119 lines
4.0 KiB
C#
119 lines
4.0 KiB
C#
// Copyright 2010-2021 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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using System;
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using Google.OrTools.Sat;
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public class BinPackingProblemSat
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{
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static void Main()
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{
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// Data.
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int bin_capacity = 100;
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int slack_capacity = 20;
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int num_bins = 5;
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int[,] items = new int[,] { { 20, 6 }, { 15, 6 }, { 30, 4 }, { 45, 3 } };
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int num_items = items.GetLength(0);
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// Model.
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CpModel model = new CpModel();
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// Main variables.
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IntVar[,] x = new IntVar[num_items, num_bins];
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for (int i = 0; i < num_items; ++i)
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{
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int num_copies = items[i, 1];
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for (int b = 0; b < num_bins; ++b)
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{
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x[i, b] = model.NewIntVar(0, num_copies, String.Format("x_{0}_{1}", i, b));
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}
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}
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// Load variables.
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IntVar[] load = new IntVar[num_bins];
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for (int b = 0; b < num_bins; ++b)
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{
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load[b] = model.NewIntVar(0, bin_capacity, String.Format("load_{0}", b));
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}
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// Slack variables.
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IntVar[] slacks = new IntVar[num_bins];
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for (int b = 0; b < num_bins; ++b)
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{
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slacks[b] = model.NewBoolVar(String.Format("slack_{0}", b));
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}
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// Links load and x.
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int[] sizes = new int[num_items];
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for (int i = 0; i < num_items; ++i)
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{
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sizes[i] = items[i, 0];
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}
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for (int b = 0; b < num_bins; ++b)
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{
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IntVar[] tmp = new IntVar[num_items];
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for (int i = 0; i < num_items; ++i)
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{
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tmp[i] = x[i, b];
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}
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model.Add(load[b] == LinearExpr.WeightedSum(tmp, sizes));
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}
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// Place all items.
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for (int i = 0; i < num_items; ++i)
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{
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IntVar[] tmp = new IntVar[num_bins];
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for (int b = 0; b < num_bins; ++b)
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{
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tmp[b] = x[i, b];
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}
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model.Add(LinearExpr.Sum(tmp) == items[i, 1]);
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}
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// Links load and slack.
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int safe_capacity = bin_capacity - slack_capacity;
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for (int b = 0; b < num_bins; ++b)
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{
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// slack[b] => load[b] <= safe_capacity.
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model.Add(load[b] <= safe_capacity).OnlyEnforceIf(slacks[b]);
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// not(slack[b]) => load[b] > safe_capacity.
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model.Add(load[b] > safe_capacity).OnlyEnforceIf(slacks[b].Not());
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}
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// Maximize sum of slacks.
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model.Maximize(LinearExpr.Sum(slacks));
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// Solves and prints out the solution.
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CpSolver solver = new CpSolver();
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CpSolverStatus status = solver.Solve(model);
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Console.WriteLine(String.Format("Solve status: {0}", status));
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if (status == CpSolverStatus.Optimal)
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{
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Console.WriteLine(String.Format("Optimal objective value: {0}", solver.ObjectiveValue));
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for (int b = 0; b < num_bins; ++b)
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{
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Console.WriteLine(String.Format("load_{0} = {1}", b, solver.Value(load[b])));
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for (int i = 0; i < num_items; ++i)
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{
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Console.WriteLine(string.Format(" item_{0}_{1} = {2}", i, b, solver.Value(x[i, b])));
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}
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}
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}
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Console.WriteLine("Statistics");
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Console.WriteLine(String.Format(" - conflicts : {0}", solver.NumConflicts()));
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Console.WriteLine(String.Format(" - branches : {0}", solver.NumBranches()));
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Console.WriteLine(String.Format(" - wall time : {0} s", solver.WallTime()));
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}
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}
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