161 lines
5.0 KiB
Python
161 lines
5.0 KiB
Python
#!/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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"""Gate Scheduling problem.
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We have a set of jobs to perform (duration, width).
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We have two parallel machines that can perform this job.
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One machine can only perform one job at a time.
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At any point in time, the sum of the width of the two active jobs does not
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exceed a max_width.
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The objective is to minimize the max end time of all jobs.
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"""
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from absl import app
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from ortools.sat.colab import visualization
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from ortools.sat.python import cp_model
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def main(_):
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"""Solves the gate scheduling problem."""
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model = cp_model.CpModel()
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jobs = [
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[3, 3], # [duration, width]
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[2, 5],
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[1, 3],
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[3, 7],
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[7, 3],
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[2, 2],
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[2, 2],
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[5, 5],
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[10, 2],
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[4, 3],
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[2, 6],
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[1, 2],
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[6, 8],
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[4, 5],
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[3, 7],
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]
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max_width = 10
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horizon = sum(t[0] for t in jobs)
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num_jobs = len(jobs)
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all_jobs = range(num_jobs)
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intervals = []
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intervals0 = []
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intervals1 = []
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performed = []
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starts = []
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ends = []
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demands = []
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for i in all_jobs:
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# Create main interval.
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start = model.new_int_var(0, horizon, "start_%i" % i)
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duration = jobs[i][0]
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end = model.new_int_var(0, horizon, "end_%i" % i)
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interval = model.new_interval_var(start, duration, end, "interval_%i" % i)
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starts.append(start)
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intervals.append(interval)
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ends.append(end)
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demands.append(jobs[i][1])
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# Create an optional copy of interval to be executed on machine 0.
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performed_on_m0 = model.new_bool_var("perform_%i_on_m0" % i)
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performed.append(performed_on_m0)
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start0 = model.new_int_var(0, horizon, "start_%i_on_m0" % i)
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end0 = model.new_int_var(0, horizon, "end_%i_on_m0" % i)
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interval0 = model.new_optional_interval_var(
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start0, duration, end0, performed_on_m0, "interval_%i_on_m0" % i
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)
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intervals0.append(interval0)
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# Create an optional copy of interval to be executed on machine 1.
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start1 = model.new_int_var(0, horizon, "start_%i_on_m1" % i)
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end1 = model.new_int_var(0, horizon, "end_%i_on_m1" % i)
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interval1 = model.new_optional_interval_var(
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start1,
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duration,
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end1,
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~performed_on_m0,
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"interval_%i_on_m1" % i,
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)
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intervals1.append(interval1)
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# We only propagate the constraint if the tasks is performed on the machine.
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model.add(start0 == start).only_enforce_if(performed_on_m0)
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model.add(start1 == start).only_enforce_if(~performed_on_m0)
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# Width constraint (modeled as a cumulative)
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model.add_cumulative(intervals, demands, max_width)
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# Choose which machine to perform the jobs on.
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model.add_no_overlap(intervals0)
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model.add_no_overlap(intervals1)
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# Objective variable.
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makespan = model.new_int_var(0, horizon, "makespan")
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model.add_max_equality(makespan, ends)
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model.minimize(makespan)
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# Symmetry breaking.
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model.add(performed[0] == 0)
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# Solve model.
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solver = cp_model.CpSolver()
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solver.solve(model)
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# Output solution.
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if visualization.RunFromIPython():
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output = visualization.SvgWrapper(solver.objective_value, max_width, 40.0)
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output.AddTitle("Makespan = %i" % solver.objective_value)
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color_manager = visualization.ColorManager()
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color_manager.SeedRandomColor(0)
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for i in all_jobs:
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performed_machine = 1 - solver.value(performed[i])
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start = solver.value(starts[i])
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d_x = jobs[i][0]
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d_y = jobs[i][1]
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s_y = performed_machine * (max_width - d_y)
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output.AddRectangle(
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start, s_y, d_x, d_y, color_manager.RandomColor(), "black", "j%i" % i
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)
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output.AddXScale()
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output.AddYScale()
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output.Display()
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else:
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print("Solution")
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print(" - makespan = %i" % solver.objective_value)
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for i in all_jobs:
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performed_machine = 1 - solver.value(performed[i])
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start = solver.value(starts[i])
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print(
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" - Job %i starts at %i on machine %i" % (i, start, performed_machine)
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)
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print("Statistics")
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print(" - conflicts : %i" % solver.num_conflicts)
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print(" - branches : %i" % solver.num_branches)
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print(" - wall time : %f s" % solver.wall_time)
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if __name__ == "__main__":
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app.run(main)
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