181 lines
6.0 KiB
Markdown
181 lines
6.0 KiB
Markdown
# Pymoo Algorithms Reference
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Comprehensive reference for optimization algorithms available in pymoo.
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## Single-Objective Optimization Algorithms
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### Genetic Algorithm (GA)
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**Purpose:** General-purpose single-objective evolutionary optimization
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**Best for:** Continuous, discrete, or mixed-variable problems
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**Algorithm type:** (μ+λ) genetic algorithm
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**Key parameters:**
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- `pop_size`: Population size (default: 100)
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- `sampling`: Initial population generation strategy
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- `selection`: Parent selection mechanism (default: Tournament)
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- `crossover`: Recombination operator (default: SBX)
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- `mutation`: Variation operator (default: Polynomial)
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- `eliminate_duplicates`: Remove redundant solutions (default: True)
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- `n_offsprings`: Offspring per generation
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**Usage:**
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```python
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from pymoo.algorithms.soo.nonconvex.ga import GA
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algorithm = GA(pop_size=100, eliminate_duplicates=True)
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```
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### Differential Evolution (DE)
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**Purpose:** Single-objective continuous optimization
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**Best for:** Continuous parameter optimization with good global search
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**Algorithm type:** Population-based differential evolution
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**Variants:** Multiple DE strategies available (rand/1/bin, best/1/bin, etc.)
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### Particle Swarm Optimization (PSO)
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**Purpose:** Single-objective optimization through swarm intelligence
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**Best for:** Continuous problems, fast convergence on smooth landscapes
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### CMA-ES
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**Purpose:** Covariance Matrix Adaptation Evolution Strategy
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**Best for:** Continuous optimization, particularly for noisy or ill-conditioned problems
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### Pattern Search
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**Purpose:** Direct search method
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**Best for:** Problems where gradient information is unavailable
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### Nelder-Mead
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**Purpose:** Simplex-based optimization
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**Best for:** Local optimization of continuous functions
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## Multi-Objective Optimization Algorithms
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### NSGA-II (Non-dominated Sorting Genetic Algorithm II)
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**Purpose:** Multi-objective optimization with 2-3 objectives
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**Best for:** Bi- and tri-objective problems requiring well-distributed Pareto fronts
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**Selection strategy:** Non-dominated sorting + crowding distance
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**Key features:**
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- Fast non-dominated sorting
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- Crowding distance for diversity
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- Elitist approach
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- Binary tournament mating selection
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**Key parameters:**
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- `pop_size`: Population size (default: 100)
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- `sampling`: Initial population strategy
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- `crossover`: Default SBX for continuous
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- `mutation`: Default Polynomial Mutation
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- `survival`: RankAndCrowding
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**Usage:**
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```python
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from pymoo.algorithms.moo.nsga2 import NSGA2
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algorithm = NSGA2(pop_size=100)
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```
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**When to use:**
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- 2-3 objectives
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- Need for distributed solutions across Pareto front
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- Standard multi-objective benchmark
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### NSGA-III
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**Purpose:** Many-objective optimization (4+ objectives)
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**Best for:** Problems with 4 or more objectives requiring uniform Pareto front coverage
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**Selection strategy:** Reference direction-based diversity maintenance
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**Key features:**
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- Reference directions guide population
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- Maintains diversity in high-dimensional objective spaces
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- Niche preservation through reference points
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- Underrepresented reference direction selection
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**Key parameters:**
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- `ref_dirs`: Reference directions (REQUIRED)
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- `pop_size`: Defaults to number of reference directions
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- `crossover`: Default SBX
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- `mutation`: Default Polynomial Mutation
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**Usage:**
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```python
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from pymoo.algorithms.moo.nsga3 import NSGA3
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from pymoo.util.ref_dirs import get_reference_directions
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ref_dirs = get_reference_directions("das-dennis", n_dim=4, n_partitions=12)
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algorithm = NSGA3(ref_dirs=ref_dirs)
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```
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**NSGA-II vs NSGA-III:**
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- Use NSGA-II for 2-3 objectives
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- Use NSGA-III for 4+ objectives
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- NSGA-III provides more uniform distribution
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- NSGA-II has lower computational overhead
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### R-NSGA-II (Reference Point Based NSGA-II)
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**Purpose:** Multi-objective optimization with preference articulation
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**Best for:** When decision maker has preferred regions of Pareto front
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### U-NSGA-III (Unified NSGA-III)
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**Purpose:** Improved version handling various scenarios
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**Best for:** Many-objective problems with additional robustness
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### MOEA/D (Multi-Objective Evolutionary Algorithm based on Decomposition)
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**Purpose:** Decomposition-based multi-objective optimization
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**Best for:** Problems where decomposition into scalar subproblems is effective
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### AGE-MOEA
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**Purpose:** Adaptive geometry estimation
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**Best for:** Multi and many-objective problems with adaptive mechanisms
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### RVEA (Reference Vector guided Evolutionary Algorithm)
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**Purpose:** Reference vector-based many-objective optimization
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**Best for:** Many-objective problems with adaptive reference vectors
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### SMS-EMOA
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**Purpose:** S-Metric Selection Evolutionary Multi-objective Algorithm
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**Best for:** Problems where hypervolume indicator is critical
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**Selection:** Uses dominated hypervolume contribution
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## Dynamic Multi-Objective Algorithms
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### D-NSGA-II
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**Purpose:** Dynamic multi-objective problems
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**Best for:** Time-varying objective functions or constraints
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### KGB-DMOEA
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**Purpose:** Knowledge-guided dynamic multi-objective optimization
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**Best for:** Dynamic problems leveraging historical information
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## Constrained Optimization
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### SRES (Stochastic Ranking Evolution Strategy)
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**Purpose:** Single-objective constrained optimization
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**Best for:** Heavily constrained problems
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### ISRES (Improved SRES)
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**Purpose:** Enhanced constrained optimization
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**Best for:** Complex constraint landscapes
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## Algorithm Selection Guidelines
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**For single-objective problems:**
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- Start with GA for general problems
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- Use DE for continuous optimization
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- Try PSO for faster convergence on smooth problems
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- Use CMA-ES for difficult/noisy landscapes
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**For multi-objective problems:**
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- 2-3 objectives: NSGA-II
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- 4+ objectives: NSGA-III
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- Preference articulation: R-NSGA-II
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- Decomposition-friendly: MOEA/D
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- Hypervolume focus: SMS-EMOA
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**For constrained problems:**
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- Feasibility-based survival selection (works with most algorithms)
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- Heavy constraints: SRES/ISRES
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- Penalty methods for algorithm compatibility
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**For dynamic problems:**
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- Time-varying: D-NSGA-II
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- Historical knowledge useful: KGB-DMOEA
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