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School of Computer Science

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Presentation on theme: "School of Computer Science"— Presentation transcript:

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 That
J1 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 3 180
90 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.


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