128 lines
4.2 KiB
Java
128 lines
4.2 KiB
Java
// 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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// [START program]
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// Solves a multiple knapsack problem using the CP-SAT solver.
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package com.google.ortools.sat.samples;
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// [START import]
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import com.google.ortools.Loader;
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import com.google.ortools.sat.CpModel;
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import com.google.ortools.sat.CpSolver;
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import com.google.ortools.sat.CpSolverStatus;
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import com.google.ortools.sat.IntVar;
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import com.google.ortools.sat.LinearExpr;
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import java.util.stream.IntStream;
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// [END import]
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/** Sample showing how to solve a multiple knapsack problem. */
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public class MultipleKnapsackSat {
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public static void main(String[] args) {
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Loader.loadNativeLibraries();
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// Instantiate the data problem.
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// [START data]
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final int[] weights = {48, 30, 42, 36, 36, 48, 42, 42, 36, 24, 30, 30, 42, 36, 36};
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final int[] values = {10, 30, 25, 50, 35, 30, 15, 40, 30, 35, 45, 10, 20, 30, 25};
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final int numItems = weights.length;
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final int[] allItems = IntStream.range(0, numItems).toArray();
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final int[] binCapacities = {100, 100, 100, 100, 100};
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final int numBins = binCapacities.length;
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final int[] allBins = IntStream.range(0, numBins).toArray();
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// [END data]
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// [START model]
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CpModel model = new CpModel();
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// [END model]
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// Variables.
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// [START variables]
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IntVar[][] x = new IntVar[numItems][numBins];
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for (int i : allItems) {
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for (int b : allBins) {
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x[i][b] = model.newBoolVar("x_" + i + "_" + b);
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}
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}
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// [END variables]
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// Constraints.
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// [START constraints]
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// Each item is assigned to at most one bin.
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for (int i : allItems) {
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IntVar[] vars = new IntVar[numBins];
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for (int b : allBins) {
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vars[b] = x[i][b];
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}
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model.addLessOrEqual(LinearExpr.sum(vars), 1);
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}
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// The amount packed in each bin cannot exceed its capacity.
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for (int b : allBins) {
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IntVar[] vars = new IntVar[numItems];
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for (int i : allItems) {
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vars[i] = x[i][b];
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}
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model.addLessOrEqual(LinearExpr.scalProd(vars, weights), binCapacities[b]);
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}
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// [END constraints]
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// Objective.
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// [START objective]
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// Maximize total value of packed items.
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IntVar[] objectiveVars = new IntVar[numItems * numBins];
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int[] objectiveValues = new int[numItems * numBins];
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for (int i : allItems) {
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for (int b : allBins) {
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int k = i * numBins + b;
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objectiveVars[k] = x[i][b];
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objectiveValues[k] = values[i];
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}
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}
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model.maximize(LinearExpr.scalProd(objectiveVars, objectiveValues));
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// [END objective]
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// [START solve]
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CpSolver solver = new CpSolver();
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final CpSolverStatus status = solver.solve(model);
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// [END solve]
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// [START print_solution]
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// Check that the problem has an optimal solution.
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if (status == CpSolverStatus.OPTIMAL) {
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System.out.println("Total packed value: " + solver.objectiveValue());
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long totalWeight = 0;
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for (int b : allBins) {
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long binWeight = 0;
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long binValue = 0;
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System.out.println("Bin " + b);
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for (int i : allItems) {
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if (solver.value(x[i][b]) > 0) {
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System.out.println("Item " + i + " weight: " + weights[i] + " value: " + values[i]);
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binWeight += weights[i];
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binValue += values[i];
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}
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}
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System.out.println("Packed bin weight: " + binWeight);
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System.out.println("Packed bin value: " + binValue);
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totalWeight += binWeight;
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}
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System.out.println("Total packed weight: " + totalWeight);
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} else {
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System.err.println("The problem does not have an optimal solution.");
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}
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// [END print_solution]
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}
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private MultipleKnapsackSat() {}
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}
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// [END program]
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