techtalk_scheduling.cs

// Copyright 2010-2021 Google LLC
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
//     http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.

using Google.OrTools.ConstraintSolver;
using Google.OrTools.Graph;
using System.Collections.Generic;
using System.Diagnostics;
using System.Linq;
using System;

public class SpeakerScheduling
{
    public class FlowAssign : NetDecisionBuilder
    {
        public FlowAssign(IntVar[] vars, int first_slot, IntVar last_slot_var)
        {
            vars_ = vars;
            first_slot_ = first_slot;
            last_slot_var_ = last_slot_var;
        }

        public override Decision Next(Solver solver)
        {
            int large = 100000;
            int number_of_variables = vars_.Length;
            long last_slot = last_slot_var_.Max();
            // Lets build a bipartite graph with equal number of nodes left and right.
            // Variables will be on the left, slots on the right.
            // We will add dummy variables when needed.
            // Arcs will have a cost x is slot x is possible for a variable, a large
            // number otherwise. For dummy variables, the cost will be 0 always.
            LinearSumAssignment matching = new LinearSumAssignment();
            for (int speaker = 0; speaker < number_of_variables; ++speaker)
            {
                IntVar var = vars_[speaker];
                for (int value = first_slot_; value <= last_slot; ++value)
                {
                    if (var.Contains(value))
                    {
                        matching.AddArcWithCost(speaker, value - first_slot_, value);
                    }
                    else
                    {
                        matching.AddArcWithCost(speaker, value - first_slot_, large);
                    }
                }
            }
            // The Matching algorithms expect the same number of left and right nodes.
            // So we fill the rest with dense zero-cost arcs.
            for (int dummy = number_of_variables; dummy <= last_slot - first_slot_; ++dummy)
            {
                for (int value = first_slot_; value <= last_slot; ++value)
                {
                    matching.AddArcWithCost(dummy, value - first_slot_, 0);
                }
            }
            if (matching.Solve() == LinearSumAssignment.Status.OPTIMAL &&
                matching.OptimalCost() < large) // No violated arcs.
            {
                for (int speaker = 0; speaker < number_of_variables; ++speaker)
                {
                    vars_[speaker].SetValue(matching.RightMate(speaker) + first_slot_);
                }
            }
            else
            {
                solver.Fail();
            }
            return null;
        }

        private IntVar[] vars_;
        private int first_slot_;
        private IntVar last_slot_var_;
    }

    private static void Solve(int first_slot)
    {
        Console.WriteLine("----------------------------------------------------");
        Solver solver = new Solver("SpeakerScheduling");

