/pymoo

name: pymoo
description: Multi-objective optimization framework. NSGA-II, NSGA-III, MOEA/D, Pareto fronts, constraint handling, benchmarks (ZDT, DTLZ), for engineering design and optimization problems.
license: Apache-2.0 license
allowed-tools: Read Write Edit Bash
compatibility: Requires Python 3.10+ and pymoo (uv pip install). Optional matplotlib for visualization plots; optional autograd for gradient-based features; optional joblib for JoblibParallelization.
metadata:
  version: "1.4"
  skill-author: K-Dense Inc.

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

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:

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:

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("zd