"""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 NSGA3from pymoo.problems import get_problemfrom pymoo.optimize import minimizefrom pymoo.util.ref_dirs import get_reference_directionsfrom pymoo.visualization.pcp import PCPimport 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()