Pymoo

# 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

### MixedVariableGA
**Purpose:** Single-objective optimization with mixed variable types
**Best for:** Problems with continuous, integer, binary, and categorical variables

**Usage:**
```python
from pymoo.core.mixed import MixedVariableGA
from pymoo.core.variable import Real, Integer, Choice, Binary

# Define problem with vars dict (see mixed-variable docs)
algorithm = MixedVariableGA(pop_size=20)
```

For multi-objective mixed-variable problems, pass a survival operator:
```python
from pymoo.algorithms.moo.nsga2 import RankAndCrowdingSurvival
algorithm = MixedVariableGA(pop_size=20, survival=RankAndCrowdingSurvival())
```

### Optuna (Mixed-Variable SOO)
**Purpose:** Single-objective mixed-variable search via Optuna wrapper
**Best for:** Hyperparameter-style mixed search when Optuna's TPE/samplers are preferred

**Usage:**
```python
from pymoo.algorithms.soo.nonconvex.optuna import Optuna
algorithm = Optuna()
```

Requires Optuna installed separately: `uv pip install optuna`

## 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

### SPEA2 (Strength Pareto Evolutionary Algorithm 2)
**Purpose:** Multi-objective optimization with external archive
**Best for:** Bi- and tri-objective problems; alternative to NSGA-II when archive-based selection is preferred
**Selection strategy:** Strength-based fitness + k-nearest-neighbor density estimation

**Key features:**
- Ext