Implement Multi-Objective Optimization (optimization.py)

optimization.py

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+import random
+import numpy as np
+import matplotlib.pyplot as plt
+from deap import base, creator, tools, algorithms
+
+# Define multi-objective optimization: Maximize utility, Minimize risk
+creator.create("FitnessMulti", base.Fitness, weights=(1.0, -1.0))  # Max utility, Min risk
+creator.create("Individual", list, fitness=creator.FitnessMulti)
+
+def evaluate(individual):
+    utility = individual[0]  # Example: Utility function
+    risk = individual[1]  # Example: Risk function (to be minimized)
+    return utility, risk
+
+toolbox = base.Toolbox()
+toolbox.register("attr_float", random.uniform, 0, 10)  # Random values between 0 and 10
+toolbox.register("individual", tools.initRepeat, creator.Individual, toolbox.attr_float, n=2)
+toolbox.register("population", tools.initRepeat, list, toolbox.individual)
+
+toolbox.register("mate", tools.cxBlend, alpha=0.5)
+toolbox.register("mutate", tools.mutGaussian, mu=0, sigma=1, indpb=0.2)
+toolbox.register("select", tools.selNSGA2)
+toolbox.register("evaluate", evaluate)
+
+def main():
+    population = toolbox.population(n=100)
+    hof = tools.HallOfFame(10)  
+    stats = tools.Statistics(lambda ind: ind.fitness.values)
+    stats.register("avg", np.mean, axis=0)
+
+    algorithms.eaMuPlusLambda(population, toolbox, mu=100, lambda_=200, 
+                              cxpb=0.7, mutpb=0.2, ngen=50, 
+                              stats=stats, halloffame=hof, verbose=True)
+
+    return population, hof
+
+if __name__ == "__main__":
+    population, hof = main()
+    pareto_front = np.array([ind.fitness.values for ind in hof])
+
+    # Plot Pareto Front
+    plt.scatter(pareto_front[:, 0], pareto_front[:, 1], c="red", label="Pareto Front")
+    plt.xlabel("Utility (Maximize)")
+    plt.ylabel("Risk (Minimize)")
+    plt.title("Pareto Front of Multi-Objective Optimization")
+    plt.legend()
+    plt.grid()
+    plt.show()