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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 School of Computer Science University of Birmingham

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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

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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.

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4 A typical Job Shop Problem Objectives Minimization of make span Minimization of cost Minimization of delays 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

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5 A 3 job 3 machine problem J1M1M2M3 J2M1M3M2 J3M3M2M1 Machining Sequence Jobs Operations Processing time Jobs Operations J1653 J2434 J31052

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6 Why Nature Inspired Algorithms 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. GA’s vs Other methods

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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.

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8 Schedule Builder!! What’s That J1M1M2M3 J2M1M3M2 J3M3M2M1 J1653 J2434 J31052

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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)

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

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11 Job 1 M1 M3 M2 Job 2 M2 M3 M1 Job 3 M2 M1 M3 Job1 & Job1 & Job2 & (b) Binary Representation (a) Machine Sequence M/c 1 J1 J3 J2 M/c 2 J3 J2 J1 M/c 3 J1 J2 J3 (c) Symbolic Representation

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

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13 2. Job Based Representation Typical chromosome [ J i J j J k ] For [ J 2 J 1 J 3 ] All operations of job 2 folllowed by 1 and then by 3 are scheduled in the available processing times.

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

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15 3. Permutation Representation (Partitioned) Chromosome is set of permutation of jobs on each machine. M1 M2 M Cross Over (SXX) Subsequence Exchange Crossover Searches for exchangeable subsequence pairs in parents, and swaps them. Job sequence matrix for 3 X 3 problem

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16 Subsequence Exchange Crossover M1 M2 M3 P P C C

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

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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

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

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20 Merits 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

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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, ….. ]

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

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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

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24 Basic Scenario OperationTime (min) Leave Shop 24hrs Leave Shop 24 hrs 10 60

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

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26 Start with heuristics 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. Select a set of jobs out of 17 to process first. (random)

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