147 lines
4.6 KiB
Python
Executable File
147 lines
4.6 KiB
Python
Executable File
#!/usr/bin/env python3
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# Copyright 2010-2022 Google LLC
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# Licensed under the Apache License, Version 2.0 (the "License");
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# you may not use this file except in compliance with the License.
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# You may obtain a copy of the License at
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#
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# http://www.apache.org/licenses/LICENSE-2.0
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#
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# Unless required by applicable law or agreed to in writing, software
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# distributed under the License is distributed on an "AS IS" BASIS,
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# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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# See the License for the specific language governing permissions and
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# limitations under the License.
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"""This model implements a variation of the ft06 jobshop.
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A jobshop is a standard scheduling problem when you must sequence a
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series of tasks on a set of machines. Each job contains one task per
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machine. The order of execution and the length of each job on each
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machine is task dependent.
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The objective is to minimize the maximum completion time of all
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jobs. This is called the makespan.
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This variation introduces a minimum distance between all the jobs on each
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machine.
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"""
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import collections
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from ortools.sat.python import cp_model
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def distance_between_jobs(x, y):
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"""Returns the distance between tasks of job x and tasks of job y."""
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return abs(x - y)
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def jobshop_ft06_distance():
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"""Solves the ft06 jobshop with distances between tasks."""
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# Creates the model.
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model = cp_model.CpModel()
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machines_count = 6
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jobs_count = 6
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all_machines = range(0, machines_count)
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all_jobs = range(0, jobs_count)
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durations = [
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[1, 3, 6, 7, 3, 6],
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[8, 5, 10, 10, 10, 4],
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[5, 4, 8, 9, 1, 7],
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[5, 5, 5, 3, 8, 9],
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[9, 3, 5, 4, 3, 1],
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[3, 3, 9, 10, 4, 1],
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]
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machines = [
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[2, 0, 1, 3, 5, 4],
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[1, 2, 4, 5, 0, 3],
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[2, 3, 5, 0, 1, 4],
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[1, 0, 2, 3, 4, 5],
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[2, 1, 4, 5, 0, 3],
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[1, 3, 5, 0, 4, 2],
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]
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# Computes horizon statically.
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horizon = 150
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task_type = collections.namedtuple("task_type", "start end interval")
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# Creates jobs.
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all_tasks = {}
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for i in all_jobs:
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for j in all_machines:
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start_var = model.NewIntVar(0, horizon, "start_%i_%i" % (i, j))
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duration = durations[i][j]
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end_var = model.NewIntVar(0, horizon, "end_%i_%i" % (i, j))
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interval_var = model.NewIntervalVar(
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start_var, duration, end_var, "interval_%i_%i" % (i, j)
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)
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all_tasks[(i, j)] = task_type(
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start=start_var, end=end_var, interval=interval_var
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)
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# Create disjuctive constraints.
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for i in all_machines:
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job_intervals = []
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job_indices = []
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job_starts = []
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job_ends = []
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for j in all_jobs:
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for k in all_machines:
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if machines[j][k] == i:
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job_intervals.append(all_tasks[(j, k)].interval)
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job_indices.append(j)
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job_starts.append(all_tasks[(j, k)].start)
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job_ends.append(all_tasks[(j, k)].end)
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model.AddNoOverlap(job_intervals)
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arcs = []
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for j1 in range(len(job_intervals)):
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# Initial arc from the dummy node (0) to a task.
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start_lit = model.NewBoolVar("%i is first job" % j1)
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arcs.append([0, j1 + 1, start_lit])
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# Final arc from an arc to the dummy node.
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arcs.append([j1 + 1, 0, model.NewBoolVar("%i is last job" % j1)])
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for j2 in range(len(job_intervals)):
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if j1 == j2:
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continue
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lit = model.NewBoolVar("%i follows %i" % (j2, j1))
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arcs.append([j1 + 1, j2 + 1, lit])
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# We add the reified precedence to link the literal with the
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# times of the two tasks.
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min_distance = distance_between_jobs(j1, j2)
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model.Add(job_starts[j2] >= job_ends[j1] + min_distance).OnlyEnforceIf(
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lit
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)
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model.AddCircuit(arcs)
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# Precedences inside a job.
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for i in all_jobs:
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for j in range(0, machines_count - 1):
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model.Add(all_tasks[(i, j + 1)].start >= all_tasks[(i, j)].end)
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# Makespan objective.
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obj_var = model.NewIntVar(0, horizon, "makespan")
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model.AddMaxEquality(
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obj_var, [all_tasks[(i, machines_count - 1)].end for i in all_jobs]
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)
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model.Minimize(obj_var)
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# Solve model.
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solver = cp_model.CpSolver()
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status = solver.Solve(model)
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# Output solution.
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if status == cp_model.OPTIMAL:
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print("Optimal makespan: %i" % solver.ObjectiveValue())
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jobshop_ft06_distance()
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