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CLARANS

CLARANS. data 10 4 2 9 6 9 5 4 9 9 8 1 5 4 0 8 8 0 4 1 6 2 8 2 9 6 7 3 2 2. Algorithm CLARANS 1.Input parameters numlocal and maxneighbor. Initialize i to 1, and mincost to a large number. k = 3 numlocal = 10 maxneighbor = 5 i = 1 mincost = 9999. Data cost K#

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CLARANS

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  1. CLARANS

  2. data 10 4 2 9 6 9 5 4 9 9 8 1 5 4 0 8 8 0 4 1 6 2 8 2 9 6 7 3 2 2 Algorithm CLARANS 1.Input parameters numlocal and maxneighbor. Initialize i to 1, and mincost to a large number. k = 3 numlocal = 10 maxneighbor = 5 i = 1 mincost = 9999

  3. Data cost K# 10 4 3.1623 3 2 9 4 2 6 9 0 2 5 4 2.2361 3 9 9 3 2 8 1 2.2361 3 5 4 2.2361 3 0 8 6.0828 2 8 0 3.1623 3 4 1 0 1 6 2 1.4142 3 8 2 1.4142 3 9 6 3.6056 3 7 3 0 3 2 2 2.2361 1 Algorithm CLARANS 2.Set current to an arbitrary node in Gn,k. 3.Set j to 1. Step 2. current = Gn,k. = {(4,1), (6,9), (7,3)} cost(current) = 34.7856 Step 3. j = 1 note: S1 and S2 are neighbors if and only if |S1  S2| = k-1

  4. Data cost K# 10 4 4.4721 3 2 9 4 2 6 9 0 2 5 4 2.2361 3 9 9 3 2 8 1 2.2361 3 5 4 2.2361 3 0 8 6.0828 2 8 0 2.8284 3 4 1 0 1 6 2 0 3 8 2 2 3 9 6 4.2426 2 7 3 1.4142 3 2 2 2.2361 1 Algorithm CLARANS 4.Consider a random neighbor S of current, and based on Equation (5) calculate the cost differential of the two nodes. 5.If S has a lower cost, set current to S, and go to Step (3). 6. Otherwise, increment j by 1. If j <= maxneighbor, go to Step (4). Step 4. random S = {(4,1), (6,9), (6,2)} cost(S) = 36.98 Step 5. -- Step 6. j = j + 1 , j = 2 j <= maxneighbor goto step (4)

  5. Data cost K# 10 4 2.8284 3 2 9 4 2 6 9 0 2 5 4 3.1623 1 9 9 3 2 8 1 1 3 5 4 3.1623 1 0 8 6.0828 2 8 0 2 3 4 1 0 1 6 2 2 3 8 2 0 3 9 6 4.1231 3 7 3 1.4142 3 2 2 2.2361 1 Algorithm CLARANS 4.Consider a random neighbor S of current, and based on Equation (5) calculate the cost differential of the two nodes. 5.If S has a lower cost, set current to S, and go to Step (3). 6. Otherwise, increment j by 1. If j <= maxneighbor, go to Step (4). Step 4. random S = {(4,1), (6,9), (8,2)} cost(S) = 35.009 Step 5. -- Step 6. j = j + 1 , j = 3 j <= maxneighbor goto step (4)

  6. Data cost K# 10 4 3.1623 3 2 9 0 2 6 9 4 2 5 4 2.2361 3 9 9 6.3246 3 8 1 2.2361 3 5 4 2.2361 3 0 8 2.2361 2 8 0 3.1623 3 4 1 0 1 6 2 1.4142 3 8 2 1.4142 3 9 6 3.6056 3 7 3 0 3 2 2 2.2361 1 Algorithm CLARANS 4.Consider a random neighbor S of current, and based on Equation (5) calculate the cost differential of the two nodes. 5.If S has a lower cost, set current to S, and go to Step (3). 6. Otherwise, increment j by 1. If j <= maxneighbor, go to Step (4). Step 4. random S = {(4,1), (2,9), (7,3)} cost(S) = 34.263 Step 5. cost(S)<cost(current) current = {(4,1), (2,9), (7,3)} goto step (3)

  7. Data cost K# 10 4 2.2361 3 2 9 0 2 6 9 4 2 5 4 3.1623 1 9 9 3 3 8 1 4 1 5 4 3.1623 1 0 8 2.2361 2 8 0 4.1231 1 4 1 0 1 6 2 2.2361 1 8 2 4.1231 1 9 6 0 3 7 3 3.6056 1 2 2 2.2361 1 Algorithm CLARANS 3.Set j to 1. 4.Consider a random neighbor S of current, and based on Equation (5) calculate the cost differential of the two nodes. 5.If S has a lower cost, set current to S, and go to Step (3). 6. Otherwise, increment j by 1. If j <= maxneighbor, go to Step (4). current = {(4,1), (2,9), (7,3)} cost(current) = 34.263 Step 3. j = 1 Step 4. random S = {(4,1), (2,9), (9,6)} cost(S) = 38.121 Step 5. -- Step 6. j = j + 1 , j = 2 j <= maxneighbor goto step (4)

  8. current = {(4,1), (2,9), (7,3)} cost(current) = 34.263 j = 1 random S = {(4,1), (2,9), (9,6)} cost(S) = 38.121 j = 2 random S = {(4,1), (2,9), (10,4)} cost(S) = 38.087 j = 3 random S = {(4,1), (5,4), (7,3)} cost(S) = 40.888 j = 4 random S = {(4,1), (9,9), (7,3)} cost(S) = 39.16 j = 5 random S = {(2,2), (2,9), (7,3)} cost(S) = 37.422 j = 6 j > maxneighbor goto step 7 Step 7. cost(current) < mincost mincost = cost(current) = 34.263 bestnode = current = {(4,1), (2,9), (7,3)} Step 8. i = i + 1 , i = 2 i < numlocal goto step (2) มีโอกาส random ได้set เดิม? หรือ current ก่อนหน้านี้ ? Algorithm CLARANS 7. Otherwise, when j > maxneighbor, compare the cost of current with mincost. If the former is less than mincost, set mincost to the cost of current, and set bestnode to current. 8. Increment i by 1. If i > numlocal, output bestnode and halt. Otherwise, go to Step (2).

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