Scheduling of Wafer Fabrication Facilities using Evolutionary Algorithms

1
Scheduling of Wafer Fabrication Facilities using
Evolutionary Algorithms

• Tsung-Che Chiang
• Department of Computer Science and Information
  Engineering
• National Taiwan Normal University
• 2010.11.04

2
Outline

• Introduction
• Wafer fab scheduling
• Evolutionary algorithms (EA)
• Six ways of applying EAs to fab scheduling
• Conclusions

3
Whats Scheduling?

• A task of allocating resources over time to
  requests under given constraints such that
  certain objectives are satisfied or optimized.
• In a production system,
• resources refer to machines, workers, vehicles,
  etc.
• requests refer to jobs
• objectives include work-in-process (WIP) level,
  on-time delivery (OTD) rate, etc.

• A task of allocating resources over time to
  requests under given constraints such that
  certain objectives are satisfied or optimized.

4
Single Machine Scheduling

• Task job sequencing

?
?
?
?
?
?
?
5
Parallel Machine Scheduling

• Tasks machine assignment job sequencing

schedule 1
time
schedule 2
time
due date (all the same)
6
Job Shop Scheduling

• Task job sequencing on each machine
• operation precedence
• dynamic arrival of jobs

M1
M2
M3
M4
M1 ?? M2 ? M3 ? M4
M1 ?? M4 ? M3 ? M2
M2 ?? M1 ? M4 ? M3
7
Flexible Job Shop Scheduling

• Tasks machine assignment job sequencing
• Machines in a stage might not be identical.

S1
S2
S3
S4
M1 ?? M2 ? M3 ? M4
M1 ?? M4 ? M3 ? M2
M2 ?? M1 ? M4 ? M3
8
Wafer Fab Scheduling

• A wafer fab can be regarded as a large-scale
  flexible job shop with additional intricacies
• batch machines
• sequence dependent setup
• dynamic arrival of customer orders
• machine breakdown maintenance

9
Wafer Fab Scheduling

• Batch machines
• batch forming
• batch sequencing

10
Wafer Fab Scheduling

• Batch machines
• start or wait

Lot2
time
Lot1
t0
t1
Lot2
time
Lot1
t0
t1
11
Wafer Fab Scheduling

• Sequence dependent setup (SDS)
• fixture changing
• program loading
• parameter tuning
• etc.

Setup is unproductive.
time
12
Wafer Fab Scheduling

• Wafer fab is a very complex system, and optimal
  scheduling is almost impossible.
• A common practice is to do scheduling by
  real-time dispatching.

13
Rule-based Dispatching
queue
14
Rule-based Dispatching

• Some advanced dispatching rules

Kim et al. 2001
Pfund et al. 2008
15
Rule-based Dispatching

• Questions
• How can we generate a good dispatching rule?
• If the rule has parameters, how can we optimize
  them?
• Can we combine different rules?
• Can we assign different rules to stages with
  different characteristics?
• Which stages are more important than others?
• What if dispatching rules are not good enough?
• ? Let the Evolutionary Algorithm help us!

16
Evolutionary Algorithms

• EAs are algorithms imitating the natural
  evolutionary process.
• EAs are
• iterative (not constructive)
• nondeterministic
• approximate (not always optimal)
• not problem-specific

17
Evolutionary Algorithms
Initial Population
Initial Population

• Flow of EA

Evaluation
Evaluation
next generation
Mating selection
Mating selection
Reproduction
Reproduction
Evaluation
Evaluation
N
Stop?
Environmental selection
Environmental selection
Y
Final Population
18
Evolutionary Algorithms

• EA for optimization (an clustering example)

19
Evolutionary Algorithms
Initial Population
Evaluation
next generation
Mating selection
Reproduction
Evaluation
N
Stop?
Environmental selection
Y
Final Population
20
Mating Selection

• Roulette wheel selection
• Individuals are selected as parents in
  probability proportional to their fitness
  (solution quality).
• K-tournament selection
• K solutions are randomly selected, and the best
  one is taken as a parent.
• Random selection

21
Environmental Selection

• Generational policy
• The offspring replace the old population.
• Steady-state policy
• The offspring replaces the worst individual in
  the old population.
• n/2n policy
• The best n individuals among 2n individuals
  survive, where n is the population size.

