Pymoo

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:

Algorithm Selection Guide

Single-Objective Problems

Multi-Objective Problems (2-3 objectives)

Many-Objective Problems (4+ objectives)

Constrained Problems

Algorithm choices are starting points, not performance guarantees. Pymoo MOEA/D does not support constraints directly.

See: references/algorithms.md for algorithm parameters and restrictions

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("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:

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)