"""
Multi-criteria decision making example using pymoo.
This script demonstrates how to select preferred solutions from
a Pareto front using various MCDM methods.
"""
from pymoo.algorithms.moo.nsga2 import NSGA2
from pymoo.problems import get_problem
from pymoo.optimize import minimize
from pymoo.mcdm.pseudo_weights import PseudoWeights
from pymoo.visualization.scatter import Scatter
from pymoo.visualization.petal import Petal
import numpy as np
def run_optimization_for_decision_making():
"""Run optimization to obtain Pareto front."""
print("Running optimization to obtain Pareto front...")
# Solve ZDT1 problem
problem = get_problem("zdt1")
algorithm = NSGA2(pop_size=100)
result = minimize(
problem,
algorithm,
('n_gen', 200),
seed=1,
verbose=False
)
print(f"Obtained {len(result.F)} solutions in Pareto front\n")
return problem, result
def apply_pseudo_weights(result, weights):
"""Apply pseudo-weights MCDM method."""
print(f"Applying Pseudo-Weights with weights: {weights}")
# Normalize objectives to [0, 1]
F_norm = (result.F - result.F.min(axis=0)) / (result.F.max(axis=0) - result.F.min(axis=0))
# Apply MCDM
dm = PseudoWeights(weights)
selected_idx = dm.do(F_norm)
selected_x = result.X[selected_idx]
selected_f = result.F[selected_idx]
print(f"Selected solution (decision variables): {selected_x}")
print(f"Selected solution (objectives): {selected_f}")
print()
return selected_idx, selected_x, selected_f
def compare_different_preferences(result):
"""Compare selections with different preference weights."""
print("="*60)
print("COMPARING DIFFERENT PREFERENCE WEIGHTS")
print("="*60 + "\n")
# Define different preference scenarios
scenarios = [
("Equal preference", np.array([0.5, 0.5])),
("Prefer f1", np.array([0.8, 0.2])),
("Prefer f2", np.array([0.2, 0.8])),
]
selections = {}
for name, weights in scenarios:
print(f"Scenario: {name}")
idx, x, f = apply_pseudo_weights(result, weights)
selections[name] = (idx, f)
# Visualize all selections
plot = Scatter(title="Decision Making - Different Preferences")
plot.add(result.F, color="lightgray", alpha=0.5, s=20, label="Pareto Front")
colors = ["red", "blue", "green"]
for (name, (idx, f)), color in zip(selections.items(), colors):
plot.add(f, color=color, s=100, marker="*", label=name)
plot.show()
return selections
def visualize_selected_solutions(result, selections):
"""Visualize selected solutions using petal diagram."""
# Get objective bounds for normalization
f_min = result.F.min(axis=0)
f_max = result.F.max(axis=0)
plot = Petal(
title="Selected Solutions Comparison",
bounds=[f_min, f_max],
labels=["f1", "f2"]
)
colors = ["red", "blue", "green"]
for (name, (idx, f)), color in zip(selections.items(), colors):
plot.add(f, color=color, label=name)
plot.show()
def find_extreme_solutions(result):
"""Find extreme solutions (best in each objective)."""
print("\n" + "="*60)
print("EXTREME SOLUTIONS")
print("="*60 + "\n")
# Best f1 (minimize f1)
best_f1_idx = np.argmin(result.F[:, 0])
print(f"Best f1 solution: {result.F[best_f1_idx]}")
print(f" Decision variables: {result.X[best_f1_idx]}\n")
# Best f2 (minimize f2)
best_f2_idx = np.argmin(result.F[:, 1])
print(f"Best f2 solution: {result.F[best_f2_idx]}")
print(f" Decision variables: {result.X[best_f2_idx]}\n")
return best_f1_idx, best_f2_idx
def main():
"""Main execution function."""
# Step 1: Run optimization
problem, result = run_optimization_for_decision_making()
# Step 2: Find extreme solutions
best_f1_idx, best_f2_idx = find_extreme_solutions(result)
# Step 3: Compare different preference weights
selections = compare_different_preferences(result)
# Step 4: Visualize selections with petal diagram
visualize_selected_solutions(result, selections)
print("="*60)
print("DECISION MAKING EXAMPLE COMPLETED")
print("="*60)
print("\nKey Takeaways:")
print("1. Different weights lead to different selected solutions")
print("2. Higher weight on an objective selects solutions better in that objective")
print("3. Visualization helps understand trade-offs")
print("4. MCDM methods help formalize decision maker preferences")
if __name__ == "__main__":
main()