pymoo

pymoo

Overview

pymoo provides a unified API for multi-objective optimization via population-based evolutionary algorithms. Users define a problem by subclassing Problem or ElementwiseProblem, specifying objectives (n_obj), decision variables (n_var), and optional constraints (n_ieq_constr). Algorithms like NSGA-II and NSGA-III return a Result object containing the Pareto-optimal population, objective values, and decision variable values. pymoo separates problem definition, algorithm configuration, operator selection, and analysis — each component is independently replaceable.

When to Use

• Optimizing a design with two or more conflicting objectives (e.g., minimizing cost while maximizing performance)
• Running evolutionary algorithms (GA, DE, PSO) as black-box optimizers when gradients are unavailable
• Performing multi-objective hyperparameter search for ML models where accuracy and inference time trade off
• Computing Pareto fronts for portfolio optimization or multi-criteria decision analysis
• Customizing crossover/mutation operators for domain-specific solution encodings (binary, permutation, real-valued)
• Benchmarking optimization algorithms on standard test problems (ZDT, DTLZ, CTP)
• Use scipy.optimize instead for single-objective, gradient-available, smooth optimization

Prerequisites

• Python packages: pymoo, numpy, matplotlib
• Data requirements: objective function(s) and optional constraint functions; variable bounds
• Environment: CPU sufficient for most problems; GPU not used by pymoo core

pip install pymoo numpy matplotlib

Quick Start

import numpy as np
from pymoo.core.problem import Problem
from pymoo.algorithms.moo.nsga2 import NSGA2
from pymoo.optimize import minimize

class SimpleBiObjective(Problem):
    def __init__(self):
        super().__init__(n_var=2, n_obj=2, xl=np.array([-2, -2]), xu=np.array([2, 2]))

    def _evaluate(self, X, out, *args, **kwargs):
        f1 = X[:, 0] ** 2 + X[:, 1] ** 2