dalam Bahasa Java
Oleh :
Jeffrey Hermanto Halimsetiawan
shadowz_029@yahoo.com.sg
tutorialpemrograman.wordpress.com
7 Februari 2010
Unbounded Knapsack Problem dalam Bahasa Java
Penjelasan Problem :
Seorang pendaki harus membawa 3 barang yaitu : makanan, obat-obatan dan baju. Makanan
memiliki nilai 4, obat-obatan 3, dan baju 5 (baju memiliki nilai paling tinggi, dst). Untuk membawa
barang-barang tersebut, sang pendaki menggunakan sebuah back pack dengan kapasitas 3 liter. Satu
unit makanan memiliki ukuran 1 liter. Satu unit obat-obatan berukuran 1/4 liter. Dan satu unit baju
berukuran 1/2 liter.
1. Justifikasi algoritma apakah yang bisa memaksimalkan nilai dari barang yang dibawa oleh
pendaki. Jelaskan alasannya!
2. Buatlah algoritmanya!
3. Analysis running time dari algoritma yang anda kembangkan!
4. Implementasikan algoritma tersebut!
Penjelasan Algoritma
Dalam kasus di atas, diperlukan sebuah algoritma yang digunakan untuk mencari nilai yang optimum
dari barang yang dibawa oleh pendaki dengan batas beban backpack pendaki. Agar didapatkan nilai
yang optimal maka digunakan algoritma unbounded-knapsack untuk memecahkan permasalah di
atas dengan pendekatan secara Dynamic Programming (DP). Algoritma unbounded knapsack atau
yang disebut juga dengan integer-knapsack merupakan pengembangan dari algoritma knapsack
dimana tidak ada batasan pengambilan jumlah sebuah item tetapi tetap memperhatikan batasan
beban (weight). Karena seorang pendaki harus membawa minimal 1 untuk semua item barang, maka
ada sedikit modifikasi algoritma unbounded knapsack yaitu setelah masing-masing diambil satu
barang, baru dilakukan dynamic programming untuk mencari nilai yang maksimal dengan weight
yang sudah dikurangi tersebut. Alasan menggunakan pendekatan secara dynamic programming
karena greedy pada permasalahan knapsack di atas tidak ditemukan adanya greedy choice sehingga
ada beberapa kasus dimana solusi greedy tidak optimal. Contoh kasusnya adalah sebagai berikut :
MAKSIMUM WEIGHT = 3
ITEM
WEIGHT
VALUE
RATIO ( VALUE / WEIGHT)
Obat
0.25
3
12
Baju
0.4
4
10
Makanan
0.95
4
4.2
Weight setelah dikurangi semua item = 3 - 0.25 - 0.95 - 0.4
= 1.4
1. Greedy : W = 0.25 * 5
= 1.25
V = 3 * 5
= 15
2. DP :
W = 0.25 * 4 + 0.4 * 1
= 1.4
V = 3 * 4 + 4 * 1
= 16
Dari contoh kasus di atas, Greedy menghasilkan value 15 sedangkan DP menghasilkan value 16
sehingga terbukti bahwa greedy tidak menghasilkan solusi yang optimal seperti pada dynamic
programming.
Langkah-langkah :
Step 1: Characterize optimal subproblems
Jika kita membawa item ke-j, kapasitas sisanya adalah nilai maksimum dari berat (weight-weights[j])
dari semua item yang mungkin dibawa.
