Consolidate skills

scientific-skills/pymoo/scripts/decision_making_example.py

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+"""
+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()