Hololens Anchor 自动布局（三）—— Black Hole Algorithm For SCP
Background
熬夜熬死了要~
总之昨夜发现了一个据说对SCP效果特棒的启发性算法-黑洞算法
Paper ：Black Hole Algorithm For SCP
具体有多好，见图：
Instance代表的数据采自 J.E.Beasley 的 OR-Library
Instances For Set Covering (OR-Library)
这个结果已经远远超过了蚁群算法(ACO)的效果：
以及效果更好的超启发的蚁群算法(ACO-HH)
Black Hole Algorithm
暂时把伪代码贴上，有精力的时候再补充和解释变量
实现Black Hole Algorithm的代码
数据结构 DataStruct.cs
class Black_Hole
{
List<Anchor> anchors;
Random random;
public int N; //子集个数
public int M; //元素个数
public int PopSize; //star个数
public int[] c; //子集cost
public int[][] a; //子集j是否包含元素i
public int[][] x; //本次迭代的可行解集
public int[][] x1; //下次迭代的可行解集
enum Shape_Type { Deta, Gama }; //将实数域转换到[0,1]的实数域
enum Transfer_Type { Standard,Static_Probability, Elitist}; //将[0,1]的实数域转换到{0，1}二进制域
public double alpha;
public bool Valid_Result;
public int[] result;
public Black_Hole()
{
anchors = new List<Anchor>();
}
public void Add(Anchor anchor)
{
this.anchors.Add(new Anchor(anchor.loc, anchor.models));
}
public void standard()
{
UpdateLength();
c = new int[N];
for (int i = 0; i < N; ++i)
{
c[i] = 1;
}
x = new int[PopSize][];
for (int i = 0; i < PopSize; ++i)
{
x[i] = new int[N];
for (int j = 0; j < N; ++j)
x[i][j] = 0;
}
x1 = new int[PopSize + 1][];
for (int i = 0; i <= PopSize; ++i)
{
x1[i] = new int[N];
for (int j = 0; j < N; ++j)
x1[i][j] = 0;
}
a = new int[PopSize + 1][];
for (int i = 0; i <= PopSize; ++i)
{
a[i] = new int[N];
for (int j = 0; j < N; ++j)
a[i][j] = 0;
}
int len;
for (int i = 0; i < N; ++i)
{
len = anchors[i].models.Count();
for (int j = 0; j < len; ++j)
{
a[i][anchors[i].models[j]] = 1;
}
}
}
public void start(int T)
{
random = new Random();
int[] f = new int[PopSize+1];
for (int i = 0; i < PopSize; ++i)
{
for (int j = 0; j < N; ++j)
{
x[i][j] = random.Next(2);
}
f[i] = cost(x[i], N);
}
int globalfit = int.MaxValue;
int t = 0;
while (t < T)
{
int minfit;
int minindex;
min(f, N, out minfit, out minindex);
if (minfit < globalfit)
{
globalfit = minfit;
for (int j = 0; j < N; ++j)
{
x[PopSize][j] = x[minindex][j];
}
}
double sum = 0;
for (int ii = 0; ii < PopSize; ++ii)
sum += cost(x[ii], N);
double R = minfit / sum;
for (int i = 0; i < PopSize; ++i)
{
double rand = random.NextDouble();
if (R > rand)
for (int j = 0; j < N; ++j)
x[i][j] = random.Next(2);
}
for (int i = 0; i < PopSize; ++i)
for (int j = 0; j < N; ++j)
{
double rand = random.NextDouble();
double tmp = x[i][j] + rand * (x[PopSize][j] - x[i][j]);
x1[i][j] = transfer(tmp, rand);
}
UpdateIteration();
}
Valid_Result = true;
result = new int[N];
for (int i = 0; i < N; ++i)
result[i] = x[PopSize][i];
}
private int cost(int[] x, int length)
{
int sum = 0;
for (int i = 0; i < length; ++i)
if (x[i] == 1)
sum++;
return sum;
}
private void min(int[] f, int length, out int min, out int index)
{
index = -1;
min = int.MaxValue;
for (int i = 0; i < length; ++i)
if (f[i] < min)
{
min = f[i];
index = i;
}
}
private double g(double tmp, Shape_Type st = Shape_Type.Deta, int type = 1)
{
if (st == Shape_Type.Deta)
{
switch (type)
{
case 1: return 1 / (1 + Math.Pow(Math.E, -2 * tmp));
case 2: return 1 / (1 + Math.Pow(Math.E, -2 * tmp));
case 3: return 1 / (1 + Math.Pow(Math.E, -tmp / 2));
case 4: return 1 / (1 + Math.Pow(Math.E, -tmp / 3));
default: break;
}
return -1;
}
else if (st == Shape_Type.Gama)
{
switch (type)
{
case 1: return Math.Abs(Erf(Math.Sqrt(Math.PI) / 2 * tmp));
case 2: return Math.Abs(Math.Tanh(tmp));
case 3: return Math.Abs(tmp / Math.Sqrt(1 + tmp * tmp));
case 4: return Math.Abs(2 / Math.PI * Math.Atan(Math.PI / 2 * tmp));
default: break;
