"""
Many-objective optimization example using pymoo.
This script demonstrates many-objective optimization (4+ objectives)
using NSGA-III on the DTLZ2 benchmark problem.
"""
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
import numpy as np
def run_many_objective_optimization():
"""Run many-objective optimization example."""
# Define the problem - DTLZ2 with 5 objectives
n_obj = 5
problem = get_problem("dtlz2", n_obj=n_obj)
# Generate reference directions for NSGA-III
# Das-Dennis method for uniform distribution
ref_dirs = get_reference_directions("das-dennis", n_obj, n_partitions=12)
print(f"Number of reference directions: {len(ref_dirs)}")
# Configure NSGA-III algorithm
algorithm = NSGA3(
ref_dirs=ref_dirs,
eliminate_duplicates=True
)
# Run optimization
result = minimize(
problem,
algorithm,
('n_gen', 300),
seed=1,
verbose=True
)
# Print results summary
print("\n" + "="*60)
print("MANY-OBJECTIVE OPTIMIZATION RESULTS")
print("="*60)
print(f"Number of objectives: {n_obj}")
print(f"Number of solutions: {len(result.F)}")
print(f"Number of generations: {result.algorithm.n_gen}")
print(f"Number of function evaluations: {result.algorithm.evaluator.n_eval}")
# Show objective space statistics
print("\nObjective space statistics:")
print(f"Minimum values per objective: {result.F.min(axis=0)}")
print(f"Maximum values per objective: {result.F.max(axis=0)}")
print("="*60)
# Visualize using Parallel Coordinate Plot
plot = PCP(
title=f"DTLZ2 ({n_obj} objectives) - NSGA-III Results",
labels=[f"f{i+1}" for i in range(n_obj)],
normalize_each_axis=True
)
plot.add(result.F, alpha=0.3, color="blue")
plot.show()
return result
if __name__ == "__main__":
result = run_many_objective_optimization()