Flexibility

Here's the code to write your own scorer directly.

from sklearn.model_selection import GridSearchCV
from sklearn.metrics import precision_score, recall_score, make_scorer

def min_recall_precision(est, X, y_true, sample_weight=None):
    y_pred = est.predict(X)
    recall = recall_score(y_true, y_pred)
    precision = precision_score(y_true, y_pred)
    return min(recall, precision)

grid = GridSearchCV(
    estimator=LogisticRegression(max_iter=1000),
    param_grid={'class_weight': [{0: 1, 1: v} for v in np.linspace(1, 20, 30)]},
    scoring={'precision': make_scorer(precision_score),
            'recall': make_scorer(recall_score),
            'min_both': min_recall_precision},
    refit='min_both',
    return_train_score=True,
    cv=10,
    n_jobs=-1
)
grid.fit(X, y);