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