}
return -1;
}
return -1;
}
private int transfer(double tmp,double rand, Transfer_Type tt =Transfer_Type.Standard)
{
if(tt == Transfer_Type.Standard)
{
if (rand < tmp)
return 1;
else
return 0;
}
return -1;
}
private void UpdateLength()
{
M = 0;
N = anchors.Count();
for (int i = 0; i < N; ++i)
{
int len = anchors[i].models.Count();
for (int j = 0; j < len; ++j)
{
if (anchors[i].models[j] > M)
{
PopSize = anchors[i].models[j];
}
}
}
M++;
}
private void UpdateIteration()
{
for (int i = 0; i < PopSize; ++i)
for (int j = 0; j < N; ++j)
x[i][j] = x1[i][j];
}
private static double Erf(double x)
{
double result = 0;
int index = 0;
do
{
index++;
} while (x / Math.Pow(10, index) > 1e-3);//设置计算精度
int maxIndex = (int)Math.Pow(10, index);
double deltaX = x / maxIndex;
for (int i = 0; i <= maxIndex; i++)
{
if (i > 0 && i < maxIndex)
{
result += 2 * Math.Exp(-Math.Pow(deltaX * i, 2));
continue;
}
else if (i == maxIndex)
{
result += Math.Exp(-Math.Pow(deltaX * i, 2));
continue;
}
else if (i == 0)
{
result += Math.Exp(-Math.Pow(deltaX * i, 2));
continue;
}
}
return result * deltaX / Math.Pow(Math.PI, 0.5);
}
}
主程序 MainWindows.xaml.cs
Black_Hole black_hole = new Black_Hole();
const int T = 50;
public void BH()
{
int[] result = new int[paths.Count()];
ConvertModelsToBH(paths);
if (BHStart(ref result))
{
String ss = "";
//some operations based on "result" array
for (int i = 0; i < result.Count(); ++i)
{
ss += result[i].ToString();
}
System.Windows.MessageBox.Show(ss);
}
}
void ConvertModelsToBH(List<BaoPath> paths)
{
for (int i = 0; i < maxn; ++i)
for (int j = 0; j < maxn; ++j)
{
pixels[i, j].value = 0;
pixels[i, j].id = "";
}
int radius = 75;//这个值要 equals 现实中的3米
int length = WallAndModelList.Count();
#region loop
for (int i = 0; i < length; ++i)
{
BaoModel bm = WallAndModelList[i];
PointD center = new PointD(bm.x, bm.y);
List<BaoSide> PointVis = new List<BaoSide>();
GetsVisibleRegion(center.X, center.Y, false, ref PointVis);
for (int ii = BInt(center.Y - radius, true); ii <= BInt(center.Y, false); ++ii)
{
double j_tmp = Math.Sqrt(radius * radius - (center.Y - ii) * (center.Y - ii));
for (int jj = BInt(center.X - j_tmp, true); jj <= BInt(center.X + j_tmp, false); ++jj)
{
if (IsPointInPolygon(jj, ii, PointVis))
{
pixels[jj, ii].Add(WallAndModelList[i].value, WallAndModelList[i].id); //可能有问题
}
}
}
for (int ii = BInt(center.Y + 1, false); ii <= BInt(center.Y + radius, false); ++ii)
{
double j_tmp = Math.Sqrt(radius * radius - (ii - center.Y) * (ii - center.Y));
for (int jj = BInt(center.X - j_tmp, true); jj <= BInt(center.X + j_tmp, false); ++jj)
{
if (IsPointInPolygon(jj, ii, PointVis))
{
pixels[jj, ii].Add(WallAndModelList[i].value, WallAndModelList[i].id); //可能有问题
}
}
}
}
#endregion
int bias = 31;
double last_value = -1;
string last_string = "null";
// int fi = -1;
// int fj = -1;
Anchor anchor;
List<int> models = new List<int>();
for (int i = 0; i < maxn; ++i)
for (int j = 0; j < maxn; ++j)
{
if (pixels[i, j].value != 0 && (!pixels[i, j].id.Equals(last_string) || pixels[i, j].value != last_value))
{
String[] ss = pixels[i, j].id.Split(',');
int len = ss.Count();
for (int k = 0; k < len; ++k)
{
if (ss[k].Count() != 0)
models.Add(int.Parse(ss[i].ToString()) + bias);
}
anchor = new Anchor(new PointD(i, j), models);
black_hole.Add(anchor);
}
}
}
bool BHStart(ref int[] result)
{
int length = black_hole.N;
black_hole.standard();
black_hole.start(T);
if (black_hole.Valid_Result)
{
for (int i = 0; i < length; ++i)
result[i] = black_hole.result[i];
return true;
}
return false;
}