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# Scatter Search Algorithm

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A brief overview about Scatter Search algorithm and and its application to job scheduling

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• Scatter: kkt. 1 menyebar, menghamburkan (papers). 2 menabur (seed). -kki. bubar, berpencar. -scattered ks. terpencar-pencar, tersebardisana-sini. -scattering kb. sejumlahkecil (of follewers).Scatter search: pencarianmenyebarDiversification: menghasilkansolusi yang berbedadanbervariatifsecarasistematikRandomize : menghasilkansolusiygtidakmemilikiperbedaan yang sistematisantarsolusi.
• Diversification : proses menciptakan solusi2 baru yang lebihbervariasi
• ### Scatter Search Algorithm

1. 1. Scatter SearchAstri PuspitasariLuthfan Hadi PramonoMedia Digital and Game Technology, Institut Teknologi Bandung, 2012
2. 2. 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
3. 3. How does SS CombineSolutions?• A, B and C is seed solutions of the reference set (generate randomly)• New solution is crated from the C linear (convex or non-convex) combination of at least two reference solutions 2• New reference set evolved by deleting old solution, adding new solution 1 A B 4 3
4. 4. How does SS Work? Diversification Improvement generation method Method Reference set(Seed Solutions) New Reference Set New Reference Set No Next iteration? Most Optimal Solution Solution Subset Generation Combination
5. 5. Scatter Search Algorithm
6. 6. Scatter Search on Job Scheduling Case Study
7. 7. Find The Most OptimalSchedule 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
8. 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
9. 9. 2. Diversification Method Calculate fitness value of each solution by calculating makespan Machine 1 Machine 2 Machine 3 Machine 4 Machine 5 Solution 1 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
10. 10. 2. Diversification Method By 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
11. 11. 3. Improvement Method• Choose two worst solutions to be Fitness Value improved Solution 1 263• Worst solution has biggest fitness value Solution 2 251 • 1st worst solution will be improved by using NEH algorithm Solution 3 272 • 2nd worst solution will be improved by using SPT algorithm Solution 4 236 Solution 5 260 Solution 6 252 Solution 7 248
12. 12. 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 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 Result of improvement  New schedule for solution 1 is 3-5-4-1-2  Makespan = 262
13. 13. 3. Improvement Method (NEH) NEH algorithm use to improve fitness value for solution 3 Calculate total time for each job 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 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 Take it to the next step  2nd Combination : Job 1 – Job 2 ; Makespan : 181
14. 14. 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
15. 15. 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 Take it to the next step 1-2-4-5 228
16. 16. 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
17. 17. New Reference Set Fitness Job Order 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
18. 18. 4. Subset Generation Fitness Job Order Value Solution 1 3-5-4-1-2 262 Rb Solution 2 3-4-2-1-5 251 Solution 3 1-2-4-5-3 234 Ra 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
19. 19. 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
20. 20. 4. Subset Generation(Type 1) Find new solutions by exchanging jobs between solution 3 and solution 4 Solution 3 New Solution 1 1 2 4 5 3 2 1 4 5 3 2 1 4 3 5 1 2 4 3 5 Solution 4 New Solution 2
21. 21. 4. Subset Generation(Type 1) Solution 3 New Solution 3 1 2 4 5 3 2 1 4 5 3 2 1 4 3 5 1 2 4 3 5 Solution 4 New Solution 4 Solution 3 New Solution 3 1 2 4 5 3 1 2 4 3 5 2 1 4 5 3 2 1 4 5 3 Solution 4 New Solution 4
22. 22. 4. Subset Generation(Type 1) Solution 3 New Solution 5 1 2 4 5 3 1 2 4 3 5 2 1 4 5 3 2 1 4 5 3 Solution 4 New Solution 6  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
23. 23. 4. Subset Generation(Type 1) Neighborhood New solution Combination Fitness New Solution 1 2-1-4-5-3 236 New Solution 2 1-2-4-3-5 234 New Solution 3 2-1-4-5-3 236 New Solution 4 1-2-4-3-5 234 Solution 3 and Solution 4 New Solution 5 1-2-4-3-5 234 New Solution 6 2-1-4-5-3 236 New Solution 7 1-2-4-3-5 234 New Solution 8 2-1-4-5-3 236 New Solution 9 1-5-4-3-2 260 New Solution 10 3-2-4-5-1 249 New Solution 11 3-2-4-1-5 242 New Solution 12 1-5-4-2-3 254 Solution 3 and Solution 1 New Solution 13 3-1-4-5-2 263 New Solution 14 5-2-4-1-3 252 New Solution 15 2-5-4-1-3 237 New Solution 16 1-3-4-5-2 263 New Solution 17 2-5-4-1-3 237 New Solution 18 3-1-4-2-5 247 New Solution 19 3-1-4-5-2 263 New Solution 20 2-5-4-3-1 239 Solution 1 and Solution 4 New Solution 21 1-5-4-3-2 260 New Solution 22 2-3-4-1-5 239 New Solution 23 3-2-4-1-5 242 New Solution 24 5-1-4-3-2 260
24. 24. 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 New Solution 17 New Solution 25 1 2 4 5 3 2 1 4 5 3 2 1 4 3 5 1 2 4 3 5 Solution 3 New Solution 26
25. 25. 4. Subset Generation(Type 2) New solution Combination Fitness New Solution 25 1-5-4-2-3 254 New Solution 26 2-1-4-5-3 236 New Solution 27 5-2-4-1-3 252 New Solution 28 1-5-4-2-3 254 New Solution 29 2-1-4-5-3 236 New 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
26. 26. The Application
27. 27. References Glover, F., M. Laguna and R. Martí (2000), “Fundamentals of Scatter Search and Path Relinking” Control and Cybernetics, 29 (3), pp. 653-684 http://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. 183-193 http://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.
28. 28. Thank You