22
Evolutionary Algorithms

• The selection mechanisms are general and
  applicable to almost all kinds of problems.
• For a specific problem, we need to
  determine/devise the solution encoding scheme and
  the associated crossover and mutation operators.

23
How can We Generate a Good Dispatching Rule?
24
Rule Generation by EAs

• How can we represent a rule?

25
Rule Generation by EAs

• Chromosome encoding

Tay, J.C. and Ho, N.B. (2008) Evolving
dispatching rules using genetic programming for
solving multi-objective flexible job-shop
problems. Computers Industrial Engineering
54453-473.
26
Rule Generation by EAs

• Crossover exchanging subtrees (sub-expressions)

2(ab)/e
eb2
2eb/e
ab2
Geiger, C.D., Uzsoy, R., and Aytug, H. (2006)
Rapid modeling and discovery of priority
dispatching rules An autonomous learning
approach. Journal of Scheduling 97-34.
27
Rule Generation by EAs

• Mutation replacing with a randomly generated
  subtree

Geiger, C.D., Uzsoy, R., and Aytug, H. (2006)
Rapid modeling and discovery of priority
dispatching rules An autonomous learning
approach. Journal of Scheduling 97-34.
28
Rule Generation by EAs

• Evaluation
• Run a simulator for a sufficiently long
  simulation time under the control of the rule to
  be evaluated.
• deterministic parts routes, machines, processing
  times, setup times.
• stochastic parts order arrivals, machine
  breakdowns
• Record the concerned objective value(s) over
  multiple runs.

29
Rule Generation by EAs

• References
• Geiger, C.D., Uzsoy, R., and Aytug, H. (2006)
  Rapid modeling and discovery of priority
  dispatching rules An autonomous learning
  approach. Journal of Scheduling 97-34.
• Geiger, C.D. and Uzsoy, R. (2008) Learning
  effective dispatching rules for batch processor
  scheduling. International Journal of Production
  Research 46(6)1431-1454.
• Tay, J.C. and Ho, N.B. (2008) Evolving
  dispatching rules using genetic programming for
  solving multi-objective flexible job-shop
  problems. Computers Industrial Engineering
  54453-473.
• None of them was applied to wafer fab scheduling.

30
How can We Optimize the Parameters of Rules?
31
Rule Optimization by EAs (I)

• Advanced dispatching rules usually have
  parameters.
• e.g. ATCSR rule (Pfund et al. 2008)
• Tuning of parameters manually is laboring.

32
Rule Optimization by EAs (I)

• Chromosome encoding

k1
k2
k3
33
Rule Optimization by EAs (I)

• Simple k-point crossover

34
Rule Optimization by EAs (I)

• Arithmetic crossover

5
2
1
3
8
w 0.4
10
1
2
5
7
y1? w?x1 (1 w)?x2 y2? (1 w)?x1 w?x2
e.g.
35
Rule Optimization by EAs (I)

• Crossover by differential evolution (DE)

There are many DE variants (DE/x/y/z) x best or
random y number of difference vectors z bin or
exp
36
Rule Optimization by EAs (I)

• Mutation
• Set a new random value within the valid range.
• Increase/decrease by a random value (e.g.
  generated by a Gaussian distribution).

37
Rule Optimization by EAs (II)

• The dispatching rule might not always assign
  correct priorities to all jobs.
• Sometimes we may need to adjust the job
  priorities manually.
• We can set priority levels to jobs. Only jobs
  with of same level are ranked by dispatching
  rules.

1st-priority queue
2nd-priority queue
38
Rule Optimization by EAs (II)

• Chromosome encoding (II)
• assume 3 jobs, each with 3 operations

Job-based
J2
J3
J1
1
1
2
Operation-based
O12
O13
O22
O23
O32
O33
O11
O21
O31
1
1
1
2
1
2
1
2
1
39
Rule Optimization by EAs (II)

• A variety of crossover and mutation operators are
  applicable.

