# Pymoo

> Framework de optimización multiobjetivo: NSGA-II, NSGA-III, MOEA/D, frentes de Pareto, manejo de restricciones y benchmarks (ZDT, DTLZ) para problemas de diseño e ingeniería.

Fuente: https://skillsagentes.com/skills/k-dense-ai/scientific-agent-skills/pymoo
Markdown: https://skillsagentes.com/skills/k-dense-ai/scientific-agent-skills/pymoo.md

Repositorio: https://github.com/K-Dense-AI/scientific-agent-skills
Autor: K-Dense-AI
Licencia: Apache-2.0 license
Actualizado: el mes pasado
Coste de contexto: 44 tok instalada, 2.6k tok al activarse, 20.8k tok con todos los archivos del bundle
Bundle: 13 archivos, 81 KB
Permisos que pide: read write edit bash

## Instalación

Un skill son archivos markdown: los mismos archivos valen para cualquier agente y lo único que cambia es el directorio de destino, es decir la bandera `--agent`. Añade `-g` para instalarlo en todos los proyectos de la máquina.

```bash
# Claude Code
npx -y skills add K-Dense-AI/scientific-agent-skills --skill pymoo --agent claude-code
# Cursor
npx -y skills add K-Dense-AI/scientific-agent-skills --skill pymoo --agent cursor
# Codex
npx -y skills add K-Dense-AI/scientific-agent-skills --skill pymoo --agent codex
# Gemini CLI
npx -y skills add K-Dense-AI/scientific-agent-skills --skill pymoo --agent gemini
# Windsurf
npx -y skills add K-Dense-AI/scientific-agent-skills --skill pymoo --agent windsurf
# Cline
npx -y skills add K-Dense-AI/scientific-agent-skills --skill pymoo --agent cline
```

## Qué hace

- Resuelve problemas de optimización mono y multiobjetivo con algoritmos como NSGA-II, NSGA-III, MOEA/D y SPEA2
- Encuentra frentes de Pareto y analiza soluciones de compromiso en problemas con objetivos en conflicto
- Ofrece problemas de referencia (ZDT, DTLZ, WFG) para comparar algoritmos
- Permite personalizar operadores genéticos (cruce, mutación, selección) y manejar restricciones
- Incluye nueve flujos de trabajo listos para ejecutar y scripts de ejemplo para cada tipo de problema

## Cuándo usarla

- El usuario resuelve problemas de optimización con uno o varios objetivos
- Necesita encontrar soluciones Pareto-óptimas y analizar trade-offs
- Quiere implementar algoritmos evolutivos (GA, DE, PSO, NSGA-II/III) o comparar contra problemas de referencia
- Trabaja con variables binarias, discretas, continuas o mixtas y necesita elegir entre soluciones competidoras

## Qué la activa

- "Optimiza este problema con NSGA-II y muéstrame el frente de Pareto"
- "Define un problema personalizado en pymoo con restricciones"
- "Compara NSGA-II y MOEA/D en el problema ZDT1"
- "Elige el algoritmo adecuado para un problema con 5 objetivos"

## Antes de instalar

- Requiere Python 3.10+ y pymoo (uv pip install pymoo); matplotlib, autograd y joblib son opcionales según la función usada.
- Necesita en el PATH: python3

## Archivos

- SKILL.md — 10 KB
- references/algorithms.md — 8 KB
- references/constraints_mcdm.md — 11 KB
- references/operators.md — 9 KB
- references/parallelization.md — 3 KB
- references/problems.md — 7 KB
- references/quick_start_workflows.md — 11 KB
- references/visualization.md — 9 KB
- scripts/custom_problem_example.py — 5 KB
- scripts/decision_making_example.py — 4 KB
- scripts/many_objective_example.py — 2 KB
- scripts/multi_objective_example.py — 2 KB
- scripts/single_objective_example.py — 2 KB

## SKILL.md

Reproducido tal cual desde K-Dense-AI/scientific-agent-skills bajo Apache-2.0 license. Esta sección es el documento original y está en inglés.

