AMETIST Meeting December 12, 2003

1
AMETIST Meeting December 1-2, 2003



Role and Potential of TAs for Industrial
Scheduling Problems

Some Thoughts and Conjectures

Sebastian Engell
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Approaches to Scheduling Problems

• Exact Branch and Bound (MI(N)LP-Solvers, e.g.
  CPLEX)
• Equation-based models
• Exact lower bounds, optimality certificates
• High modelling effort, unintuitive
• Equivalent formulations lead to different
  behaviours of the solver
• High computing times for large problems
• Genetic Algorithms
• Can efficiently provide solutions to large and
  nonlinear problems
• Model can be algorithmic
• Highly constrained problems require tailored
  algorithms with heuristics
• Relative quality of the solution cannot be
  assessed
• Constraint Programming
• Efficient for highly constrained problems
• Intuitive models
• Not well suited for cost optimisation

3
Approaches to Scheduling Problems (2)

• Heuristic Branch and Bound
• can be much more effective than classical MILP
• problem class specific, tailored algorithms
• no optimality certificates
• Timed Automata
• universal modelling paradigm for many scheduling
  problems
• modular, graphical and intuitive
• uncertainty can be modelled easily (intervals for
  durations)
• powerful tools
• models become large for large problems
• classes of constraints
• optimality certificates
• performance

4
The Users View

• Realistic scheduling problems are too large to be
  solved to optimality by any single available
  general purpose method
• Combination of methods, e.g. TA with MILP-solvers
• Integration of heuristics in a transparent
  fashion
• Models need to be formulated and maintained
  modelling effort is a critical parameter for
  success in applications
• Timed automata are very promising in this respect
• Real problems contain uncertainties must be
  modelled
• Timed automata provide models with uncertain
  parameters
• More general uncertainties?
• Real problems are highly constrained
• Advantageous for TA-based solvers
• Classes of constraints that can be handled?

5
Conclusions and Further Work

• TA-based analysis is a relatively new technology
  compared e.g. to constraint programming and MILP
  solvers
• The assessment of its potential will require some
  time as well as the further improvement of the
  performance of the tools Thanks to the Case
  Study providers!
• Open issues
• Quick feasible solutions and risk assessment are
  more important than strict optimality!
• Solutions should be uncertainty-conscious best
  case, worst case, average performance, risk
  conscious
• Combinations of solution algorithms for improved
  range and performance