Artificiel Bee Colony (ABC) Algorithme

1. Artificiel Bee Colony (ABC) Algorithme Elham Seifossadat Faegheh Javadi Isfahan University of Technology Fall 2010

2. A BEE COLONY OPTIMIZATION ALGORITHM TO JOB SHOP SCHEDULING • Job shop scheduling problems are considered to be a member of a large class of intractable numerical problems known as NP-hard. • Job shop scheduling is concerned with finding a sequential allocation of competing resources that optimizes a particular objective function. Isfahan University of Technology Fall 2010

3. A BEE COLONY OPTIMIZATION ALGORITHM TO JOB SHOP SCHEDULING • A finite set J of n jobs to be processed on a finite set M of m machines. • Each job Ji must be processed on every machine and consists of a chain of mi operations Oi1, Oi2,…,Oim which have to be scheduled in a pre-determined given order. • Oij is the jth operation of job Ji which has to be processed on a machine Mx for a processing time period of τij without interruption and preemption. Isfahan University of Technology Fall 2010 Isfahan University of Technology Fall 2010 3

4. A BEE COLONY OPTIMIZATION ALGORITHM TO JOB SHOP SCHEDULING • Each machine can process only one job and each job can be processed by only one machine at a time. • The longest duration in which all operations of all jobs are completed is referred to as the makespan Cmax. • Isfahan University of Technology Fall 2010 Isfahan University of Technology Fall 2010 4

5. A BEE COLONY OPTIMIZATION ALGORITHM TO JOB SHOP SCHEDULING • Ai be the set of ordered pairs of operations constrained by the precedence relations for each job Ji. • For each machine Mx, the set Ex describes the set of all pairs of operations to be performed on the machine. • For each operation Oij, let its earliest possible process start time be Tij. • Isfahan University of Technology Fall 2010 Isfahan University of Technology Fall 2010 5

6. A BEE COLONY OPTIMIZATION ALGORITHM TO JOB SHOP SCHEDULING Isfahan University of Technology Fall 2010

7. A BEE COLONY OPTIMIZATION ALGORITHM TO JOB SHOP SCHEDULING Isfahan University of Technology Fall 2010

8. A BEE COLONY OPTIMIZATION ALGORITHM TO JOB SHOP SCHEDULING Isfahan University of Technology Fall 2010

9. A BEE COLONY OPTIMIZATION ALGORITHM TO JOB SHOP SCHEDULING • The challenge is to adapt the self-organization behavior of the colony for solving job shop scheduling problems. • There are two major characteristics of the bee colony in searching for food sources: waggle dance and forage (or nectar exploration). Isfahan University of Technology Fall 2010

10. A BEE COLONY OPTIMIZATION ALGORITHM TO JOB SHOP SCHEDULING • waggle dance • A forager fi on return to the hive from nectar exploration will attempt with probability p to perform waggle dance on the dance floor with duration D = di A, • it will also attempt with probability ri to observe and follow a randomly selected dance. Isfahan University of Technology Fall 2010

11. A BEE COLONY OPTIMIZATION ALGORITHM TO JOB SHOP SCHEDULING Profitability rating for a forager: Isfahan University of Technology Fall 2010

12. A BEE COLONY OPTIMIZATION ALGORITHM TO JOB SHOP SCHEDULING The bee colony’s average profitability rating: Isfahan University of Technology Fall 2010

13. A BEE COLONY OPTIMIZATION ALGORITHM TO JOB SHOP SCHEDULING The dance duration: Isfahan University of Technology Fall 2010

14. A BEE COLONY OPTIMIZATION ALGORITHM TO JOB SHOP SCHEDULING Adjusting Probability of Following a Waggle Dance: Isfahan University of Technology Fall 2010

15. A BEE COLONY OPTIMIZATION ALGORITHM TO JOB SHOP SCHEDULING • Forage (Nectar Exploration) • A population of L foragers is defined in the colony. • When a forager is at a specific node, it can only move to next node that is defined in a list of presently allowed nodes, imposed by precedence constraints of operations. Isfahan University of Technology Fall 2010

16. A BEE COLONY OPTIMIZATION ALGORITHM TO JOB SHOP SCHEDULING A forager chooses the next node from the list according to the state transition rule: Isfahan University of Technology Fall 2010

17. A BEE COLONY OPTIMIZATION ALGORITHM TO JOB SHOP SCHEDULING The rating ρij of the edge (directed) between node I and node j is given by: Isfahan University of Technology Fall 2010