# Pymoo - Multi-Objective Optimization in Python

## Overview

Pymoo is a comprehensive Python framework for optimization with emphasis on multi-objective problems. Solve single and multi-objective optimization using state-of-the-art algorithms (NSGA-II/III, MOEA/D, SPEA2), benchmark problems (ZDT, DTLZ), customizable genetic operators, and multi-criteria decision making methods. Excels at finding trade-off solutions (Pareto fronts) for problems with conflicting objectives. Current stable release: **pymoo 0.6.1.6** (November 2025).

## Installation

```bash
uv pip install pymoo
```

For reproducible environments, pin a version: `uv pip install "pymoo==0.6.1.6"`.

**Dependencies:** NumPy (2.x compatible since 0.6.1.3), SciPy, matplotlib (visualization). Autograd is optional for gradient-based features (since 0.6.1.3).

**Documentation:** https://pymoo.org/ — LLM-friendly index: https://pymoo.org/llms.txt

## When to Use This Skill

This skill should be used when:
- Solving optimization problems with one or multiple objectives
- Finding Pareto-optimal solutions and analyzing trade-offs
- Implementing evolutionary algorithms (GA, DE, PSO, NSGA-II/III)
- Working with constrained optimization problems
- Benchmarking algorithms on standard test problems (ZDT, DTLZ, WFG)
- Customizing genetic operators (crossover, mutation, selection)
- Visualizing high-dimensional optimization results
- Making decisions from multiple competing solutions
- Handling binary, discrete, continuous, or mixed-variable problems

## Core Concepts

### The Unified Interface

Pymoo uses a consistent `minimize()` function for all optimization tasks:

```python
from pymoo.optimize import minimize

result = minimize(
    problem,        # What to optimize
    algorithm,      # How to optimize
    termination,    # When to stop
    seed=1,
    verbose=True
)
```

**Result object contains:**
- `result.X`: Decision variables of optimal solution(s)
- `result.F`: Objective values of optimal solution(s)
- `result.G`: Constraint violations (if constrained)
- `result.algorithm`: Algorithm object with history

### Problem Definition Styles

Pymoo supports three problem definition styles:

- **`Problem`**: Vectorized — `_evaluate` receives a batch of solutions (matrix)
- **`ElementwiseProblem`**: One solution per call — recommended for custom problems and parallel evaluation
- **`FunctionalProblem`**: Define objectives and constraints as separate functions without subclassing

### Problem Types

**Single-objective:** One objective to minimize/maximize
**Multi-objective:** 2-3 conflicting objectives → Pareto front
**Many-objective:** 4+ objectives → High-dimensional Pareto front
**Constrained:** Objectives + inequality/equality constraints
**Mixed-variable:** Continuous, integer, binary, and categorical variables in one problem
**Dynamic:** Time-varying objectives or constraints

## Quick Start Workflows

Nine runnable workflows are in
[references/quick_start_workflows.md](references/quick_start_workflows.md):

| # | Workflow | Use when |
| --- | --- | --- |
| 1 | Single-objective optimization | one objective, GA or DE |
| 2 | Multi-objective (2-3 objectives) | NSGA-II and a Pareto front |
| 3 | Many-objective (4+ objectives) | NSGA-III or reference-direction methods |
| 4 | Custom problem definition | subclassing `Problem` / `ElementwiseProblem` |
| 5 | Constraint handling | inequality and equality constraints |
| 6 | Decision making from a Pareto front | scalarization and MCDM selection |
| 7 | Visualization | scatter, PCP, radviz, and heatmap views |
| 8 | Parallel evaluation | threads, processes, or Dask for expensive objectives |
| 9 | Mixed-variable optimization | integer, binary, and categorical variables |

## Algorithm Selection Guide

### Single-Objective Problems

| Algorithm | Best For | Key Features |
|-----------|----------|--------------|
| **GA** | General-purpose | Flexible, customizable operators |
| **DE** | Continuous optimization | Good global search |
| **PSO** | Smooth landscapes | Fast convergence |
| **CMA-ES** | Difficult/noisy problems | Self-adapting |