Job-based
J2
J3
J1
1
1
2
Operation-based
O12
O13
O22
O23
O32
O33
O11
O21
O31
1
1
1
2
1
2
1
2
1
40
Rule Optimization by EAs (II)

• References
• Chiang, T.C. and Fu, L.C. (2004) Parameter tuning
  of production scheduling rules by an ant
  system-embedded genetic algorithm. In Proceedings
  of IEEE International Conference on Robotics,
  Automation, and Mechatronics, pp. 1089 1094.
• Chiang, T.C. and Fu, L.C. (2008) A rule-centric
  memetic algorithm to minimize the number of tardy
  jobs in the job shop. International Journal of
  Production Research. 46(24)6913-6931.

41
Can We Combine Different Dispatching Rules?
42
Rule Combination by EAs

• A simple way to generate a new rule is to combine
  existing rules.
• We can combine them in two ways
• apply one rule at time in a predefined order
• aggregate the priorities obtained by rules into a
  single priority value

43
Rule Combination by EAs

• Chromosome encoding (I)
• Assume there are six rules.
• If there are more than one job with the same
  priority value by rule 2, apply rule 1. If rule 1
  still cannot distinguish them, apply rule 4.
  Repeat until the single best job is identified or
  all rules are applied.

2
1
4
6
3
5
44
Rule Combination by EAs

• Chromosome encoding (I)
• A more advanced way of applying rules
  hierarchically.

Rule 2
Rule 1
the first half jobs based on priority values by
rule 2
45
Rule Combination by EAs

• Chromosome encoding (II)
• Assume there are 4 rules.
• The aggregated priority value is0.2?pri(FIFO)
  0.3?pri(SPT) 0.4?pri(EDD) 0.1?pri(ATCSR)

FIFO SPT EDD ATCSR
0.2
0.3
0.4
0.1
46
Rule Combination by EAs

• Chromosome encoding (II)
• Since ranges of priority values by different
  rules may be different, we usually need to
  normalize them into the same range.

SPT ATCSR
120 30 20 60 0.008 0.03
0.04 0.01
47
Rule Combination by EAs

• Chromosome encoding (III)
• Assume there are 4 rules.
• Rules are applied hierarchically. Meanwhile, the
  weighted priority values are accumulated.

2
0.3
4
0.2
3
0.4
1
0.1
rule index
rule weight
48
Rule Combination by EAs

• Chromosome encoding (III)

Rule 2
? 0.3
Rule 2

Rule 4
? 0.2
49
Rule Combination by EAs

• To my best knowledge, theres no study adopting
  encoding schemes (I) and (III).
• There are research opportunities.
• Encoding scheme (II) were already used with the
  idea to be described next.

50
Can We Assign Different Rules to Stages with
Different Characteristics?
51
Rule Selection by EAs

• Operations in different stages may have quite
  different characteristics.
• For stages where processing times of operations
  are almost equal, the SPT rule is useless.
• For stages where setup times are long, saving the
  number of setups could be the best policy.

S1
S2
S3
S4
52
Rule Selection by EAs

• Many studies have shown that setting different
  rules to stages could achieve better performance
  than setting an identical rule.
• Miragliotta and Perona (2005). Decentralised,
  multi-objective driven scheduling for reentrant
  shops A conceptual development and a test case
  European Journal of Operational Research
  167644-662.
• Wu et al. (2008) Dispatching for make-to-order
  wafer fabs with machine-dedication and mask
  set-up chracteristics. International Journal of
  Production Research 46(14)3993-4009.
• Most of them set rules based on expert
  experience.

53
Rule Selection by EAs

• Chromosome encoding (I)
• Assume there are five stages.

