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Driver Scheduling Using Genetic Algorithms with Embedded Combinatorial Traits

  • Ann S. K. Kwan
  • Raymond S. K. Kwan
  • Anthony Wren
Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 471)

Abstract

The integer linear programming (ILP) based optimization approaches to driver scheduling have had most success. However there is scope for a Genetic Algorithm (GA) approach, which is described in this paper, to make improvements in terms of computational efficiency, robustness, and capability to tackle large data sets. The question “What makes a good fit amongst potential shifts in forming a schedule?” is pursued to identify combinatorial traits associated with the data set. Such combinatorial traits are embedded into the genetic structure, so that they would play some role in the evolutionary process. They could be effective in narrowing down the solution space and they could assist in evaluating the fitness of individuals in the population.

The first stage of research uses as a starting point the continuous solution resulting from relaxing the integer requirement of an ILP model for driver scheduling. The continuous solution consists of a relatively small set of shifts, which usually contains a high proportion of the shifts in the integer solution obtained. The aim is to derive a GA to evolve from the non-integer solution to yield some elite schedules for further exploitation of combinatorial traits. This first stage is already very effective, yielding in some test cases schedules as good as those found by ILP.

The second stage of research is still ongoing. The aim is to extract from the fittest individuals in the population various forms of combinatorial traits. The genetic structures are then dynamically transformed to make use of the traits in future generations.

Keywords

Integer Linear Programming Work Piece Continuous Solution Integer Solution Prefer Shift 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Beasley, J.E./Chu, P.C. (1996): A genetic algorithm for the set covering problem, in: European J.O.R., 94, 392 – 404.Google Scholar
  2. Davis, L. (1991): Handbook of genetic algorithms. (Van Nostrand Reinhold).Google Scholar
  3. Fores, S./Proll, L./Wren, A. (1997): An improved ILP system for driver scheduling. in: Preprints of the 7th International workshop on computer-aided scheduling of public transport, Boston, US.Google Scholar
  4. Goldberg, D.E. (1989): Genetic algorithms in search, optimization and machine learning. (Addison-Wesley).Google Scholar
  5. Hernandez, L.F.G./Corne, D.W. (1996): Evolutionary divide and conquer of the set covering problem. in: T.C. Fogarty (ed.): Evolutionary Computing, (Springer) 198–208.CrossRefGoogle Scholar
  6. Kwan, A.S.K./Kwan, R.S.K./Parker, M.E./Wren, A. (1997): Producing train driver schedules under different operating strategies. in: Preprints of the 7th International workshop on computer-aided scheduling of public transport, Boston, US.Google Scholar
  7. Michalewicz, Z. (1994): Genetic algorithms + data structures = evolution programs. Second, extended edition. (Springer-Verlag).Google Scholar
  8. Ryan, D.M. (1980): ZIP — a zero-one integer programming package for scheduling, Computer Science and Systems Division, Atomic Energy Research Establishment, Harwell, Oxfordshire.Google Scholar
  9. Wren, A./Rousseau, J.-M. (1995): Bus driver scheduling — An overview. in: J.R. Daduna /I. Branco/J.M.P. Paixao (editors) Computer-aided transit scheduling. (Springer-Verlag) 173 – 187.CrossRefGoogle Scholar
  10. Wren, A./Wren, D.O. (1995): A genetic algorithm for public transport driver scheduling. in: Computers Ops Res, 22, 101 – 110.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Ann S. K. Kwan
    • 1
  • Raymond S. K. Kwan
    • 1
  • Anthony Wren
    • 1
  1. 1.Scheduling and Constraint Management Group, School of Computer StudiesUniversity of LeedsLeedsUK

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