1. School of Computer Science
University of Birmingham
Application of Nature Inspired Genetic Algorithms For Job Shop Scheduling
Bhuvan Sharma
Research Associate
Advanced Computation in Design and Decision Making Group
University West of England, Bristol, UK

2. Aim of Presentation Understanding job shop scheduling
Why Nature Inspired Algorithms
Issues in GA, when applied to job shop problems
Review of various approaches within GA
Practical Problem from Rolls Royce
My approach

3. Job Shop Scheduling Job : A piece of work that goes through series of
operations.
Shop : A place for manufacturing or repairing of
goods or machinery.
Scheduling : Decision process aiming to deduce the
order of processing.

4. A typical Job Shop Problem
Parameters
Number of jobs
Number of operations within each job
Processing time of each operation within each job
Machining sequence of operations within each job
Objectives
Minimization of make span
Minimization of cost
Minimization of delays

5. A 3 job 3 machine problem Processing time Jobs Operations
Machining Sequence
Jobs Operations J1 6 5 3 J2 4 J3 10 2 J1 M1 M2 M3 J2 J3

6. Why Nature Inspired Algorithms
GA’s vs Other methods
Evaluation on a set of points. Better search.
Better chances for global optimal solution.
Suitable for Multi-objective optimisation.
Flexibility, because constraints can be taken care of.
Evaluation on a point each time.
Often terminate into local optima.
Not suited for multi-objective optimisation.
Not flexible, driven by heuristics, constraints not handled easily.

7. Issues in Genetic Algorithms when applied to job shop problems
Representation of schedule(phenotype) by suitable
genotype.
Conversion of genotype to phenotype
Choice of Schedule Builder
Type of Crossover and Mutation to be used
Avoiding Premature convergence.

8. Schedule Builder!! What’s ThatJ1 M1 M2 M3 J2 J3 J1 6 5 3 J2 4 J3 10 2

9. Representation schemes for schedules in job shop
Conventional Binary representation
Job Based Representation
Permutation Representation (Partitioned)
Permutation Representation (Repetitive)
Priority Rule Based Representation (Random /
guided)

10. 1. Binary Representation
Genotype is binary matrix of
Rows = Number of job pairs
Columns = Number of machines
Interpretation
Mij = 0 / 1 depending on whether job1
is executed later or prior to job2.

11. Job M1 M M2
Job M2 M M1
Job M2 M M3
(a) Machine Sequence
Job1 &
Job1 &
Job2 &
(b) Binary Representation
M/c J1 J3 J2
M/c J3 J2 J1
M/c J1 J2 J3
(c) Symbolic Representation

12. Crossover Demerits The crossover applied is simple one point
Redundancy in representation.
2mj(j-1)/2 bits are required for (!j)m schedules.
Forcing techniques required for replacement of
illegal schedules.

13. 2. Job Based Representation
Typical chromosome [ Ji Jj Jk ]
For [ J2 J1 J3 ]
All operations of job 2 folllowed by 1 and then by 3 are scheduled in the available processing times.

14. Merits Demerits Scheduling is very easy
Always yields a feasible schedule, hence forcing
not required.
Demerits
Approach is very constrained
Not many possibilities are explored

15. 3. Permutation Representation (Partitioned)
Chromosome is set of permutation of jobs on
each machine.
M M M3
Job sequence matrix for 3 X 3 problem
Cross Over (SXX)
Subsequence Exchange Crossover
Searches for exchangeable subsequence pairs
in parents, and swaps them.

16. Subsequence Exchange Crossover
M M M3 P P C C

17. Merits Demerits GA operators used for TSP can be applied here
Simple representation
Demerits
Does not always give active schedules
Robust Schedule builder is required
SXX does not always guarantee a crossover

18. 4. Permutation Representation (Repetitive)
Also known as operation based representation
Typical genotype is a unpartitioned permutation
with m repetitions for each job. M M M

19. Crossover (PPX) Precedence Preservation Crossover (PPX)
The offspring inherits partial characteristic
of both parents P P C

20. Merits Demerits Very simple representation
All decoding leads to active schedules
Schedule building is straightforward
Crossover results in passing of characteristics from
both parents in most cases.
Demerits
Problem of Premature convergence
This is often case with long chromosomes

21. 5. Priority(Random/Guided)Rule Based Representation
Characteristics
Use of GT Algorithm, with one of priority rule
used in ith iteration to select ith operation
Priority rules could be assigned randomly, or
guided by heuristics.
Representation
[ SPT, LPT, MTPT, LTPT, MLFT, ….. ]

22. Crossover Merits Demerits Both PPX and SXX can be used
Always give feasible active schedules
Incorporates heuristics to an extent
Demerits
Problem of fast, premature convergence of
first few genes in the chromosome

23. Practical Problem from Rolls Royce
Parameters
17 batches of jobs
10 operations per job
4 identical machines, each can perform any
operation subject to tool set
Constraints
Only one tool-set for each operation
Opn. 2 must not begin until opn 1 is complete
Opn 3-9 can be performed in any sequence
Opn 10 should be the last for each batch of job

24. Basic Scenario Operation Time (min) 1 120 2 288 Leave Shop 24hrs 3 18090 5 6 7 60 8 9
24 hrs 10

25. My Approach Representation Crossover Permutation based
The catch here is that it is permutation of machines
not jobs
For eg. [ : | 10 ]
Crossover
Precedence Preservation Crossover (PPX)

26. Start with heuristics Schedule builder
Select a set of jobs out of 17 to process first. (random)
Schedule builder
Identify conflicting set of jobs
Selection of one from conflicting set based on
one of heuristic priority rules
Change toolset for machine as it finishes requisite
jobs. Change is guided by time factor.