Download - Scatter Search Algorithm
Scatter SearchAstri Puspitasari Luthfan Hadi Pramono
Media Digital and Game Technology, Institut Teknologi Bandung, 2012
What is Scatter Search?Metaheuristic and Global Optimization
algorithm
Use diversification (extrapolation) and intensifications (interpolation) strategies, not randomize
Combining a set of diverse and high quality candidate solutions by considering the weights and constraints of each solution
Introduced in 1970’s , proposed by Fred Glover in 1977
How does SS Combine Solutions?• A, B and C is seed solutions of
the reference set (generate randomly)
• New solution is crated from the linear (convex or non-convex) combination of at least two reference solutions
• New reference set evolved by deleting old solution, adding new solution
B
C
A
2
3
4
1
How does SS Work?
Improvement Method
Diversification generation
method
Subset GenerationSolution Combination
Next iteration?
Reference set (Seed
Solutions)
New Reference Set New Reference Set
Most Optimal Solution
Yes
No
Scatter Search Algorithm
Scatter Search on Job Scheduling
Case Study
Find The Most Optimal Schedule Using SS !
Machine 1
Machine 2
Machine 3
Machine 4
Machine 5
Job 1 23 10 40 26 27
Job 2 30 18 30 39 37
Job 3 12 2 13 31 6
Job 4 50 4 8 15 41
Job 5 21 33 8 12 8
1. Set Up Parameter Number of seed solution P = 7 (choose randomly)
Solution 1 : 4-3-1-5-2 Solution 2 : 3-4-2-1-5 Solution 3 : 3-4-5-1-2 Solution 4 : 2-1-4-3-5 Solution 5 : 1-5-4-3-2 Solution 6 : 5-2-1-4-3 Solution 7 : 1-5-2-4-3
Reference set R = 3; Ra=2 (best solution) and
Rb=1 (worst solution)
Number of iteration = 1
2. Diversification MethodCalculate fitness value of each solution by calculating
makespan
Solution 1
Machine 1 Machine 2 Machine 3 Machine 4 Machine 5
Start End Start End Start End Start End Start End
Job 1 0 50 50 54 54 62 62 77 77 118
Job 2 50 62 62 64 64 77 77 108 118 124
Job 3 62 85 85 95 95 135 135 161 161 188
Job 4 85 106 106 139 139 147 161 173 188 196
Job 5 106 136 139 157 157 187 187 226 226 263
Makespan = 263
2. Diversification MethodBy doing the same for the rest solutions, then
Fitness Value
Solution 1 263
Solution 2 251
Solution 3 272
Solution 4 236
Solution 5 260
Solution 6 252
Solution 7 248
3. Improvement Method
• Choose two worst solutions to be improved
• Worst solution has biggest fitness value • 1st worst solution will be improved
by using NEH algorithm
• 2nd worst solution will be improved by using SPT algorithm
Fitness Value
Solution 1 263
Solution 2 251
Solution 3 272
Solution 4 236
Solution 5 260
Solution 6 252
Solution 7 248
3. Improvement Method (SPT) SPT algorithm use to improve fitness value for solution 1
Calculate total time consume for each job, then order job ascending by total time
Result of improvement
New schedule for solution 1 is 3-5-4-1-2
Makespan = 262
Machine 1 Machine 2 Machine 3 Machine 4 Machine 5 Total
Job 1 23 10 40 26 27 126
Job 2 30 18 30 39 37 154
Job 3 12 2 13 31 6 64
Job 4 50 4 8 15 41 118
Job 5 21 33 8 12 8 82
3. Improvement Method (NEH) NEH algorithm use to improve fitness value for solution 3
Calculate total time for each job
Order job descending by the total time consume : 2 - 1 - 4 - 5 - 3
Take top two job on the order (Job 2 and Job 1), then calculate the makespan for each combination
1st combination : Job 1- Job 2 ; Makespan : 179
2nd Combination : Job 1 – Job 2 ; Makespan : 181
Machine 1 Machine 2 Machine 3 Machine 4 Machine 5 Total
Job 1 23 10 40 26 27 126
Job 2 30 18 30 39 37 154
Job 3 12 2 13 31 6 64
Job 4 50 4 8 15 41 118
Job 5 21 33 8 12 8 82
Take it to the next step
3. Improvement Method (NEH) 1-2 combination is the most optimal combination
Combine the 3rd job (job 4) with 1-2 combination
Combinations : 1-2-4, 1-4-2, and 4-1-2
Fitness value for each combination :
Combination Fitness
4-1-2 229
1-4-2 227
1-2-4 220 Take it to the next step
3. Improvement Method (NEH) 4-1-2 combination is the most optimal combination
Combine the 4th job (job 5) with 4-1-2 combination
Combinations : 5-1-2-4, 1-5-2-4, 1-2-5-4, 1-2-4-5
Fitness value for each combination :
Combination Fitness
5-1-2-4 251
1-5-2-4 242
1-2-5-4 228
1-2-4-5 228
Take it to the next step
3. Improvement Method (NEH) 1-2-4-5 combination is the most optimal combination
Combine the 5th job (job 3) with 4-1-2 combination
Combinations : 3-1-2-4-5 , 1-3-2-4-5 , 1-2-3-4-5, 1-2-4-3-5, 1-2-4-5-3
Fitness value for each combination :
Combination Fitness
3-1-2-4-5 240
1-3-2-4-5 255
