The goal of this research is to find a methodology that is designed to fit the need of a semiconductor equipment scheduler. As a result of the experiments, we found that the proposed method has very good performance for scheduling job numbers range between 3 and 10. It is capable of finding the global optimum quickly and efficiently. It has a better success rate than the original PSO in tested cases.
As the job count gets bigger, the method that uses pre-calculated permutations starts to show its limitation. The resources required for storing the permutations increase exponentially and may be impossible to store all possible permutations.
Using runtime-calculated permutations will help relief the problem with slightly decreased performance.
There are lots of differences between one-dimensional PSO and the original PSO in terms of the behavior and performance. Performance-wise, one-dimensional PSO has advantage over original PSO as it uses only simple calculation to create the permutation, while original PSO requires a sorting mechanism, which is
computationally expensive to sort the rankings of each job in order to create the permutation. Furthermore, the time for calculating the schedule increases dramatically as job count grows.
The behaviors of the methods are also very different. By looking at the converging trend, it looks as if original PSO is converging quickly and much faster than the method proposed. However, the true meaning is that, using proposed method, we are able to search the search space more thoroughly as the search space has been reduced to a finite discrete space without duplicated permutations. This enables us to find more local optimums. In other words, it is more likely to find the global optimum. Each method has its advantage and is up to the user to choose between possibilities of finding global optimum or shorter converging time.
There are a few areas that we can further study. The method that we used to generate permutations is not the only method. We believe that there are other methods for creating the permutation set. We may be able to find a better function for constructing a search space with smoother fitness distribution line and resulting in better search results. We believe that optimizing the particle initializations and
It is obvious that the one-dimensional PSO is suitable for combinatorial problems. Since we have converted the search space to a one-dimensional search space, we may be able to apply one-dimensional optimization methodologies to solve the scheduling problem more efficiently. These are works that we believe to be worth further exploration.
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Appendix A: Job Sets Used for Experiments
7 Jobs case:
10 Jobs case:
Step Job
Number 1 2 3
1 40 90 74 2 71 3 43 3 98 80 69 4 28 36 43 5 64 35 11 6 43 95 54 7 22 38 40
8 15 552 96
9 65 44 69 10 70 50 16
Appendix B: 9 Jobs Search Results
Fitness Fitness Fitness Fitness Fitness Run
Fitness Fitness Fitness Fitness Fitness
Appendix C: 8 Jobs Converge Trend Data
Run
Vita
Education
2005-2007 M.S. in Computer Science College of Computer Science,
National Chiao Tung University, Hsinchu, Taiwan
1995-1997 B.S. in Electrical Engineering
Department of Electrical and Engineering,
National Taiwan Institute of Technology, Taipei, Taiwan
Work Experiences
2003-Present Engineering Manager
Systematic Designs Int. (SDI)/Facet Technology, Hsinchu, Taiwan
1997-2003 CIM (Computer Integrated Manufacturing) Engineer Systematic Designs Int. (SDI), Vancouver, WA, USA
1993-1994 Customer Support Engineer
Chien Kung Computer Co., Kaohsiung, Taiwan