I need to solve the TSP problem with the branch and bound algorithm. Here's the code. The problem is, the code works only in small instances (i.e. three cities), but also it isn't working every time.
I've been looking for some mistakes but I couldn't find any. The costs matrix is the macierz in my code and number of cities is stored in variable ileMiast. I think the rest is clear. Don't bother to the sort function or the FinalMatrix array. It's just to present the final order.
public double branchibound(int cities)
{
double totalCost = 0;
FinalMatrix = new ArrayList(ileMiast);
/*
* The ReducedCostMatrix calculates the reduced
* cost matrix
* */
totalCost = this.ReducedCostMatrix(cities);
/*
* Now we would work on the reduced cost
* Matrix to check which nodes to be inluded
* yet or not.
* */
int count = 0;
for (int i = 0; i < cities; i++)
for (int j = 0; j < cities; j++)
{
double[][] tempReduceRow = new double[cities][];
for (int l = 0; l < cities; l++)
tempReduceRow[l] = new double[cities];
for (int l = 0; l < cities; l++)
for (int m = 0; m < cities; m++)
tempReduceRow[l][m] = ReducedMatrix[l][m];
double[][] tempReduceCol = new double[cities][];
for (int l = 0; l < cities; l++)
tempReduceCol[l] = new double[cities];
for (int l = 0; l < cities; l++)
for (int m = 0; m < cities; m++)
tempReduceCol[l][m] = ReducedMatrix[l][m];
/*
* We only include those edges with value 0.
* Now, we will have only those with minimum left
* child and maximum right child.
* */
if (ReducedMatrix[i][j] == 0)
{
OmitLeft(i, j, ref tempReduceRow);
double LBound = totalCost + ReducedCostMatrix(cities, ref tempReduceRow);
OmitRight(i, j, ref tempReduceCol);
double RBound = totalCost + ReducedCostMatrix(cities, ref tempReduceCol);
FinalMatrix.Add(new double[] { LBound, RBound, count });
}
}
//sort();
return totalCost;
}
private void sort()
{
double[] values = new double[3];
double[] a = new double[3];
values = (double[])this.FinalMatrix[0];
int i = 0;
int prevIndex = 0;
for (i = 0; i < this.FinalMatrix.Count; i++)
for (int j = 0; j < this.FinalMatrix.Count; j++)
{
a = (double[])this.FinalMatrix[j];
if (a[1] > values[1] || a[0] < values[0])
{
FinalMatrix[prevIndex] = FinalMatrix[j];
FinalMatrix[j] = values;
values = a;
prevIndex = j;
}
}
}
public String getString()
{
String str = new String('A', 20);
str = "";
foreach (double[] a in this.FinalMatrix)
str += (char)(a[2]);
return str;
}
private void OmitLeft(int row, int col, ref double[][] temp)
{
for (int j = 0; j < temp.Length; j++)
temp[row][j] = -1;
for (int j = 0; j < temp.Length; j++)
temp[j][col] = -1;
}
private void OmitRight(int row, int col, ref double[][] temp)
{
temp[row][col] = -1;
}
private double ReducedCostMatrix(int cities)
{
double minBound = 0;
ReducedMatrix = new double[cities][];
for (int i = 0; i < cities; i++)
ReducedMatrix[i] = new double[cities];
/*
* Here we make a new Reduced Matrix
* by copying the original matrix
* into the new one.
* */
for (int i = 0; i < cities; i++)
for (int j = 0; j < cities; j++)
ReducedMatrix[i][j] = macierz[i][j];
minBound = ReducedRows(cities);
minBound += ReducedCols(cities);
return minBound;
}
private double ReducedCostMatrix(int cities, ref double[][] temp)
{
double minBound = 0;
minBound = ReducedRows(cities, ref temp);
minBound += ReducedCols(cities, ref temp);
return minBound;
}
private double ReducedRows(int cities)
{
double min = 65535;
bool flag = false;
double minBound = 0;
for (int i = 0; i < cities; i++)
{
min = 65535;
for (int j = 0; j < cities; j++)
if (this.ReducedMatrix[i][j] < min && this.ReducedMatrix[i][j] != -1)
{
min = this.ReducedMatrix[i][j];
flag = true;
}
if (flag)
{
this.SubtractRow(i, min);
minBound += min;
}
}
return minBound;
}
private double ReducedRows(int cities, ref double[][] temp)
{
double min = 65535;
double minBound = 0;
for (int i = 0; i < cities; i++)
{
min = 65535;
bool flag = true;
for (int j = 0; j < cities; j++)
if (temp[i][j] < min && temp[i][j] != -1)
{
min = temp[i][j];
flag = false;
}
if (!flag)
{
this.SubtractRow(i, min, ref temp);
minBound += min;
}
}
return minBound;
}
private double ReducedCols(int cities)
{
double min = 65535;
double minBound = 0;
for (int j = 0; j < cities; j++)
{
for (int i = 0; i < cities; i++)
if (this.ReducedMatrix[i][j] < min && this.ReducedMatrix[i][j] != -1)
min = ReducedMatrix[i][j];
this.SubtractCol(j, min);
minBound += min;
}
return minBound;
}
private double ReducedCols(int cities, ref double[][] temp)
{
double min = 65535;
double minBound = 0;
for (int j = 0; j < cities; j++)
{
for (int i = 0; i < cities; i++)
if (temp[i][j] < min && temp[i][j] != -1)
min = temp[i][j];
SubtractCol(j, min, ref temp);
minBound += min;
}
return minBound;
}
private void SubtractRow(int row, double sub)
{
for (int j = 0; j < this.ReducedMatrix[0].Length; j++)
if (this.ReducedMatrix[row][j] == -1)
continue;
else
this.ReducedMatrix[row][j] -= sub;
}
private void SubtractRow(int row, double sub, ref double[][] temp)
{
for (int j = 0; j < temp[0].Length; j++)
if (temp[row][j] == -1)
continue;
else
temp[row][j] -= sub;
}
private void SubtractCol(int col, double sub)
{
for (int j = 0; j < this.ReducedMatrix[0].Length; j++)
if (this.ReducedMatrix[j][col] == -1)
continue;
else
this.ReducedMatrix[j][col] -= sub;
}
private void SubtractCol(int col, double sub, ref double[][] temp)
{
for (int j = 0; j < temp.Length; j++)
if (temp[j][col] == -1)
continue;
else
temp[j][col] -= sub;
}
Thanks in advance
