P. Pongcharoen, D.J. Stewardson, C. Hicks and P.M. Braiden. University of Newcastle upon Tyne

1. Applying Designed Experiments to Optimise the Performance of Genetic Algorithmsfor 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!)msequences, e.g. n=5 m=3 => 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

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(Ec+Ep) +  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 = £106,975+1,471.5(COP)-1,561.8(MOP)-1,256.3(%M)-943(%C*P/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 questionsPlease