18. A BEE COLONY OPTIMIZATION ALGORITHM TO JOB SHOP SCHEDULING Isfahan University of Technology Fall 2010

19. A BEE COLONY OPTIMIZATION ALGORITHM TO JOB SHOP SCHEDULING • The performance of the honey bee colony scheduling approach is studied by evaluating them on the following 82 job shop problem instances. • The sizes of these problems range from 6 to 50 jobs and 5 to 20 machines. Isfahan University of Technology Fall 2010

20. A BEE COLONY OPTIMIZATION ALGORITHM TO JOB SHOP SCHEDULING Isfahan University of Technology Fall 2010

21. A BEE COLONY OPTIMIZATION ALGORITHM TO JOB SHOP SCHEDULING Isfahan University of Technology Fall 2010

22. Bee Colony Optimization (BCO) Isfahan University of Technology Fall 2010

23. Bee Colony Optimization (BCO) • There are two alternating phases (forward pass and backward pass) constituting single step in the BCO algorithm. • The hive is an non-natural object, with no precise location and does not influence the algorithm execution. Isfahan University of Technology Fall 2010

24. Bee Colony Optimization (BCO) • In each forward pass, every artificial bee visits NC solution components, creates partial solution, and after that returns to the hive. Isfahan University of Technology Fall 2010

25. Bee Colony Optimization (BCO) Isfahan University of Technology Fall 2010

26. Bee Colony Optimization (BCO) • In the backward pass, all artificial bees share information about the quality of their partial solutions. Having all solutions evaluated, each bee decides with a certain probability whether it will stay loyal to its solution or not. Isfahan University of Technology Fall 2010

27. Bee Colony Optimization (BCO) Isfahan University of Technology Fall 2010

28. Bee Colony Optimization (BCO) Isfahan University of Technology Fall 2010

29. Bee Colony Optimization (BCO) • When all solutions are completed the best one is determined, it is used to update global best solution and an iteration of the BCO is accomplished. • At this point all B solutions are deleted, and the new iteration could start. The BCO runs iteration by iteration until a stopping condition is met. Isfahan University of Technology Fall 2010

30. Bee Colony Optimization (BCO) • B - The number of bees in the hive; • NC - The number of constructive moves during one forward pass. Isfahan University of Technology Fall 2010

31. Bee Colony Optimization (BCO) (1) Initialization: an empty solution is assigned to each bee; (2) For each bee: // (the forward pass) (a) Set k = 1; // (count constructive moves in the forward pass) (b) Evaluate all possible constructive moves; (c) Choose one move using the roulette wheel; (d) k = k + 1; If k ≤ NC Goto step (b). (3) All bees are back to the hive; // (backward pass starts) (4) Evaluate (partial) objective function value for each bee; (5) Each bee decides randomly whether to continue its own exploration and become a recruiter, or to become a follower; (6) For each follower, choose a new solution from recruiters by the roulette wheel; (7) If solutions are not completed Goto step 2; (8) Evaluate all solution and find the best one; (9) If the stopping criteria is not met Goto step 2; (10) Output the best solution found. Isfahan University of Technology Fall 2010

32. Bee Colony Optimization (BCO) • Loyalty decision Isfahan University of Technology Fall 2010

33. Bee Colony Optimization (BCO) • Recruiting process Isfahan University of Technology Fall 2010

34. Scheduling Independent Tasks by BCO • Let T = {1, 2, . . . , n} be a given set of independent tasks, and P = {1, 2, . . .,m} a set of identical machines. • The processing time of task i (i = 1, 2, . . . , n) is denoted by li. Isfahan University of Technology Fall 2010

35. Scheduling Independent Tasks by BCO • Probability pi that specific bee chooses task i was equal: Isfahan University of Technology Fall 2010

36. Scheduling Independent Tasks by BCO • Probability pj that specific bee chooses processor j was calculated as: Isfahan University of Technology Fall 2010

37. Scheduling Independent Tasks by BCO Isfahan University of Technology Fall 2010

38. References • A BEE COLONY OPTIMIZATION ALGORITHM TO JOB SHOP SCHEDULING- Chong, Low, Sivakumar, and Gay-Proceedings of the 2006 Winter Simulation Conference. • Bee Colony Optimization: The Applications Survey - DUˇSAN TEODOROVI´C TATJANA DAVIDOVI´C and MILICA ˇSELMI´C- ACM Transactions on Computational Logic,2011. Isfahan University of Technology Fall 2010

39. Thanks for your attention!