### Multi-Objective Problems (2-3 objectives)

| Algorithm | Best For | Key Features |
|-----------|----------|--------------|
| **NSGA-II** | Standard benchmark | Fast, reliable, well-tested |
| **SPEA2** | Archive-based MOO | Strength-based fitness, external archive |
| **R-NSGA-II** | Preference regions | Reference point guidance |
| **MOEA/D** | Decomposable problems | Scalarization approach |

### Many-Objective Problems (4+ objectives)

| Algorithm | Best For | Key Features |
|-----------|----------|--------------|
| **NSGA-III** | 4-15 objectives | Reference direction-based |
| **RVEA** | Adaptive search | Reference vector evolution |
| **AGE-MOEA** | Complex landscapes | Adaptive geometry |

### Constrained Problems

| Approach | Algorithm | When to Use |
|----------|-----------|-------------|
| Feasibility-first | Any algorithm | Large feasible region |
| Specialized | SRES, ISRES | Heavy constraints |
| Penalty | GA + penalty | Algorithm compatibility |

**See:** `references/algorithms.md` for comprehensive algorithm reference

## Benchmark Problems

### Quick problem access:
```python
from pymoo.problems import get_problem

# Single-objective
problem = get_problem("rastrigin", n_var=10)
problem = get_problem("rosenbrock", n_var=10)

# Multi-objective
problem = get_problem("zdt1")        # Convex front
problem = get_problem("zdt2")        # Non-convex front
problem = get_problem("zdt3")        # Disconnected front

# Many-objective
problem = get_problem("dtlz2", n_obj=5, n_var=12)
problem = get_problem("dtlz7", n_obj=4)
```

**See:** `references/problems.md` for complete test problem reference

## Genetic Operator Customization

### Standard operator configuration:
```python
from pymoo.algorithms.soo.nonconvex.ga import GA
from pymoo.operators.crossover.sbx import SBX
from pymoo.operators.mutation.pm import PM

algorithm = GA(
    pop_size=100,
    crossover=SBX(prob=0.9, eta=15),
    mutation=PM(eta=20),
    eliminate_duplicates=True
)
```

### Operator selection by variable type:

**Continuous variables:**
- Crossover: SBX (Simulated Binary Crossover)
- Mutation: PM (Polynomial Mutation)

**Binary variables:**
- Crossover: TwoPointCrossover, UniformCrossover
- Mutation: BitflipMutation

**Permutations (TSP, scheduling):**
- Crossover: OrderCrossover (OX)
- Mutation: InversionMutation

**See:** `references/operators.md` for comprehensive operator reference

## Performance and Troubleshooting

### Common issues and solutions:

**Problem: Algorithm not converging**
- Increase population size
- Increase number of generations
- Check if problem is multimodal (try different algorithms)
- Verify constraints are correctly formulated

**Problem: Poor Pareto front distribution**
- For NSGA-III: Adjust reference directions
- Increase population size
- Check for duplicate elimination
- Verify problem scaling

**Problem: Few feasible solutions**
- Use constraint-as-objective approach
- Apply repair operators
- Try SRES/ISRES for constrained problems
- Check constraint formulation (should be g <= 0)

**Problem: High computational cost**
- Reduce population size
- Decrease number of generations
- Use simpler operators
- Enable parallel evaluation via `elementwise_runner` (see Workflow 8)

### Best practices:

1. **Normalize objectives** when scales differ significantly
2. **Set random seed** for reproducibility
3. **Save history** to analyze convergence: `save_history=True`
4. **Visualize results** to understand solution quality
5. **Compare with true Pareto front** when available
6. **Use appropriate termination criteria** (generations, evaluations, tolerance)
7. **Tune operator parameters** for problem characteristics

## Resources

This skill includes comprehensive reference documentation and executable examples:

