在or-tools python中为调度问题添加软约束

from ortools.sat.python import cp_model

def create_model():
    model = cp_model.CpModel()

    num_tasks = 5
    num_workers = 3
    task_durations = [3, 2, 5, 1, 4]
    start_times = [model.NewIntVar(0, cp_model.INT_MAX, f'start_{i}') for i in range(num_tasks)]
    end_times = [model.NewIntVar(0, cp_model.INT_MAX, f'end_{i}') for i in range(num_tasks)]

    # 硬约束：每个任务只能由一个工人完成
    for i in range(num_tasks):
        model.Add(sum(worker == i for worker in workers) == 1)

    # 软约束：任务的延迟惩罚
    delay_penalty = 10
    for i in range(num_tasks):
        model.Add(end_times[i] <= start_times[i] + task_durations[i])
        model.Minimize(sum(delay_penalty * (end_times[i] - start_times[i] - task_durations[i]) for i in range(num_tasks)))

    solver = cp_model.CpSolver()
    status = solver.Solve(model)

    if status == cp_model.OPTIMAL:
        for i in range(num_tasks):
            print(f'Task {i} starts at {solver.Value(start_times[i])} and ends at {solver.Value(end_times[i])}')
    else:
        print('No solution found.')

create_model()