Custom

Here's the code for the custom metric.

def min_recall_precision(y_true, y_pred):
    recall = recall_score(y_true, y_pred)
    precision = precision_score(y_true, y_pred)
    return min(recall, precision)

Here's the code for the train set performance chart.

from sklearn.model_selection import GridSearchCV

grid = GridSearchCV(
    estimator=LogisticRegression(max_iter=1000),
    scoring={'precision': make_scorer(precision_score),
            'recall': make_scorer(recall_score),
            'min_both': make_scorer(min_recall_precision)},
    param_grid={'class_weight': [{0: 1, 1: v} for v in range(1, 4)]},
    refit='precision',
    return_train_score=True,
    cv=10,
    n_jobs=-1
)
grid.fit(X, y);

To plot it all you need this code.

plt.figure(figsize=(12, 4))
df_results = pd.DataFrame(grid.cv_results_)
for score in ['mean_train_recall', 'mean_train_precision', 'mean_test_min_both']:
    plt.scatter(x=[_[1] for _ in df_results['param_class_weight']],
                y=df_results[score.replace('test', 'train')],
                label=score)
plt.legend();