bundled-skills-pymoo

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SKILL.md

Pymoo - Multi-Objective Optimization in Python

Routing Boundary

Use this skill only for pymoo, NSGA-II/NSGA, Pareto-front analysis, multi-objective optimization, constrained optimization, and pymoo algorithm implementation. Do not use it for generic optimization planning, experiment design, gradient descent, Bayesian modeling, PyMC, or causal analysis.

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:

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)

from pymoo.algorithms.soo.nonconvex.ga import GA
from pymoo.problems import get_problem
from pymoo.optimize import minimize

# Built-in problem
problem = get_problem("rastrigin", n_var=10)

# Configure Genetic Algorithm
algorithm = GA(
    pop_size=100,
    eliminate_duplicates=True
)

# Optimize
result = minimize(
    problem,
    algorithm,
    ('n_gen', 200),
    seed=1,
    verbose=True
)

print(f"Best solution: {result.X}")
print(f"Best objective: {result.F[0]}")

from pymoo.algorithms.moo.nsga2 import NSGA2
from pymoo.problems import get_problem
from pymoo.optimize import minimize
from pymoo.visualization.scatter import Scatter

# Bi-objective benchmark problem
problem = get_problem("zdt1")

# NSGA-II algorithm
algorithm = NSGA2(pop_size=100)

# Optimize
result = minimize(problem, algorithm, ('n_gen', 200), seed=1)

# Visualize Pareto front
plot = Scatter()
plot.add(result.F, label="Obtained Front")
plot.add(problem.pareto_front(), label="True Front", alpha=0.3)
plot.show()

print(f"Found {len(result.F)} Pareto-optimal solutions")

from pymoo.algorithms.moo.nsga3 import NSGA3
from pymoo.problems import get_problem
from pymoo.optimize import minimize
from pymoo.util.ref_dirs import get_reference_directions
from pymoo.visualization.pcp import PCP

# Many-objective problem (5 objectives)
problem = get_problem("dtlz2", n_obj=5)

# Generate reference directions (required for NSGA-III)
ref_dirs = get_reference_directions("das-dennis", n_dim=5, n_partitions=12)

# Configure NSGA-III
algorithm = NSGA3(ref_dirs=ref_dirs)

# Optimize
result = minimize(problem, algorithm, ('n_gen', 300), seed=1)

# Visualize with Parallel Coordinates
plot = PCP(labels=[f"f{i+1}" for i in range(5)])
plot.add(result.F, alpha=0.3)
plot.show()

from pymoo.core.problem import ElementwiseProblem
import numpy as np

class MyProblem(ElementwiseProblem):
    def __init__(self):
        super().__init__(
            n_var=2,              # Number of variables
            n_obj=2,              # Number of objectives
            xl=np.array([0, 0]),  # Lower bounds
            xu=np.array([5, 5])   # Upper bounds
        )

    def _evaluate(self, x, out, *args, **kwargs):
        # Define objectives
        f1 = x[0]**2 + x[1]**2
        f2 = (x[0]-1)**2 + (x[1]-1)**2

        out["F"] = [f1, f2]

class ConstrainedProblem(ElementwiseProblem):
    def __init__(self):
        super().__init__(
            n_var=2,
            n_obj=2,
            n_ieq_constr=2,        # Inequality constraints
            n_eq_constr=1,         # Equality constraints
            xl=np.array([0, 0]),
            xu=np.array([5, 5])
        )

    def _evaluate(self, x, out, *args, **kwargs):
        # Objectives
        out["F"] = [f1, f2]

        # Inequality constraints (g <= 0)
        out["G"] = [g1, g2]

        # Equality constraints (h = 0)
        out["H"] = [h1]

from pymoo.algorithms.moo.nsga2 import NSGA2

# Works automatically with constrained problems
algorithm = NSGA2(pop_size=100)
result = minimize(problem, algorithm, termination)

# Check feasibility
feasible = result.CV[:, 0] == 0  # CV = constraint violation
print(f"Feasible solutions: {np.sum(feasible)}")

from pymoo.constraints.as_penalty import ConstraintsAsPenalty

# Wrap problem to convert constraints to penalties
problem_penalized = ConstraintsAsPenalty(problem, penalty=1e6)

from pymoo.constraints.as_obj import ConstraintsAsObjective

# Treat constraint violation as additional objective
problem_with_cv = ConstraintsAsObjective(problem)

from pymoo.algorithms.soo.nonconvex.sres import SRES

# SRES has built-in constraint handling
algorithm = SRES()

from pymoo.mcdm.pseudo_weights import PseudoWeights
import numpy as np

# After obtaining result from multi-objective optimization
# Normalize objectives
F_norm = (result.F - result.F.min(axis=0)) / (result.F.max(axis=0) - result.F.min(axis=0))

# Define preferences (must sum to 1)
weights = np.array([0.3, 0.7])  # 30% f1, 70% f2

# Apply decision making
dm = PseudoWeights(weights)
selected_idx = dm.do(F_norm)

# Get selected solution
best_solution = result.X[selected_idx]
best_objectives = result.F[selected_idx]

print(f"Selected solution: {best_solution}")
print(f"Objective values: {best_objectives}")

from pymoo.visualization.scatter import Scatter

plot = Scatter(title="Bi-objective Results")
plot.add(result.F, color="blue", alpha=0.7)
plot.show()

plot = Scatter(title="Tri-objective Results")
plot.add(result.F)  # Automatically renders in 3D
plot.show()

from pymoo.visualization.pcp import PCP

plot = PCP(
    labels=[f"f{i+1}" for i in range(n_obj)],
    normalize_each_axis=True
)
plot.add(result.F, alpha=0.3)
plot.show()

from pymoo.visualization.petal import Petal

plot = Petal(
    bounds=[result.F.min(axis=0), result.F.max(axis=0)],
    labels=["Cost", "Weight", "Efficiency"]
)
plot.add(solution_A, label="Design A")
plot.add(solution_B, label="Design B")
plot.show()

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

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

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

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

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)

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
)

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

uv pip install pymoo

bundled-skills-pymoo

Summary

SKILL.md

Pymoo - Multi-Objective Optimization in Python

Routing Boundary

Overview

When to Use This Skill

Core Concepts

The Unified Interface

Problem Types

Quick Start Workflows

Workflow 1: Single-Objective Optimization

Workflow 2: Multi-Objective Optimization (2-3 objectives)

Workflow 3: Many-Objective Optimization (4+ objectives)

Workflow 4: Custom Problem Definition

Workflow 5: Constraint Handling

Workflow 6: Decision Making from Pareto Front

Workflow 7: Visualization

Algorithm Selection Guide

Single-Objective Problems

Multi-Objective Problems (2-3 objectives)

Many-Objective Problems (4+ objectives)

Constrained Problems

Benchmark Problems

Quick problem access:

Genetic Operator Customization

Standard operator configuration:

Operator selection by variable type:

Performance and Troubleshooting

Common issues and solutions:

Best practices:

Resources

references/

scripts/

Additional Notes

Related skills