        // the slots each speaker is available
        int[][] speaker_availability = {
            new int[] { 1,  3,  4,  6,  7,  10, 12, 13, 14, 15, 16, 18, 19, 20, 21, 22, 23, 24, 25, 33, 34, 35,
                        36, 37, 38, 39, 40, 41, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 59 },
            new int[] { 1,  2,  7,  8,  10, 11, 16, 17, 18, 21, 22, 23, 24, 25, 33, 34, 35, 36, 37, 38,
                        39, 40, 42, 43, 44, 45, 46, 47, 48, 49, 52, 53, 54, 55, 56, 57, 58, 59, 60 },
            new int[] { 5,  6,  7,  10, 12, 14, 16, 17, 21, 22, 23, 24, 33, 35, 37, 38,
                        39, 40, 41, 42, 43, 44, 45, 46, 51, 53, 55, 56, 57, 58, 59 },
            new int[] { 1,  2,  3,  4,  5,  6,  7,  11, 13, 14, 15, 16, 20, 24, 25, 33, 34, 35, 37, 38,
                        39, 40, 41, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 58, 59, 60 },
            new int[] { 4,  7,  8,  9,  16, 17, 19, 20, 21, 22, 23, 24, 25, 33, 34, 35, 36,
                        37, 38, 39, 40, 41, 42, 43, 49, 50, 51, 53, 55, 56, 57, 58, 59, 60 },
            new int[] { 4,  7,  9,  11, 12, 13, 14, 15, 16, 17, 18, 22, 23, 24, 33, 34,
                        35, 36, 38, 39, 42, 44, 46, 48, 49, 51, 53, 54, 55, 56, 57 },
            new int[] { 1, 2, 3, 4, 5, 6, 7, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 54, 55, 56, 57, 58, 59, 60 },
            new int[] { 1,  3,  11, 14, 15, 16, 17, 21, 22, 23, 24, 25, 33, 35, 36, 37, 39, 40,
                        41, 42, 43, 44, 45, 47, 48, 49, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60 },
            new int[] { 1,  2,  3,  4,  5,  7,  8,  9,  10, 11, 13, 18, 19, 20, 21, 22, 23, 24, 25, 33, 34, 35,
                        36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 50, 51, 52, 53, 54, 55, 56, 57, 59, 60 },
            new int[] { 24, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 45,
                        49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60 },
            new int[] { 1,  2,  3,  4,  5,  6,  7,  8,  9,  10, 11, 12, 13, 14, 16, 17, 18,
                        19, 20, 22, 23, 24, 25, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43,
                        44, 45, 46, 47, 48, 50, 51, 52, 53, 55, 56, 57, 58, 59, 60 },
            new int[] { 3,  4,  5,  6,  13, 15, 16, 17, 18, 19, 21, 22, 24, 25, 33, 34, 35,
                        36, 37, 39, 40, 41, 42, 43, 44, 45, 47, 52, 53, 55, 57, 58, 59, 60 },
            new int[] { 4,  5,  6,  8,  11, 12, 13, 14, 17, 19, 20, 22, 23, 24, 25, 33, 34,
                        35, 36, 37, 39, 40, 41, 42, 43, 47, 48, 49, 50, 51, 52, 55, 56, 57 },
            new int[] { 2,  3,  4,  5,  6,  7,  8,  9,  10, 11, 12, 13, 14, 15, 16, 17, 18, 19,
                        20, 21, 22, 23, 24, 25, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44,
                        45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60 },
            new int[] { 12, 25, 33, 35, 36, 37, 39, 41, 42, 43, 48, 51, 52, 53, 54, 57, 59, 60 },
            new int[] { 4, 8, 16, 17, 19, 23, 25, 33, 34, 35, 37, 41, 44, 45, 47, 48, 49, 50 },
            new int[] { 3, 23, 24, 25, 33, 35, 36, 37, 38, 39, 40, 42, 43, 44, 49, 50, 53, 54, 55, 56, 57, 58, 60 },
            new int[] { 7,  13, 19, 20, 22, 23, 24, 25, 33, 34, 35, 38, 40, 41,
                        42, 44, 45, 46, 47, 48, 49, 52, 53, 54, 58, 59, 60 }
        };

        // how long each talk lasts for each speaker
        int[] durations = { 1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1 };
        int sum_of_durations = durations.Sum();

        int number_of_speakers = durations.Length;
        // calculate the total number of slots (maximum in the availability array)
        // (and add the max durations)
        int last_slot = (from s in Enumerable.Range(0, number_of_speakers) select speaker_availability[s].Max()).Max();
        Console.WriteLine("Scheduling {0} speakers, for a total of {1} slots, during [{2}..{3}]", number_of_speakers,
                          sum_of_durations, first_slot, last_slot);

        // Start variable for all talks.
        IntVar[] starts = new IntVar[number_of_speakers];
        // We store the possible starts for all talks filtered from the
        // duration and the speaker availability.
        int[][] possible_starts = new int [number_of_speakers][];

        for (int speaker = 0; speaker < number_of_speakers; ++speaker)
        {
            int duration = durations[speaker];
            // Let's filter the possible starts.
            List<int> filtered_starts = new List<int>();
            int availability = speaker_availability[speaker].Length;
            for (int index = 0; index < availability; ++index)
            {
                bool ok = true;
                int slot = speaker_availability[speaker][index];
                if (slot < first_slot)
                {
                    continue;
                }
                for (int offset = 1; offset < duration; ++offset)
                {
                    if (index + offset >= availability ||
                        speaker_availability[speaker][index + offset] != slot + offset)
                    {
                        // discontinuity.
                        ok = false;
                        break;
                    }
                }
                if (ok)
                {
                    filtered_starts.Add(slot);
                }
                possible_starts[speaker] = filtered_starts.ToArray();
            }
            starts[speaker] = solver.MakeIntVar(possible_starts[speaker], "start[" + speaker + "]");
        }