S2
S3
S5
S1
S4
1 FIFO 2 SPT 3 EDD 4 ATCSR
1
1
4
3
2
S5
S1
S2
S3
S4
54
Rule Selection by EAs

• References (I)
• Herrmann, J.W., Lee, C.Y., and Hinchman, J.
  (1995) Global job shop scheduling with a genetic
  algorithm. Production Operations Management
  4(1)30-45.
• Chen, J.H., Fu, L.C., Lin, M.H., Huang, A.C.
  (2001) Petri-net and GA-based approach to
  modeling, scheduling, and performance evaluation
  for wafer fabrication. IEEE Transactions on
  Robotics and Automation 17(5)619-636.
• Yang, T., Kuo, Y., and Cho, C. (2007) A genetic
  algorithms simulation approach for the
  multi-attribute combinatorial dispatching
  decision problem. European Journal of Operational
  Research 1761859-1873.

55
Rule Selection by EAs

• Chromosome encoding (II)
• Rule selection rule combination
• Assume there are three stages and four rules.

S2
S3
S1
0.5
0.1
0.2
0.3
0.2
0.2
0.3
0.3
0.4
0.3
0.3
0
FIFO SPT EDD ATCSR
56
Rule Selection by EAs

• References (II)
• Chiang, T.C. and Fu, L.C. (2006) Multiobjective
  job shop scheduling using genetic algorithm with
  cyclic fitness assignment. In Proceedings of IEEE
  Congress on Evolutionary Computation, pp. 11035
  11042.
• Chiang, T.C., Shen, Y.S., and Fu, L.C. (2008) A
  new paradigm for rule-based scheduling in the
  wafer probe center. International Journal of
  Production Research, 46(15)4111-4133.

57
Rule Selection by EAs

• In addition to machine-wise combination of rules,
  many researchers proposed state-dependent
  combination of rules.
• Chen et al. (2004) Dynamic state-dependent
  dispatching for wafer fabrication. International
  Journal of Production Research 42(21)4547-4562.
• Lee et al. (2009) Multi-objective scheduling and
  real-time dispatching for the semiconductor
  manufacturing system. Computers Operations
  Research 36866-884.

58
Rule Selection by EAs

• EAs can also help to determine the
  state-dependent combination of rules.
• As far as I know, the only one related work is
• Liu and Wu (2004) Genetic algorithm using
  sequence rule chain for multi-objective
  optimization in re-entrant micro-electronic
  production line. Robotics and Computer-Integrated
  Manufacturing 20225-236.

59
Which Stages are More Important than Others?
60
Model Understanding/Simplification by EAs

• In the wafer fab, stages with higher machine
  utilization and longer queueing time are usually
  more important to scheduling.
• Identifying these critical stages can help us to
  focus on rule design for these stages.
• Meanwhile, identifying non-critical stages can
  reduce the size of model and save simulation time.

61
Model Understanding/Simplification by EAs

• In the literature, the critical stages were
  identified by heuristics.
• Kim, Y. D., Shim, S. O., Choi, B., and Hwang, H.
  (2003) Simplification methods for accelerating
  simulation-based real-time scheduling in a
  semiconductor wafer fabrication facility. IEEE
  Transactions on Semiconductor Manufacturing,
  16(2)290298.
• Piplani, R. and Puah, S. A. (2004) Simplification
  strategies for simulation models of semiconductor
  facilities. Journal of Manufacturing Technology
  Management, 15(7)618625.
• Johnson, R. T., Fowler, J. W., and Mackulak, G.
  T. (2005) A discrete event simulation model
  simplification technique. In Proceedings of the
  2005 Winter Simulation Conference, pages
  2172?2176.

62
Model Understanding/Simplification by EAs

• Chromosome encoding
• Assume there are 2 routes, with 4 and 5 stages,
  respectively.

S11 S12 S13 S14 S21 S22
S23 S24 S25
0
1
1
0
0
0
1
0
0
S11
S12
S13
S14
63
Model Understanding/Simplification by EAs

• Evaluation
• Run the simulator on the reduced model.
• The reduced stages are usually replaced by
  constant delays.
• In other words, they are treated as stages with
  infinite machines.
• Record the deviation of concerned measures from
  those obtained by simulating on the original
  (complete) model.

