"""Custom problem definition example using pymoo. This script demonstrates how to define a custom optimization problemand solve it using pymoo.""" from pymoo.core.problem import ElementwiseProblemfrom pymoo.algorithms.moo.nsga2 import NSGA2from pymoo.optimize import minimizefrom pymoo.visualization.scatter import Scatterimport numpy as np  class MyBiObjectiveProblem(ElementwiseProblem):    """    Custom bi-objective optimization problem.     Minimize:        f1(x) = x1^2 + x2^2        f2(x) = (x1-1)^2 + (x2-1)^2     Subject to:        0 <= x1 <= 5        0 <= x2 <= 5    """     def __init__(self):        super().__init__(            n_var=2,                    # Number of decision variables            n_obj=2,                    # Number of objectives            n_ieq_constr=0,            # Number of inequality constraints            n_eq_constr=0,             # Number of equality constraints            xl=np.array([0, 0]),       # Lower bounds            xu=np.array([5, 5])        # Upper bounds        )     def _evaluate(self, x, out, *args, **kwargs):        """Evaluate objectives for a single solution."""        # Objective 1: Distance from origin        f1 = x[0]**2 + x[1]**2         # Objective 2: Distance from (1, 1)        f2 = (x[0] - 1)**2 + (x[1] - 1)**2         # Return objectives        out["F"] = [f1, f2]  class ConstrainedProblem(ElementwiseProblem):    """    Custom constrained bi-objective problem.     Minimize:        f1(x) = x1        f2(x) = (1 + x2) / x1     Subject to:        x2 + 9*x1 >= 6          (g1 <= 0)        -x2 + 9*x1 >= 1         (g2 <= 0)        0.1 <= x1 <= 1        0 <= x2 <= 5    """     def __init__(self):        super().__init__(            n_var=2,            n_obj=2,            n_ieq_constr=2,            # Two inequality constraints            xl=np.array([0.1, 0.0]),            xu=np.array([1.0, 5.0])        )     def _evaluate(self, x, out, *args, **kwargs):        """Evaluate objectives and constraints."""        # Objectives        f1 = x[0]        f2 = (1 + x[1]) / x[0]         out["F"] = [f1, f2]         # Inequality constraints (g <= 0)        # Convert g1: x2 + 9*x1 >= 6  →  -(x2 + 9*x1 - 6) <= 0        g1 = -(x[1] + 9 * x[0] - 6)         # Convert g2: -x2 + 9*x1 >= 1  →  -(-x2 + 9*x1 - 1) <= 0        g2 = -(-x[1] + 9 * x[0] - 1)         out["G"] = [g1, g2]  def solve_custom_problem():    """Solve custom bi-objective problem."""     print("="*60)    print("CUSTOM PROBLEM - UNCONSTRAINED")    print("="*60)     # Define custom problem    problem = MyBiObjectiveProblem()     # Configure algorithm    algorithm = NSGA2(pop_size=100)     # Solve    result = minimize(        problem,        algorithm,        ('n_gen', 200),        seed=1,        verbose=False    )     print(f"Number of solutions: {len(result.F)}")    print(f"Objective space range:")    print(f"  f1: [{result.F[:, 0].min():.3f}, {result.F[:, 0].max():.3f}]")    print(f"  f2: [{result.F[:, 1].min():.3f}, {result.F[:, 1].max():.3f}]")     # Visualize    plot = Scatter(title="Custom Bi-Objective Problem")    plot.add(result.F, color="blue", alpha=0.7)    plot.show()     return result  def solve_constrained_problem():    """Solve custom constrained problem."""     print("\n" + "="*60)    print("CUSTOM PROBLEM - CONSTRAINED")    print("="*60)     # Define constrained problem    problem = ConstrainedProblem()     # Configure algorithm    algorithm = NSGA2(pop_size=100)     # Solve    result = minimize(        problem,        algorithm,        ('n_gen', 200),        seed=1,        verbose=False    )     # Check feasibility    feasible = result.CV[:, 0] == 0  # Constraint violation = 0     print(f"Total solutions: {len(result.F)}")    print(f"Feasible solutions: {np.sum(feasible)}")    print(f"Infeasible solutions: {np.sum(~feasible)}")     if np.any(feasible):        F_feasible = result.F[feasible]        print(f"\nFeasible objective space range:")        print(f"  f1: [{F_feasible[:, 0].min():.3f}, {F_feasible[:, 0].max():.3f}]")        print(f"  f2: [{F_feasible[:, 1].min():.3f}, {F_feasible[:, 1].max():.3f}]")         # Visualize feasible solutions        plot = Scatter(title="Constrained Problem - Feasible Solutions")        plot.add(F_feasible, color="green", alpha=0.7, label="Feasible")         if np.any(~feasible):            plot.add(result.F[~feasible], color="red", alpha=0.3, s=10, label="Infeasible")         plot.show()     return result  if __name__ == "__main__":    # Run both examples    result1 = solve_custom_problem()    result2 = solve_constrained_problem()     print("\n" + "="*60)    print("EXAMPLES COMPLETED")    print("="*60)