import optuna

def multi_objective(trial: optuna.Trial) -> tuple[float, float, float, float, float]:
    x = trial.suggest_float("x", -5, 5)
    y = trial.suggest_float("y", -5, 5)
    return x**2 + y**2, (x - 2)**2 + (y - 2)**2, (x + 2)**2 + (y + 2)**2, (x + 2)**2 + (y - 2)**2 , (x - 2)**2 + (y + 2)**2

def objective(trial: optuna.Trial, n_objectives: int) -> tuple[float, ...]:
    values = multi_objective(trial)
    return values[:n_objectives]

n_objectives = 5
sampler = optuna.samplers.TPESampler(seed=0, multivariate=True)
study = optuna.create_study(sampler=sampler, directions=["minimize"]*n_objectives)
study.optimize(lambda trial: objective(trial, n_objectives), n_trials=400)
print((study.trials[-1].datetime_complete - study.trials[0].datetime_start).total_seconds())