"""
Custom problem definition example using pymoo.
This script demonstrates how to define a custom optimization problem
and solve it using pymoo.
"""
from pymoo.core.problem import ElementwiseProblem
from pymoo.algorithms.moo.nsga2 import NSGA2
from pymoo.optimize import minimize
from pymoo.visualization.scatter import Scatter
import 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)