Pymoo Algorithms Reference

Comprehensive reference for optimization algorithms available in pymoo.

Single-Objective Optimization Algorithms

Genetic Algorithm (GA)

Purpose: General-purpose single-objective evolutionary optimization Best for: Continuous, discrete, or mixed-variable problems Algorithm type: (μ+λ) genetic algorithm

Key parameters:

pop_size: Population size (default: 100)
sampling: Initial population generation strategy
selection: Parent selection mechanism (default: Tournament)
crossover: Recombination operator (default: SBX)
mutation: Variation operator (default: Polynomial)
eliminate_duplicates: Remove redundant solutions (default: True)
n_offsprings: Offspring per generation

Usage:

python

from pymoo.algorithms.soo.nonconvex.ga import GA
algorithm = GA(pop_size=100, eliminate_duplicates=True)

Differential Evolution (DE)

Purpose: Single-objective continuous optimization Best for: Continuous parameter optimization with good global search Algorithm type: Population-based differential evolution

Variants: Multiple DE strategies available (rand/1/bin, best/1/bin, etc.)

Particle Swarm Optimization (PSO)

Purpose: Single-objective optimization through swarm intelligence Best for: Continuous problems, fast convergence on smooth landscapes

CMA-ES

Purpose: Covariance Matrix Adaptation Evolution Strategy Best for: Continuous optimization, particularly for noisy or ill-conditioned problems

Pattern Search

Purpose: Direct search method Best for: Problems where gradient information is unavailable

Nelder-Mead

Purpose: Simplex-based optimization Best for: Local optimization of continuous functions

Multi-Objective Optimization Algorithms

NSGA-II (Non-dominated Sorting Genetic Algorithm II)

Purpose: Multi-objective optimization with 2-3 objectives Best for: Bi- and tri-objective problems requiring well-distributed Pareto fronts Selection strategy: Non-dominated sorting + crowding distance

Key features:

Fast non-dominated sorting
Crowding distance for diversity
Elitist approach
Binary tournament mating selection

Key parameters:

pop_size: Population size (default: 100)
sampling: Initial population strategy
crossover: Default SBX for continuous
mutation: Default Polynomial Mutation
survival: RankAndCrowding

Usage:

python

from pymoo.algorithms.moo.nsga2 import NSGA2
algorithm = NSGA2(pop_size=100)

When to use:

2-3 objectives
Need for distributed solutions across Pareto front
Standard multi-objective benchmark

NSGA-III

Purpose: Many-objective optimization (4+ objectives) Best for: Problems with 4 or more objectives requiring uniform Pareto front coverage Selection strategy: Reference direction-based diversity maintenance

Key features:

Reference directions guide population
Maintains diversity in high-dimensional objective spaces
Niche preservation through reference points
Underrepresented reference direction selection

Key parameters:

ref_dirs: Reference directions (REQUIRED)
pop_size: Defaults to number of reference directions
crossover: Default SBX
mutation: Default Polynomial Mutation

Usage:

python

from pymoo.algorithms.moo.nsga3 import NSGA3
from pymoo.util.ref_dirs import get_reference_directions

ref_dirs = get_reference_directions("das-dennis", n_dim=4, n_partitions=12)
algorithm = NSGA3(ref_dirs=ref_dirs)

NSGA-II vs NSGA-III:

Use NSGA-II for 2-3 objectives
Use NSGA-III for 4+ objectives
NSGA-III provides more uniform distribution
NSGA-II has lower computational overhead

R-NSGA-II (Reference Point Based NSGA-II)

Purpose: Multi-objective optimization with preference articulation Best for: When decision maker has preferred regions of Pareto front

U-NSGA-III (Unified NSGA-III)

Purpose: Improved version handling various scenarios Best for: Many-objective problems with additional robustness

MOEA/D (Multi-Objective Evolutionary Algorithm based on Decomposition)

Purpose: Decomposition-based multi-objective optimization Best for: Problems where decomposition into scalar subproblems is effective

AGE-MOEA

Purpose: Adaptive geometry estimation Best for: Multi and many-objective problems with adaptive mechanisms

RVEA (Reference Vector guided Evolutionary Algorithm)

Purpose: Reference vector-based many-objective optimization Best for: Many-objective problems with adaptive reference vectors

SMS-EMOA

Purpose: S-Metric Selection Evolutionary Multi-objective Algorithm Best for: Problems where hypervolume indicator is critical Selection: Uses dominated hypervolume contribution

Dynamic Multi-Objective Algorithms

D-NSGA-II

Purpose: Dynamic multi-objective problems Best for: Time-varying objective functions or constraints

KGB-DMOEA

Purpose: Knowledge-guided dynamic multi-objective optimization Best for: Dynamic problems leveraging historical information

Constrained Optimization

SRES (Stochastic Ranking Evolution Strategy)

Purpose: Single-objective constrained optimization Best for: Heavily constrained problems

ISRES (Improved SRES)

Purpose: Enhanced constrained optimization Best for: Complex constraint landscapes

Algorithm Selection Guidelines

For single-objective problems:

Start with GA for general problems
Use DE for continuous optimization
Try PSO for faster convergence on smooth problems
Use CMA-ES for difficult/noisy landscapes

For multi-objective problems:

2-3 objectives: NSGA-II
4+ objectives: NSGA-III
Preference articulation: R-NSGA-II
Decomposition-friendly: MOEA/D
Hypervolume focus: SMS-EMOA

For constrained problems:

Feasibility-based survival selection (works with most algorithms)
Heavy constraints: SRES/ISRES
Penalty methods for algorithm compatibility

For dynamic problems:

Time-varying: D-NSGA-II
Historical knowledge useful: KGB-DMOEA