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. Targets stable pymoo 0.6.2, reviewed 2026-10-01 against current official docs and native toy runs.

Installation

uv pip install "pymoo==0.6.2"

For reproducible environments, pin a version: uv pip install "pymoo==0.6.2".

Dependencies: The released 0.6.2 wheel requires NumPy, SciPy, moocore, autograd, cma, matplotlib, alive_progress, and Deprecated. NumPy 2.x is supported. The current installation prose describes some dependencies as optional; the released package metadata governs installation. Joblib, Optuna and dill are separate dependencies for the corresponding recipes.

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: Raw inequality values (g(x) <= 0 is feasible)
• result.H: Raw equality residuals
• result.CV: Aggregated constraint violation under the configured tolerances
• result.algorithm: Final algorithm state; history is retained when requested

Check feasibility before plotting or selecting: If no feasible solution was found, result.X and result.F can be None. With return_least_infeasible=True, a returned candidate can still violate constraints; report its CV and residuals instead of calling it feasible. Re-evaluate chosen candidates against the original physical constraints after any normalization or repair. See the result contract.

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; negate a maximization objective and record the conversion 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 workflows and context-dependent adaptation snippets are in references/quick_start_workflows.md:

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