        List<IntVar>[] contributions_per_slot = new List<IntVar>[last_slot + 1];
        for (int slot = first_slot; slot <= last_slot; ++slot)
        {
            contributions_per_slot[slot] = new List<IntVar>();
        }
        for (int speaker = 0; speaker < number_of_speakers; ++speaker)
        {
            int duration = durations[speaker];
            IntVar start_var = starts[speaker];
            foreach (int start in possible_starts[speaker])
            {
                for (int offset = 0; offset < duration; ++offset)
                {
                    contributions_per_slot[start + offset].Add(start_var.IsEqual(start));
                }
            }
        }
        // Force the schedule to be consistent.
        for (int slot = first_slot; slot <= last_slot; ++slot)
        {
            solver.Add(solver.MakeSumLessOrEqual(contributions_per_slot[slot].ToArray(), 1));
        }

        // Add minimum start info.
        for (int speaker = 0; speaker < number_of_speakers; ++speaker)
        {
            solver.Add(starts[speaker] >= first_slot);
        }

        // Creates makespan.
        IntVar[] end_times = new IntVar[number_of_speakers];
        for (int speaker = 0; speaker < number_of_speakers; speaker++)
        {
            end_times[speaker] = (starts[speaker] + (durations[speaker] - 1)).Var();
        }
        IntVar last_slot_var = end_times.Max().VarWithName("last_slot");

        // Add trivial bound to objective.
        last_slot_var.SetMin(first_slot + sum_of_durations - 1);

        // Redundant scheduling constraint.
        IntervalVar[] intervals = solver.MakeFixedDurationIntervalVarArray(starts, durations, "intervals");
        DisjunctiveConstraint disjunctive = solver.MakeDisjunctiveConstraint(intervals, "disjunctive");
        solver.Add(disjunctive);

        //
        // Search
        //
        List<IntVar> short_talks = new List<IntVar>();
        List<IntVar> long_talks = new List<IntVar>();
        for (int speaker = 0; speaker < number_of_speakers; ++speaker)
        {
            if (durations[speaker] == 1)
            {
                short_talks.Add(starts[speaker]);
            }
            else
            {
                long_talks.Add(starts[speaker]);
            }
        }
        OptimizeVar objective_monitor = solver.MakeMinimize(last_slot_var, 1);
        DecisionBuilder long_phase =
            solver.MakePhase(long_talks.ToArray(), Solver.CHOOSE_MIN_SIZE_LOWEST_MIN, Solver.ASSIGN_MIN_VALUE);
        DecisionBuilder short_phase = new FlowAssign(short_talks.ToArray(), first_slot, last_slot_var);
        DecisionBuilder obj_phase =
            solver.MakePhase(last_slot_var, Solver.CHOOSE_FIRST_UNBOUND, Solver.ASSIGN_MIN_VALUE);
        DecisionBuilder main_phase = solver.Compose(long_phase, short_phase, obj_phase);

        solver.NewSearch(main_phase, objective_monitor);
        while (solver.NextSolution())
        {
            Console.WriteLine("\nLast used slot: " + (last_slot_var.Value()));
            Console.WriteLine("Speakers (start..end):");
            for (int s = 0; s < number_of_speakers; s++)
            {
                long sstart = starts[s].Value();
                Console.WriteLine("  - speaker {0,2}: {1,2}..{2,2}", (s + 1), sstart, (sstart + durations[s] - 1));
            }
        }

        Console.WriteLine("\nSolutions: {0}", solver.Solutions());
        Console.WriteLine("WallTime: {0}ms", solver.WallTime());
        Console.WriteLine("Failures: {0}", solver.Failures());
        Console.WriteLine("Branches: {0} ", solver.Branches());
        solver.EndSearch();
    }

    public static void Main(String[] args)
    {
        int start = 17;
        if (args.Length == 1)
        {
            start = int.Parse(args[0]);
        }
        Stopwatch s = new Stopwatch();
        s.Start();
        Solve(start);
        s.Stop();
        Console.WriteLine("Finished in " + s.ElapsedMilliseconds + " ms");
    }
}