Step 2: Recursive algorithm
Pseudocode Rekursif :
Algoritma recKnapsack(weight, best[],weights[],values[],itemKnown[],n)
{
i, space, max -1, maxi 0, t; if (best[weight] >= 0)
return best[weight]; for i from 1 to n
if ((space = weight-weights[i]) >= 0)
if ((t = recKnapsack(space) + values[i]) > max) { max t; maxi i; } best[weight] max; itemKnown[weight] maxi; return max; }
Step 3: Dynamic programming algorithm
Pseudocode Algoritma
Algoritma Knapsack(weight,best[],weights[],values[],n)
{
i, space, m, t, itemKnown[]; for m from 1 to weight for i from 0 to n { if ((space = m-weights[i]) >= 0) { t = best[space] + values[i]; if (t >= best[m]) { best[m] t; itemKnown[m] i; } } }
solution[itemKnown[m]]++; return best[c];
}
Step 4 : Contructing optimal solution
Algoritma printOptimalSolution(weight,best[],weights[],values[],itemKnown[],n) { wt 0, val 0; for j from 0 to n if ( best[j] > 0 ) {
print ("%d of item %d (%d wt, %d val)\n", best[j], j, weights[j], values [j] ); wt += best [j] * weights[j];
val += best [j] * values [j]; }
print("Total weight: %d\nTotal profit: %d\n", wt, val); }
Analisa Running Time
t(n)
=
t(n)
=
Sehingga order of growth memenuhi :
Implementasi :
package ub;
import java.util.Arrays;
import java.util.StringTokenizer;
public class MainFrame extends javax.swing.JFrame {
public MainFrame() { initComponents();
this.setTitle("FP PAAL Kelas A - Unbounded Knapsack"); }
int unboundedKnapsack(int c, int n, int[] weights, int[] values, int[] solution )
{
int i, space, m, t, best[], bestItem[]; bestItem = new int [c+1]; best = new int [c+1]; Arrays.fill(best, 0); for ( m = 1; m <= c; m++ ) for (i = 0; i < n; i++) { if ( (space = m-weights[i]) >= 0 ) { t = best[space] + values[i]; if ( t >= best[m] )
{
best[m] = t; bestItem[m] = i; }
}
for (int iterator : best){
areaOutput.append(iterator + " "); } areaOutput.append("\n"); } for (m=c; m>0 ; m-=weights[bestItem[m]] ) solution[bestItem[m]]++; return best[c]; }
private void computeUnboundedKnapsack() {
if (txtValues.getText().matches("") || txtWeights.getText().matches("") || txtMaxWeight.getText().matches("") || txtN.getText().matches("")){ areaOutput.setText("ERROR! Ada field yang masih kosong!");
return; }
int n; // jumlah item
int [] values; // nilai dari setiap item int [] weights; // berat dari setiap item int maxWeight, sisaWeight, totalValue = 0, i; double[] tempWeight; try { n = Integer.parseInt(txtN.getText()); weights = new int[n];
values = new int[n];
tempWeight = new double[n]; } catch (NumberFormatException nfe){
areaOutput.setText("ERROR! Input n tidak sesuai format!"); return;
} try {
maxWeight = Integer.parseInt(txtMaxWeight.getText()); } catch (NumberFormatException nfe){
areaOutput.setText("ERROR! Input kapasitas tidak sesuai format!"); return;
}
StringTokenizer tokensValues = new StringTokenizer(txtValues.getText()); StringTokenizer tokensWeight = new StringTokenizer(txtWeights.getText());
if (tokensValues.countTokens() != tokensWeight.countTokens() || tokensWeight.countTokens() != n){
areaOutput.setText("ERROR! Jumlah input values/weights dengan n tidak sesuai");
return; }
double minWeight = maxWeight; for (i=0;i<n;i++)
{
tempWeight[i]= Double.parseDouble(awal); if(tempWeight[i]<minWeight) minWeight = tempWeight[i]; } System.out.println(minWeight); for (i=0;i<n;i++) {
