[refactor] Modify MO simple based on the Optuna code convention

multi_objective/quadratic_simple.py

@@ -1,30 +1,33 @@
 """
 Optuna example that optimizes simple quadratic functions.
 
-In this example, we optimize simple quadratic functions.
+In this example, we optimize two objective values.
+Unlike a single-objective optimization, an optimization gives the trade-off between two objectives.
+As a result, we get best trade-offs between two objectives, a.k.a Pareto solutions.
 
 """
 
 import optuna
 
 
-# Define simple 2-dimensional objective functions.
+# Define two objective functions.
+# We would like to minimize obj1 and maximize obj2.
 def objective(trial):
     x = trial.suggest_float("x", -100, 100)
     y = trial.suggest_categorical("y", [-1, 0, 1])
     obj1 = x**2 + y
     obj2 = -((x - 2) ** 2 + y)
-    return [obj1, obj2]
+    return obj1, obj2
 
 
 if __name__ == "__main__":
-    # We minimize obj1 and maximize obj2.
+    # We minimize the first objective value and maximize the second objective value.
     study = optuna.create_study(directions=["minimize", "maximize"])
     study.optimize(objective, n_trials=500, timeout=1)
 
-    pareto_front = [t.values for t in study.best_trials]
-    pareto_sols = [t.params for t in study.best_trials]
+    print("Number of finished trials: ", len(study.trials))
 
-    for i, (params, values) in enumerate(zip(pareto_sols, pareto_front)):
-        print(f"The {i}-th Pareto solution and its objective values")
-        print("\t", params, values)
+    for i, best_trial in enumerate(study.best_trials):
+        print(f"The {i}-th Pareto solution was found at Trial#{best_trial.number}.")
+        print(f"  Params: {best_trial.params}")
+        print(f"  Values: {best_trial.values}")