### references/
Detailed documentation for in-depth understanding:

- **algorithms.md**: Complete algorithm reference with parameters, usage, and selection guidelines
- **problems.md**: Benchmark test problems (ZDT, DTLZ, WFG) with characteristics
- **operators.md**: Genetic operators (sampling, selection, crossover, mutation) with configuration
- **visualization.md**: All visualization types with examples and selection guide
- **constraints_mcdm.md**: Constraint handling techniques and multi-criteria decision making methods
- **parallelization.md**: Parallel evaluation with StarmapParallelization and JoblibParallelization

**Search patterns for references:**
- Algorithm details: `grep -r "NSGA-II\|NSGA-III\|MOEA/D" references/`
- Constraint methods: `grep -r "Feasibility First\|Penalty\|Repair" references/`
- Visualization types: `grep -r "Scatter\|PCP\|Petal" references/`

### scripts/
Executable examples demonstrating common workflows:

- **single_objective_example.py**: Basic single-objective optimization with GA
- **multi_objective_example.py**: Multi-objective optimization with NSGA-II, visualization
- **many_objective_example.py**: Many-objective optimization with NSGA-III, reference directions
- **custom_problem_example.py**: Defining custom problems (constrained and unconstrained)
- **decision_making_example.py**: Multi-criteria decision making with different preferences

**Run examples:**
```bash
python3 scripts/single_objective_example.py
python3 scripts/multi_objective_example.py
python3 scripts/many_objective_example.py
python3 scripts/custom_problem_example.py
python3 scripts/decision_making_example.py
```

## Additional Notes

**Common patterns:**
- Use `ElementwiseProblem` for custom problems (or `FunctionalProblem` for function-based definitions)
- Use `vars` dict with typed variables for mixed-variable problems
- Constraints formulated as `g(x) <= 0` and `h(x) = 0`
- Reference directions required for NSGA-III
- Normalize objectives before MCDM
- Use appropriate termination: `('n_gen', N)` or `get_termination("f_tol", tol=0.001)`

## Dónde encaja

- Categoría: [Datos y analítica](https://skillsagentes.com/categorias/datos-analitica.md) — Consulta, limpia y visualiza datos sin salir del agente.
- Creador: [K-Dense-AI](https://skillsagentes.com/creators/k-dense-ai.md) — 163 skills en el directorio
- [Todas las skills](https://skillsagentes.com/skills.md)
- [Ranking de instalaciones](https://skillsagentes.com/ranking.md)

## Otras skills del mismo repositorio

- [Citation Management](https://skillsagentes.com/skills/k-dense-ai/scientific-agent-skills/citation-management.md): Gestión integral de citas académicas: busca en OpenAlex, PubMed y Google Scholar, extrae metadatos precisos, valida citas y genera entradas BibTeX correctamente formateadas.
- [Scientific Slides](https://skillsagentes.com/skills/k-dense-ai/scientific-agent-skills/scientific-slides.md): Crea decks de diapositivas y presentaciones para charlas de investigación: PowerPoint, presentaciones de conferencia, seminarios, defensas de tesis. Da estructura, plantillas, guía de tiempos y validación visual.
- [Literature Review](https://skillsagentes.com/skills/k-dense-ai/scientific-agent-skills/literature-review.md): Realiza revisiones bibliográficas sistemáticas y completas usando varias bases académicas (PubMed, arXiv, bioRxiv, Semantic Scholar). Genera markdown y PDF con citas verificadas en varios estilos (APA, Nature, Vancouver).
- [Infographics](https://skillsagentes.com/skills/k-dense-ai/scientific-agent-skills/infographics.md): Crea infografías profesionales con Nano Banana Pro AI y refinamiento iterativo inteligente. Usa Gemini 3.6 Flash para revisar la calidad e integra investigación con Perplexity Sonar. Soporta 10 tipos, 8 estilos y paletas para daltonismo.
- [Latex Posters](https://skillsagentes.com/skills/k-dense-ai/scientific-agent-skills/latex-posters.md): Crea pósteres de investigación profesionales en LaTeX con beamerposter, tikzposter o baposter, para conferencias y comunicación científica: layout, colores, columnas múltiples e integración de figuras.

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