weights[i] = (int) (tempWeight[i]/minWeight);
values[i] = (int) (Integer.parseInt(tokensValues.nextToken())); System.out.println(weights[i]+" "+values[i]);
}
int[] solution = new int[n]; maxWeight /= minWeight; sisaWeight = maxWeight; for (i=0;i<n;i++){ totalValue += values[i]; sisaWeight -= weights[i]; solution[i] = 1; } System.out.println(maxWeight+"-"+sisaWeight);
int hasil = unboundedKnapsack(sisaWeight, n, weights, values, solution) + totalValue;
areaOutput.append("\nNilai maksimumnya : "+hasil+"\n");
printOptimalSolution(n, solution, weights, values, minWeight); }
private void printOptimalSolution(int n, int[] solution, int[] weights, int[] values, double minWeight){
int i, totalWeight = 0, totalValue = 0; for ( i = 0; i < n; i++ ) if ( solution[i] > 0 ) {
areaOutput.append("Item ke-"+i+" sebanyak "+ solution[i] + " [Weight : "+weights[i] * minWeight +" - Value : "+values[i]+"]\n");
totalWeight += solution[i] * weights[i]; totalValue += solution[i] * values[i]; }
areaOutput.append("Berat Total : "+totalWeight+"\nNilai Maksimum : "+totalValue+"\n");
}
@SuppressWarnings("unchecked")
// <editor-fold defaultstate="collapsed" desc="Generated Code">//GEN-BEGIN:initComponents
private void initComponents() {
txtWeights = new javax.swing.JTextField(); txtValues = new javax.swing.JTextField(); txtN = new javax.swing.JTextField(); jLabel1 = new javax.swing.JLabel(); jLabel2 = new javax.swing.JLabel(); jLabel3 = new javax.swing.JLabel();
jScrollPane1 = new javax.swing.JScrollPane(); areaOutput = new javax.swing.JTextArea(); getButton = new javax.swing.JButton(); jLabel4 = new javax.swing.JLabel();
txtMaxWeight = new javax.swing.JTextField();
jLabel1.setText("Weight[n]"); jLabel2.setText("Value[n]"); jLabel3.setText("n"); areaOutput.setColumns(20); areaOutput.setRows(5); jScrollPane1.setViewportView(areaOutput); getButton.setText("Get Optimal Value..");
getButton.addActionListener(new java.awt.event.ActionListener() { public void actionPerformed(java.awt.event.ActionEvent evt) { getButtonActionPerformed(evt);
} });
jLabel4.setText("Max Weight"); javax.swing.GroupLayout layout = new javax.swing.GroupLayout(getContentPane()); getContentPane().setLayout(layout); layout.setHorizontalGroup( layout.createParallelGroup(javax.swing.GroupLayout.Alignment.LEADING) .addGroup(layout.createSequentialGroup() .addGroup(layout.createParallelGroup(javax.swing.GroupLayout.Alignment.LEADING) .addGroup(layout.createSequentialGroup() .addGap(131, 131, 131) .addComponent(getButton)) .addGroup(layout.createSequentialGroup() .addGap(38, 38, 38) .addComponent(jScrollPane1, javax.swing.GroupLayout.PREFERRED_SIZE, 317, javax.swing.GroupLayout.PREFERRED_SIZE))) .addContainerGap(45, Short.MAX_VALUE)) .addGroup(javax.swing.GroupLayout.Alignment.TRAILING, layout.createSequentialGroup() .addContainerGap() .addGroup(layout.createParallelGroup(javax.swing.GroupLayout.Alignment.TRAILING) .addGroup(layout.createSequentialGroup() .addComponent(jLabel4) .addGap(55, 55, 55) .addComponent(txtMaxWeight, javax.swing.GroupLayout.DEFAULT_SIZE, 139, Short.MAX_VALUE)) .addGroup(javax.swing.GroupLayout.Alignment.LEADING, layout.createSequentialGroup() .addComponent(jLabel3) .addGap(106, 106, 106) .addComponent(txtN, javax.swing.GroupLayout.DEFAULT_SIZE, 