1-2-3-4-5 237
1-2-4-3-5 234
1-2-4-5-3 234 NEH Result
New Reference Set
Job Order Fitness Value
Solution 1 3-5-4-1-2 262
Solution 2 3-4-2-1-5 251
Solution 3 1-2-4-5-3 234
Solution 4 2-1-4-3-5 236
Solution 5 1-5-4-3-2 260
Solution 6 5-2-1-4-3 252
Solution 7 1-5-2-4-3 248
4. Subset GenerationJob Order Fitness
ValueSolution
1 3-5-4-1-2 262
Solution 2 3-4-2-1-5 251
Solution 3 1-2-4-5-3 234
Solution 4 2-1-4-3-5 236
Solution 5 1-5-4-3-2 260
Solution 6 5-2-1-4-3 252
Solution 7 1-5-2-4-3 248 Reference set R = 3; Ra=2 (best solution); Rb=1 (worst solution)
R-1 = 2 max type subset
Ra
Rb
4. Subset Generation(Type 1)a1 = solution 3 ; a2 = solution 4 ; b = solution 1
Each subset type-1 has 2 values
Every subset is a set combination of a1, a2, and b
Subset type 1 : (a1,a2) , (a1,b), (a2,b) = (3,4), (3,1), (4,1)
Find new combination solution by using neighborhoods method Find diverse value between job order one each
subset combination solutions
4. Subset Generation (Type 1) Find new solutions by exchanging jobs between solution
3 and solution 4
1 2 4 5 3
Solution 3
2 1 4 3 5
Solution 4
1 4 5 3
New Solution 1
2
2 4 3 5
New Solution 2
1
4. Subset Generation (Type 1)
1 2 4 5 3
Solution 3
2 1 4 3 5
Solution 4
1 4 5 3
New Solution 3
2
2 4 3 5
New Solution 4
1
1 2 4 5 3
Solution 3
2 1 4 5 3
Solution 4
2 4 3 5
New Solution 3
1
1 4 5 3
New Solution 4
2
4. Subset Generation (Type 1)
Do neighborhood method for the rest member of subset type 1 Exchanging jobs between solution 3 and solution 1 Exchanging jobs between solution 4 and solution 1
1 2 4 5 3
Solution 3
2 1 4 5 3
Solution 4
2 4 3 5
New Solution 5
1
1 4 5 3
New Solution 6
2
4. Subset Generation (Type 1)
Neighborhood New solution Combination Fitness
Solution 3 and Solution 4
New Solution 1 2-1-4-5-3 236New Solution 2 1-2-4-3-5 234New Solution 3 2-1-4-5-3 236New Solution 4 1-2-4-3-5 234New Solution 5 1-2-4-3-5 234New Solution 6 2-1-4-5-3 236New Solution 7 1-2-4-3-5 234New Solution 8 2-1-4-5-3 236
Solution 3 and Solution 1
New Solution 9 1-5-4-3-2 260New Solution 10 3-2-4-5-1 249New Solution 11 3-2-4-1-5 242New Solution 12 1-5-4-2-3 254New Solution 13 3-1-4-5-2 263New Solution 14 5-2-4-1-3 252New Solution 15 2-5-4-1-3 237New Solution 16 1-3-4-5-2 263
Solution 1 and Solution 4
New Solution 17 2-5-4-1-3 237New Solution 18 3-1-4-2-5 247New Solution 19 3-1-4-5-2 263New Solution 20 2-5-4-3-1 239New Solution 21 1-5-4-3-2 260New Solution 22 2-3-4-1-5 239New Solution 23 3-2-4-1-5 242New Solution 24 5-1-4-3-2 260
4. Subset Generation (Type 2) Each subset type-2 has 3 values
Every subset is a set combination of a1, a2, and b
Subset type 1 : (a2,b) a1 = (4,1) 3
The most optimal combination of neighborhood (4,1) is New Solution 17
Find new combination solutions by using neighborhood method on New Solution 17 and Solution 3
1 2 4 5 3
New Solution 17
2 1 4 3 5
Solution 3
1 4 5 3
New Solution 25
2
2 4 3 5
New Solution 26
1
4. Subset Generation (Type 2)
New solution Combination FitnessNew Solution 25 1-5-4-2-3 254New Solution 26 2-1-4-5-3 236New Solution 27 5-2-4-1-3 252New Solution 28 1-5-4-2-3 254New Solution 29 2-1-4-5-3 236New Solution 30 5-2-4-1-3 252
The most optimal combination of 37 solution (7 seed + 30 new) is Solution 3 (1-2-4-5-3), with Fitness value = 234
The Application
References Glover, F., M. Laguna and R. Martí (2000), “Fundamentals of Scatter Search and Path
Relinking” Control and Cybernetics, 29 (3), pp. 653-684http://leeds.colorado.edu/Faculty/Laguna/articles/ss3.pdf (Last Access: March 24th 2003).
Laguna, M. (2002), “Scatter Search” in Handbook of Applied Optimization, P. M. Pardalos and M. G. C. Resende (Eds.), Oxford University Press, pp. 183-193http://www-bus.colorado.edu/Faculty/Laguna/articles/ss1.pdf (Last Access: March 24th 2003).
Marti, R., M. Laguna and F. Glover (2003), “Principle of Scatter Search”, Technical Report, Universidad de Valencia, Valencia.
Harris, Jason and S. Coe, (2005), “Introduction to Scatter Search”, Lecture handout: Paper Review, University of Guelph, Guelph.
Raharjo, Aliong (2007), “Analyzing The Comparison Between Genetic Algorithm and Scatter Search Algorithm on Flowshop Scheduling Matter With Makespan Criterion”, Industrial Engineering Project, Petra Christian University, Surabaya.
Nugroho, Susetyo (2004), “Analyzing System of Surabaya Public Transportation Route Using Scatter Search Algorithm”, Information System Project, STIKOM Surabaya, Surabaya.
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