Add simples examples for multi-objective and constrained optimizations

README.md

@@ -6,6 +6,8 @@ This page contains a list of example codes written with Optuna.
 ### Simple Black-box Optimization
 
 * [Quadratic function](./quadratic_simple.py)
+- [Quadratic multi-objective function](./multi_objective/quadratic_simple.py)
+- [Quadratic function with constraints](./quadratic_simple_constraint.py)
 
 ### Examples with ML Libraries
 

multi_objective/quadratic_simple.py

@@ -0,0 +1,30 @@
+"""
+Optuna example that optimizes simple quadratic functions.
+
+In this example, we optimize simple quadratic functions.
+
+"""
+
+import optuna
+
+
+# Define simple 2-dimensional objective functions.
+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]
+
+
+if __name__ == "__main__":
+    # We minimize obj1 and maximize obj2.
+    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]
+
+    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)

quadratic_simple_constraint.py

@@ -0,0 +1,49 @@
+"""
+Optuna example that optimizes a simple quadratic function with constraints.
+
+In this example, we optimize a simple quadratic function with constraints.
+
+Please check https://optuna.readthedocs.io/en/stable/faq.html#id16 as well.
+
+"""
+
+import optuna
+
+
+# Define a simple 2-dimensional objective function with constraints.
+def objective(trial):
+    x = trial.suggest_float("x", -100, 100)
+    y = trial.suggest_categorical("y", [-1, 0, 1])
+    return x**2 + y
+
+
+# Define a function that returns constraints.
+def constraints(trial):
+    params = trial.params
+    x, y = params["x"], params["y"]
+    # c1 <= 0 and c2 <= 0 must be satisfied.
+    c1 = 3 * x * y + 10
+    c2 = x * y + 30
+    return [c1, c2]
+
+
+if __name__ == "__main__":
+    # We minimize obj1 and maximize obj2.
+    sampler = optuna.samplers.TPESampler(constraints_func=constraints)
+    study = optuna.create_study(sampler=sampler)
+    study.optimize(objective, n_trials=500, timeout=1)
+
+    best_trial_id, best_value, best_params = None, float("inf"), None
+    for t in study.trials:
+        infeasible = any(c > 0.0 for c in t.system_attrs["constraints"])
+        if infeasible:
+            continue
+        if best_value > t.value:
+            best_value = t.value
+            best_params = t.params.copy()
+            best_trial_id = t._trial_id
+
+    if best_trial_id is None:
+        print("All trials violated the constraints.")
+    else:
+        print(f"Best value is {best_value} with params {best_params}")