Application of Nature Inspired Genetic Algorithms For Job Shop Scheduling

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Application of Nature Inspired Genetic Algorithms
For Job Shop Scheduling
School of Computer Science University of
Birmingham

• Bhuvan Sharma
• Research Associate
• Advanced Computation in Design and Decision
  Making Group
• University West of England, Bristol, UK
• bhuvan.sharma_at_uwe.ac.uk

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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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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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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

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

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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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Schedule Builder!! Whats That
J1 M1 M2 M3
J2 M1 M3 M2
J3 M3 M2 M1
J1 6 5 3
J2 4 3 4
J3 10 5 2
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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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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.

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Job 1 M1 M3 M2 Job 2 M2 M3
M1 Job 3 M2 M1 M3
(a) Machine Sequence
Job1 2 1 1 0 Job1 3 1 1 0 Job2 3
0 1 0 (b) Binary Representation
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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Crossover

• The crossover applied is simple one point
• crossover.

Demerits

• Redundancy in representation.
• 2mj(j-1)/2 bits are required for (!j)m
  schedules.
• Forcing techniques required for replacement of
• illegal schedules.

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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.

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Demerits
Merits

• Scheduling is very easy
• Always yields a feasible schedule, hence forcing
• not required.

• Approach is very constrained
• Not many possibilities are explored

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3. Permutation Representation (Partitioned)

• Chromosome is set of permutation of jobs on
• each machine.

M1 M2
M3 1 3 2 3 2 1
3 1 2
Job sequence matrix for 3 X 3 problem
Cross Over (SXX)

• Subsequence Exchange Crossover
• Searches for exchangeable subsequence pairs
• in parents, and swaps them.

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Subsequence Exchange Crossover
M1 M2
M3 P0 1 2 3 6 4 5 3 2 1 5 6 4 2 3
5 6 1 4 P1 6 2 1 3 4 5 3 2 6 4 5 1 6
3 5 4 2 1 C0 2 1 3 4 6 5 3 2 5 1 6 4
2 6 3 5 1 4 C1 6 1 2 3 4 5 3 2 6 4
1 5 3 5 6 4 2 1
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Merits

• 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

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4. Permutation Representation (Repetitive)

• Also known as operation based representation
• Typical genotype is a unpartitioned permutation
• with m repetitions for each job.

1 2 2 3 1 3 2
1 3 M1 1
3 2 M2 2 3
1 M3 2 1
3
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Crossover (PPX)

• Precedence Preservation Crossover (PPX)
• The offspring inherits partial characteristic
• of both parents

P0 3 2 2 3 1 1 3 1 2
0 1 1 1 0 0 1 0 1 P1
2 3 3 2 1 3 1 1 2 C1 3 2
3 2 1 1 3 1 2
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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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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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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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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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Basic Scenario
Operation Time (min)
1 120
2 288
Leave Shop 24hrs
3 180
4 90
5 288
6 120
7 60
8 60
9 90
Leave Shop 24 hrs
10 60
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My Approach
Representation

• Permutation based
• The catch here is that it is permutation of
  machines
• not jobs
• For eg. 3 5 9 6 7 4 8 10

Crossover

• Precedence Preservation Crossover (PPX)

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Start with heuristics
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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