds values back into feasible region Use case: Box-constrained continuous problems

Projection Repair

Purpose: Project infeasible solutions onto feasible region Use case: Linear constraints

Custom Repair

Purpose: Domain-specific constraint handling Implementation: Extend Repair class

Example:

from pymoo.core.repair import Repair

class MyRepair(Repair):
    def _do(self, problem, X, **kwargs):
        # Modify X to satisfy constraints
        # Return repaired X
        return X

Operator Configuration Guidelines

Parameter Tuning

Crossover probability:

• High (0.8-0.95): Standard for most problems
• Lower: More emphasis on mutation

Mutation probability:

• 1/n_var: Standard recommendation
• Higher: More exploration, slower convergence
• Lower: Faster convergence, risk of premature convergence

Distribution indices (eta):

• Crossover eta (15-30): Higher for local search
• Mutation eta (20-50): Higher for exploitation

Problem-Specific Selection

Continuous problems:

• Crossover: SBX
• Mutation: Polynomial Mutation
• Selection: Tournament

Binary problems:

• Crossover: Two-point or Uniform
• Mutation: Bitflip
• Selection: Tournament

Permutation problems:

• Crossover: Order Crossover (OX)
• Mutation: Inversion or Scramble
• Selection: Tournament

Mixed-variable problems:

• Use appropriate operators per variable type
• Ensure operator compatibility

String-Based Configuration

Pymoo supports convenient string-based operator specification:

from pymoo.algorithms.soo.nonconvex.ga import GA

algorithm = GA(
    pop_size=100,
    sampling="real_random",
    crossover="real_sbx",
    mutation="real_pm"
)

Available strings:

• Sampling: "real_random", "real_lhs", "bin_random", "perm_random"
• Crossover: "real_sbx", "real_de", "int_sbx", "bin_ux", "bin_hux"
• Mutation: "real_pm", "int_pm", "bin_bitflip", "perm_inv"

Operator Combination Examples

Standard Continuous GA:

from pymoo.operators.sampling.rnd import FloatRandomSampling
from pymoo.operators.crossover.sbx import SBX
from pymoo.operators.mutation.pm import PM
from pymoo.operators.selection.tournament import TournamentSelection

sampling = FloatRandomSampling()
crossover = SBX(prob=0.9, eta=15)
mutation = PM(eta=20)
selection = TournamentSelection()

Binary GA:

from pymoo.operators.sampling.rnd import BinaryRandomSampling
from pymoo.operators.crossover.pntx import TwoPointCrossover
from pymoo.operators.mutation.bitflip import BitflipMutation

sampling = BinaryRandomSampling()
crossover = TwoPointCrossover()
mutation = BitflipMutation(prob=0.05)

Permutation GA (TSP):

from pymoo.operators.sampling.rnd import PermutationRandomSampling
from pymoo.operators.crossover.ox import OrderCrossover
from pymoo.operators.mutation.inversion import InversionMutation

sampling = PermutationRandomSampling()
crossover = OrderCrossover()
mutation = InversionMutation()