如何向 Google OR-Tools 作业车间示例添加截止日期？

Question

我是 Google OR-Tools（以及一般的约束编程）的新手，我正在尝试向 Jobshop 示例添加截止日期，但它并没有真正起作用。

可以在此处找到我使用的工作车间示例：https://developers.google.com/optimization/scheduling/job_shop#entire-program

我改变了一些东西：

我在 jobs_data 和 task_type namedtuple 中添加了 deadline 参数。
然后我在模型中添加了一个截止日期变量。
最后，我向模型添加了一个约束，其中 task.end 必须小于或等于截止日期。 model.Add(all_tasks[job_id, task_id].end <= all_tasks[job_id, task_id].deadline)

但是没用。它确实做了一些事情，因为它输出的时间表发生了变化，当我输入不可能的截止日期时，它得到 returns 0 个结果。但它没有正确考虑截止日期。我做错了什么？

这是我修改后的版本得到的输出：

Optimal Schedule Length: 11
Machine 0: job_0_0   job_1_0
           [0,3]     [3,5]
Machine 1: job_2_0   job_0_1   job_1_2
           [0,4]     [4,6]     [6,10]
Machine 2: job_1_1   job_0_2   job_2_1
           [5,6]     [6,8]     [8,11]

如您所见，作业 0 的截止日期为 7，但在时间表中它在 8 结束。

这是我修改后的完整示例：

from __future__ import print_function

import collections

# Import Python wrapper for or-tools CP-SAT solver.
from ortools.sat.python import cp_model


def MinimalJobshopSat():
    """Minimal jobshop problem."""
    # Create the model.
    model = cp_model.CpModel()

    jobs_data = [  # task = (machine_id, processing_time).
        [(0, 3, 7), (1, 2, 7), (2, 2, 7)],  # Job0
        [(0, 2, 12), (2, 1, 12), (1, 4, 12)],  # Job1
        [(1, 4, 12), (2, 3, 12)]  # Job2
    ]

    machines_count = 1 + max(task[0] for job in jobs_data for task in job)
    all_machines = range(machines_count)

    # Computes horizon dynamically as the sum of all durations.
    horizon = sum(task[1] for job in jobs_data for task in job)

    # Named tuple to store information about created variables.
    task_type = collections.namedtuple('task_type', 'start end deadline interval')
    # Named tuple to manipulate solution information.
    assigned_task_type = collections.namedtuple('assigned_task_type',
                                                'start job index duration')

    # Creates job intervals and add to the corresponding machine lists.
    all_tasks = {}
    machine_to_intervals = collections.defaultdict(list)

    for job_id, job in enumerate(jobs_data):
        for task_id, task in enumerate(job):
            machine = task[0]
            duration = task[1]
            deadline = task[2]
            suffix = '_%i_%i' % (job_id, task_id)
            start_var = model.NewIntVar(0, horizon, 'start' + suffix)
            end_var = model.NewIntVar(0, horizon, 'end' + suffix)
            interval_var = model.NewIntervalVar(start_var, duration, end_var,
                                                'interval' + suffix)
            deadline_var = model.NewIntVar(deadline, deadline,
                                                'deadline' + suffix)
            all_tasks[job_id, task_id] = task_type(
                start=start_var, end=end_var, deadline=deadline_var, interval=interval_var)
            machine_to_intervals[machine].append(interval_var)

    # Create and add disjunctive constraints.
    for machine in all_machines:
        model.AddNoOverlap(machine_to_intervals[machine])

    # Precedences inside a job.
    for job_id, job in enumerate(jobs_data):
        for task_id in range(len(job) - 1):
            model.Add(all_tasks[job_id, task_id].end <= all_tasks[job_id, task_id].deadline)
            model.Add(all_tasks[job_id, task_id +
                                1].start >= all_tasks[job_id, task_id].end)

    # Makespan objective.
    obj_var = model.NewIntVar(0, horizon, 'makespan')
    model.AddMaxEquality(obj_var, [
        all_tasks[job_id, len(job) - 1].end
        for job_id, job in enumerate(jobs_data)
    ])
    model.Minimize(obj_var)

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

    if status == cp_model.OPTIMAL:
        # Create one list of assigned tasks per machine.
        assigned_jobs = collections.defaultdict(list)
        for job_id, job in enumerate(jobs_data):
            for task_id, task in enumerate(job):
                machine = task[0]
                assigned_jobs[machine].append(
                    assigned_task_type(
                        start=solver.Value(all_tasks[job_id, task_id].start),
                        job=job_id,
                        index=task_id,
                        duration=task[1]))

        # Create per machine output lines.
        output = ''
        for machine in all_machines:
            # Sort by starting time.
            assigned_jobs[machine].sort()
            sol_line_tasks = 'Machine ' + str(machine) + ': '
            sol_line = '           '

            for assigned_task in assigned_jobs[machine]:
                name = 'job_%i_%i' % (assigned_task.job, assigned_task.index)
                # Add spaces to output to align columns.
                sol_line_tasks += '%-10s' % name

                start = assigned_task.start
                duration = assigned_task.duration
                sol_tmp = '[%i,%i]' % (start, start + duration)
                # Add spaces to output to align columns.
                sol_line += '%-10s' % sol_tmp

            sol_line += '\n'
            sol_line_tasks += '\n'
            output += sol_line_tasks
            output += sol_line

        # Finally print the solution found.
        print('Optimal Schedule Length: %i' % solver.ObjectiveValue())
        print(output)


MinimalJobshopSat()

Answer 1

它不起作用，因为您在为优先级创建的 for 循环中引入了约束。创建一个新循环并从 for task_id in range(len(job) - 1).

中删除 -1

您还可以在创建 end_var 时通过限制其上限来设置截止日期。

此外，这个 github 问题有一些您可以使用的想法：https://github.com/google/or-tools/issues/960

如何向 Google OR-Tools 作业车间示例添加截止日期？

How to add deadlines to the Google OR-Tools jobshop example?

python

constraint-programming

or-tools