64
Model Understanding/Simplification by EAs

• References
• Chiang, T.C. (2010) Model simplification for
  accelerating simulation-based evaluation of
  dispatching rules in wafer fabrication
  facilities, to appear in Proceedings of the 11th
  International Conference on Control, Automation,
  Robotics, and Vision.

65
What If Dispatching Rules Are Not Good Enough?
66
Single Stage Scheduling by EAs

• Rule-based scheduling is computationally
  efficient and its performance is acceptable.
• Sometimes acceptable is not enough.
• We can apply the EA to optimize the schedule of a
  small-scale subsystem, for example, a single
  stage.

S11
S12
S13
S14
67
Single Stage Scheduling by EAs

• Chromosome encoding
• Assume there are two jobs, each visiting the
  target stage for three times.
• Assume there are four machines.

J1
M2
J2
M1
J2
M3
J1
M4
J1
M2
J2
M1
68
Single Stage Scheduling by EAs

• Crossover

J1
M2
J2
M1
J2
M3
J1
M4
J1
M2
J2
M1
J1
M1
J1
M1
J2
M2
J2
M2
J1
M4
J2
M3
J1
M2
J1
M2
J2
M1
69
Single Stage Scheduling by EAs

• Mutation
• Changing the operation sequence by insertion or
  swap.
• Changing the machine assignment by random
  assignment or swap.

J1
M2
J2
M1
J2
M3
J1
M4
J1
M2
J2
M1
M3
70
Single Stage Scheduling by EAs

• There have been a lot of literature on parallel
  (batch) machine scheduling.
• Horng, S.M, Fowler, J.W., and Cochran, J.K.
  (2000) A genetic algorithm approach to manage ion
  implantation in wafer fabrication. International
  Journal of Manufacturing Technology and
  Management 1(2/3)156-172.
• Qu, P. and Mason, S.J. (2005) Metaheuristic
  scheduling of 300-mm lots containing multiple
  orders. IEEE Transactions on Semiconductor
  Manufacturing 18(4)633-643.
• Chiang, T.C., Cheng, H.C., and Fu, L.C. (2010)
  Minimizing total weighted tardiness on parallel
  batch machines with incompatible job families and
  dynamic job arrival. Computers Operations
  Research 37(12)2257-2269.

71
Single Stage Scheduling by EAs

• However, none of them was evaluated in the
  stochastic wafer fab environment.
• The following study is close.
• Mönch, L, Schabacker, R., Pabst, D., and Fowler,
  J.W. (2007) Genetic algorithm-based subproblem
  solution procedures for a modified shifting
  bottleneck heuristic for complex job shops.
  European Journal of Operational Research
  1772100-2118.

72
Conclusions
73
Conclusions

• The EA can help wafer fab scheduling in many
  different ways.
• Generating good dispatching rules.
• Optimizing rule parameters.
• Combining rules through value aggregation or
  hierarchical invocation.
• Assigning suitable rules to different stages or
  states.
• Identifying critical stages.
• Scheduling a single stage optimally.

74
Conclusions

• For researchers in production scheduling, there
  are many research opportunities for applying EAs
  (or other metaheuristics) to fab scheduling.
• Only rule selection and machine-wise rule
  combination have been investigated.
• Other topics are not studied or not evaluated in
  the fab environment.

75
Conclusions

• For researchers in evolutionary computation, fab
  scheduling is a good application for these
  topics
• Multiobjective optimization
• Robust optimization
• Expensive optimization

76
Conclusions

• In this talk, we also demonstrated how EAs can
  solve problems with the following nature
• expression construction (rule generation)
• real-value optimization (parameter optimization)
• sequencing (single stage scheduling)
• selection, assignment, or clustering (rule
  selection)
• manipulation of domain heuristics (rule
  combination)
• You may resort EAs to solve your research problem.

77
Thank you very much
for your attention!