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Applying Designed Experiments to Optimise the Performance of Genetic Algorithms for Scheduling Capit

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Title: Applying Designed Experiments to Optimise the Performance of Genetic Algorithms for Scheduling Capit


1
Applying Designed Experiments to Optimise the
Performance of Genetic Algorithms for Scheduling
Capital Products
P. Pongcharoen, D.J. Stewardson, C. Hicks and
P.M. Braiden. University of Newcastle upon Tyne
2
Scheduling
  • The allocation of resources over time to perform
    a collection of tasks (Baker 1974)
  • Scheduling problems in their static and
    deterministic forms are extremely simple to
    describe and formulate, but are difficult to
    solve (King and Spakis 1980)

3
Scheduling Problems
  • Involve complex combinatorial optimisation
  • For n jobs on m machines there are potentially
    (n!)m sequences, e.g. n5 m3 gt 1.7 million
    sequences.
  • Most problems can only be solved by inefficient
    non-deterministic polynomial (NP) algorithms.
  • Even a computer can take large amounts of time to
    solve only moderately large problems

4
Scheduling the Production of Capital Goods
  • Deep and complex product structures
  • Long routings with many types of operations on
    multiple machines
  • Multiple constraints such as assembly, operation
    precedence and resource constraints.

5
Product Structure
Feature 2 Products, 118 Machining, 17 Assembly
and 17 machines
6
(No Transcript)
7
Conventional Optimisation Algorithms
  • Integer Linear Programming
  • Dynamic Programming
  • Branch and Bound

These methods rely on enumerative search and are
therefore only suitable for small problems
8
More Recent Approaches
  • Simulated Annealing
  • Taboo Search
  • Genetic Algorithms
  • Characteristics
  • Stochastic search.
  • Suitable for combinatorial optimisation problems.
  • Due to combinatorial explosion, they may not
    search the whole problem space. Thus, an optimal
    solution is not guaranteed.

9
GA developed for production scheduling
10
Chromosome representation
11
Crossover Operations
12
Mutation Operations
13
Fitness function
Minimise ? Pe(EcEp) ? Pt(Tp) Where Ec
max (0, Dc - Fc) Ep max (0, Dp -
Fp) Tp max (0, Fp - Dp)
14
First Stage (Screening) Experiment
15
Analysis of Variance (Screening Experiment)
16
Relative performance of COP and MOP (Screening
Experiment)
17
Analysis of Variance (Second Stage Experiment)
18
Relative Performance of COP and MOP (Second Stage
Experiment)
19
Regression Analysis
Penalty cost 106,9751,471.5(COP)-1,561.8(MOP)-
1,256.3(M)-943(CP/G)
20
Interaction Diagram for P/G and COP
21
Conclusions
  • BCGA scheduling tool is influenced by a large
    number of factors.
  • The investigation of the best genetic operators
    and parameters requires an efficient experimental
    design to enable the work to be performed within
    a reasonable time.
  • The sequential strategy has been very effective
    in minimising the amount of time and
    computational resources

22
Conclusions (continue)
  • The screening experiment reduced number of
    crossover and mutation operators.
  • The second experiment showed that the choice of
    operators was statistically significant.
  • It also found that the low level of P/G
    combination produced the best results when used
    with the EERX crossover operator.
  • The different findings emerging from previous
    work suggests that appropriate GA operators and
    parameters may be case dependent.

23
Any questions Please
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