139, Short.MAX_VALUE)) .addGroup(layout.createSequentialGroup() .addGroup(layout.createParallelGroup(javax.swing.GroupLayout.Alignment.LEADING) .addGroup(javax.swing.GroupLayout.Alignment.TRAILING, layout.createSequentialGroup() .addComponent(jLabel1) .addGap(64, 64, 64)) .addGroup(layout.createSequentialGroup() .addComponent(jLabel2) .addGap(72, 72, 72))) .addGroup(layout.createParallelGroup(javax.swing.GroupLayout.Alignment.TRAILING, false) .addComponent(txtValues, javax.swing.GroupLayout.Alignment.LEADING)
.addComponent(txtWeights, javax.swing.GroupLayout.Alignment.LEADING, javax.swing.GroupLayout.DEFAULT_SIZE, 139, Short.MAX_VALUE)))) .addGap(139, 139, 139)) ); layout.setVerticalGroup( layout.createParallelGroup(javax.swing.GroupLayout.Alignment.LEADING) .addGroup(javax.swing.GroupLayout.Alignment.TRAILING, layout.createSequentialGroup() .addGap(27, 27, 27) .addGroup(layout.createParallelGroup(javax.swing.GroupLayout.Alignment.BASELINE) .addComponent(txtWeights, javax.swing.GroupLayout.PREFERRED_SIZE, javax.swing.GroupLayout.DEFAULT_SIZE, javax.swing.GroupLayout.PREFERRED_SIZE) .addComponent(jLabel1)) .addGap(18, 18, 18) .addGroup(layout.createParallelGroup(javax.swing.GroupLayout.Alignment.BASELINE) .addComponent(txtValues, javax.swing.GroupLayout.PREFERRED_SIZE, javax.swing.GroupLayout.DEFAULT_SIZE, javax.swing.GroupLayout.PREFERRED_SIZE) .addComponent(jLabel2)) .addGap(18, 18, 18) .addGroup(layout.createParallelGroup(javax.swing.GroupLayout.Alignment.BASELINE) .addComponent(jLabel3) .addComponent(txtN, javax.swing.GroupLayout.PREFERRED_SIZE, javax.swing.GroupLayout.DEFAULT_SIZE, javax.swing.GroupLayout.PREFERRED_SIZE)) .addPreferredGap(javax.swing.LayoutStyle.ComponentPlacement.RELATED) .addGroup(layout.createParallelGroup(javax.swing.GroupLayout.Alignment.BASELINE) .addComponent(txtMaxWeight, javax.swing.GroupLayout.PREFERRED_SIZE, javax.swing.GroupLayout.DEFAULT_SIZE, javax.swing.GroupLayout.PREFERRED_SIZE) .addComponent(jLabel4)) .addPreferredGap(javax.swing.LayoutStyle.ComponentPlacement.RELATED, 18, Short.MAX_VALUE) .addComponent(jScrollPane1, javax.swing.GroupLayout.PREFERRED_SIZE, javax.swing.GroupLayout.DEFAULT_SIZE, javax.swing.GroupLayout.PREFERRED_SIZE) .addGap(30, 30, 30) .addComponent(getButton) .addGap(20, 20, 20)) ); pack(); }// </editor-fold>//GEN-END:initComponents
private void getButtonActionPerformed(java.awt.event.ActionEvent evt) {//GEN-FIRST:event_getButtonActionPerformed
areaOutput.setText(""); computeUnboundedKnapsack();
}//GEN-LAST:event_getButtonActionPerformed public static void main(String args[]) {
java.awt.EventQueue.invokeLater(new Runnable() { public void run() {
new MainFrame().setVisible(true); }
}); }
// Variables declaration - do not modify//GEN-BEGIN:variables private javax.swing.JTextArea areaOutput;
private javax.swing.JButton getButton; private javax.swing.JLabel jLabel1; private javax.swing.JLabel jLabel2; private javax.swing.JLabel jLabel3; private javax.swing.JLabel jLabel4;
private javax.swing.JScrollPane jScrollPane1; private javax.swing.JTextField txtMaxWeight; private javax.swing.JTextField txtN;
private javax.swing.JTextField txtValues; private javax.swing.JTextField txtWeights;
// End of variables declaration//GEN-END:variables }
