davila7/claude-code-templates/pymoo
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Multi-objective optimization framework. NSGA-II, NSGA-III, MOEA/D, Pareto fronts, constraint handling, benchmarks (ZDT, DTLZ), for engineering design and optimization problems.
Install
npx vskill@latest install davila7/claude-code-templates/pymooSKILL.md
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), 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.
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:
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 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 Dynamic: Time-varying objectives or constraints
Quick Start Workflows
Workflow 1: Single-Objective Optimization
When: Optimizing one objective function
Steps:
- Define or select problem
- Choose single-objective algorithm (GA, DE, PSO, CMA-ES)
- Configure termination criteria
- Run optimization
- Extract best solution
Example:
See: scripts/single_objective_example.py for complete example
Workflow 2: Multi-Objective Optimization (2-3 objectives)
When: Optimizing 2-3 conflicting objectives, need Pareto front
Algorithm choice: NSGA-II (standard for bi/tri-objective)
Steps:
- Define multi-objective problem
- Configure NSGA-II
- Run optimization to obtain Pareto front
- Visualize trade-offs
- Apply decision making (optional)
Example:
See: scripts/multi_objective_example.py for complete example
Workflow 3: Many-Objective Optimization (4+ objectives)
When: Optimizing 4 or more objectives
Algorithm choice: NSGA-III (designed for many objectives)
Key difference: Must provide reference directions for population guidance
Steps:
- Define many-objective problem
- Generate reference directions
- Configure NSGA-III with reference directions
- Run optimization
- Visualize using Parallel Coordinate Plot
Example:
See: scripts/many_objective_example.py for complete example
Workflow 4: Custom Problem Definition
When: Solving domain-specific optimization problem
Steps:
- Extend
ElementwiseProblemclass - Define
__init__with problem dimensions and bounds - Implement
_evaluatemethod for objectives (and constraints) - Use with any algorithm
Unconstrained example:
Constrained example:
Constraint formulation rules:
- Inequality: Express as
g(x) <= 0(feasible when ≤ 0) - Equality: Express as
h(x) = 0(feasible when = 0) - Convert
g(x) >= bto-(g(x) - b) <= 0
See: scripts/custom_problem_example.py for complete examples
Workflow 5: Constraint Handling
When: Problem has feasibility constraints
Approach options:
1. Feasibility First (Default - Recommended)
2. Penalty Method
3. Constraint as Objective
4. Specialized Algorithms
See: references/constraints_mcdm.md for comprehensive constraint handling guide
Workflow 6: Decision Making from Pareto Front
When: Have Pareto front, need to select preferred solution(s)
Steps:
- Run multi-objective optimization
- Normalize objectives to [0, 1]
- Define preference weights
- Apply MCDM method
- Visualize selected solution
Example using Pseudo-Weights:
Other MCDM methods:
- Compromise Programming: Select closest to ideal point
- Knee Point: Find balanced trade-off solutions
- Hypervolume Contribution: Select most diverse subset
See:
scripts/decision_making_example.pyfor complete examplereferences/constraints_mcdm.mdfor detailed MCDM methods
Workflow 7: Visualization
Choose visualization based on number of objectives:
2 objectives: Scatter Plot
3 objectives: 3D Scatter
4+ objectives: Parallel Coordinate Plot
Solution comparison: Petal Diagram
See: references/visualization.md for all visualization types and usage
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 | |
| 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:
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Source
- SKILL.md in the repositoryCheckingcli-tool/components/skills/scientific/pymoo/SKILL.md
Popularity
- Repository stars
- 22,344
- Repository forks
- 2,122
- Repository npm downloads, 7 days
- 5,078
- 7-day trend score
- 70
Stars and forks are for the whole GitHub repository, not this skill alone. Downloads are for the repository's npm package. Refreshed 17 Mar 2026, 7 months ago.
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