Download An Amended Genetic Algorithm for Job Scheduling on Parallel

A Genetic Algorithm with Sub-Indexed Partitioning
Genes and its Application to Production Scheduling of
Parallel Machines
Chichang Jou
Department of Information Management,
Tamkang University
Motivation and Objectives
 Goal of Production Scheduling

To seek optimal combination of short
manufacturing time, stable inventory, balanced
human and machine utilization rate, and short
average customer waiting time
 Motivation


Scheduling requirement from an electronics factory
Investigation of scheduling algorithms
 Objectives
A solution based on genetic algorithms
 A new approach in solving production scheduling of
parallel machines
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Background and Scope
 Scheduling Classification




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Products: single products / multiple products
Orders: make-to-stock / build-to-order
Production: job shop / flow shop
Stages: single stage / multiple stage
Machines: single machine / multiple machine
 Scope

multiple products, build-to-order, job shop, multiple
stage, multiple machine (parallel)
 A NP-hard problem
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Related Work
 Traditional Optimization


Time consuming and easily trapped in local optimum
Not applicable to real production
 Heuristic rules




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SPT (shortest processing time)
EDD (earliest due date)
SLK (least slack time)
Advantages:good speed and easy to understand
Disadvantages: hard to find acceptable solutions in some
cases
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Related Work
 Approximation Algorithms


Simulated Annealing, Hill Climbing, Tabu Search, Genetic
Algorithms, etc.
All of them are




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Probability based
Having a fitness function to evaluate the effectiveness of a solution
Gradually approaching the optimal solution step by step
Having a method to jump off local optimum
Advantages of Genetic Algorithms

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Evolution mechanism ----- crossover, mutation, reproduction
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Our Differences
 Close to real production


Adjustable beginning date, due date, earliness cost, tardiness
cost
Introducing machine setup cost, machine idleness cost into
fitness function
 New chromosome design for complete solution space
 Modification of the algorithm

bounce, select
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Working Environment of
the Electronics Plant
 Products: power supplies, motherboards, and barebones
 Supported with an MRP system
 Jobs need to flow through workstations of SMT, DIP, and
PCG machines, with 4, 3, and 3 parallel assembly lines
respectively
 Production plan has been continuously interrupted by
cancelled orders or new higher priority jobs
 Manual scheduling had to be performed based on previous
experiences
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Expected Workflow of
Production Jobs
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Introduction to Genetic Algorithms
 chromosome
 gene
 flow chart
 search space
Fitness value
Search space
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Design of Chromosome
 Suppose there are n jobs to be assigned to m
machines. A chromosome is modeled by a sequence
of the following n+m-1 distinct genes:
 Example:




Chromosome: 1 2 *2 3 *1 4 5
Jobs 1, 2 are assigned to machine 1
Jobs 3 are assigned to machine 2
Jobs 4, 5 are assigned machine 3
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Fitness Functions
 Fitness Function
For each schedule s
F (Cs , d s ,U s , Rs ) 

[ i ( Esi )   i (Tsi )]  U s  Rs
i
Esi (Csi , d i )  max( 0, Lsi )
Tsi (Csi , di )  max( 0, Lsi )
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Initial Solutions
 Example:
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Evolution Mechanisms
 Crossover
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Evolution Mechanisms
 Mutation:
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Evolution Mechanisms
 Reproduction:
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Just copy the chromosome of the parent to its next
generation
Ensure no worse next generation
Good results may be generated by crossover between
different generations
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System Implementation
Main User Interface:
A. Job table
C. Performance indicators
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B. Result schedule
D. Related supporting functions
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Experimental Parameters
job
priority
earliness cost
function
low
 i ( E si )  2
medium
high
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tardiness cost
function
 i (Tsi )  5
i ( Esi )  2 Esi  2
i (Tsi )  5Tsi  5
i (Esi )  2 Esi2  2 Esi  2
i (Tsi)  5Tsi2 5Tsi 5
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Experimental Results
 Cross comparison of our results using our fitness
function with those with Cheng’s fitness function
Using Our Fitness Function
allocating genes
distinguishable
identical
1.000
1.004
2.02%
1.91%
best fitness function value
119
120
worst fitness function value
127
127
ratio of average fitness function
value
(standard deviation)/ average
fitness function value
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Experimental Results
Using Cheng’s Fitness Function
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allocating genes
distinguishable
identical
ratio of average fitness
function value
1.000
1.049
(standard deviation) / average
fitness function value
5.39%
6.46%
best fitness function value
120
121
worst fitness function value
137
151
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Experimental Results
 Comparison of Fitness Functions
whether consider
machine setup and
idleness costs
total processing
time
total tardiness
time
total idleness
time
No
311.810
10.700
27.810
Yes
307.200
10.410
23.220
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Experimental Results
 Two additional steps:
 selection
selection of good chromosomes
 ranking
 probabilistic choice


bounce
detection of premature convergence
 bounce

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Experimental Results
Modified Algorithm:
initial
select chromosomes
with ordered probability
mutation
crossover
reproduction
rank fitness function values
reach max.
generation?
bounce the
best solution
yes
no
no
premature
convergence?
yes
record the best solution
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Experimental Results
 Effects of the two additional steps:
normal
genetic
algorithm
add
selection
step
add
bounce
step
add
selection,
bounce
steps
average fitness function
value
1.12
1.03
1.04
1.00
standard deviation of
fitness function values
21.18
5.07
2.55
2.11
(standard deviation) /
average fitness function
value
15.33%
4.02%
2.00%
1.71%
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Conclusions
 Our Characteristics

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Closer to the optimal solution than other genetic
algorithms
Small deviation of solutions in each run
More suitable for real production with realistic
considerations
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Future Research Topics
 Defining new modules of genetic algorithms
 Improving the structure of the genetic algorithms
 Other application of genetic algorithms
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