We introduced the probability of existence of an activity and used it to represent that an activity in the original problem definition does not necessarily have to execute in a solution
Scheduling Alternative Activities
National Conference on Artificial Intelligence, pp.680-687, (1999)
In realistic scheduling problems, there may be choices among resources or among process plans. We formulate a constraint-based representation of alternative activities to model problems containing such choices. We extend existing constraint-directed scheduling heuristic commitment tech- niques and propagators to reason directly about the ...更多
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- Scheduling problems addressed in the constraint-directed scheduling literature typically have a static activity definition: each activity must be scheduled on its specified resource(s).
- It is common, in real-world scheduling problems to have a wider space of choices.
- For it is sufficient to understand that they represent alternative paths in the activity network and, in a final solution, only one of the alternative paths can be present.
- Part of the scheduling problem, is to decide if A2, A3, and A4 will execute, or if A6 and A7 will execute
- Scheduling problems addressed in the constraint-directed scheduling literature typically have a static activity definition: each activity must be scheduled on its specified resource(s)
- Because the CBA propagator cannot be used when one or both members of an activity pair have a probability of existence value of less than 1 (Beck, 1999), the CBASlackPEX heuristic calculates the biased-slack on such activity pairs even if their time windows do not overlap
- We introduced the probability of existence (PEX) of an activity and used it to represent that an activity in the original problem definition does not necessarily have to execute in a solution
- Experimental results indicate that incorporating probability of existence values into the texture-based heuristics results in significantly higher quality commitments and better overall search performance
- Performance differences are especially large when there is a wide range of probability of existence values in a problem
- A key contribution of this work is the applicability of our representation of alternative activities to a wide variety of real-world scheduling problems
- PEX values into the texture-based heuristics results in significantly higher quality commitments and better overall search performance.
- Performance differences are especially large when there is a wide range of PEX values in a problem.
- Experimental results validate the use of PEX-edgefinding which, in most cases, leads to significantly better overall search performance.
- The authors have introduced a mechanism to explicitly reason about choosing not to take certain actions in order to achieve an overall goal
- Such reasoning has relevance in many areas of artificial intelligence.
- The experiments present interesting and conflicting results. While SumHeightPEX outperforms CBASlackPEX with PEX-edge-finding, their relative performance without PEXedge-finding is inconsistent: little difference is observed in Experiment 1, while, in Experiment 2, SumHeightPEX is significantly better.
- Recall that in the original CBASlack heuristic, the most critical activity pair is one that is not already sequenced and that has the smallest biased-slack.
- Because the CBA propagator cannot be used when one or both members of an activity pair have a PEX value of less than 1 (Beck, 1999), the CBASlackPEX heuristic calculates the biased-slack on such activity pairs even if their time windows do not overlap.
- Heuristic commitment techniques and two edge-finding propagators were extended to account for PEX values
- Table1: PEX Values for a Subset of the Nodes in Figure 2
- Table2: The Six Algorithms Used in the Experiments
- Table3: The Characteristics of the Problems in Experiment 1
- Table4: The Distribution of Alternative Resources for the Problems in Experiment 2
- It was funded in part by the Natural Sciences Engineering and Research Council, IRIS Research Network, Manufacturing Research Corporation of Ontario, Baan Limited, and Digital Equipment of Canada. Thanks to Andrew Davenport and Angela Glover for discussion of and comments on previous versions of this paper
- Baptiste, P. and Le Pape, C. (1995). Disjunctive constraints for manufacturing scheduling: Principles and extensions. In Proceedings of the Third International Conference on Computer Integrated Manufacturing.
- Baptiste, P. and Le Pape, C. (1996). Edge-finding constraint propagation algorithms for disjunctive and cumulative scheduling. In Proceedings of the 15th Workshop of the UK Planning and Scheduling Special Interest Group. Available from http://www.hds.utc.fr/baptiste/.
- Beck, J. C. (1999). Texture measurements as a basis for heuristic commitment techniques in constraint-directed scheduling. PhD thesis, University of Toronto. Forthcoming.
- Beck, J. C., Davenport, A. J., Sitarski, E. M., and Fox, M. S. (1997a). Beyond contention: extending texture-based scheduling heuristics. In Proceedings of AAAI-97. AAAI Press, Menlo Park, California.
- Beck, J. C., Davenport, A. J., Sitarski, E. M., and Fox, M. S. (1997b). Texture-based heuristics for scheduling revisited. In Proceedings of AAAI-97. AAAI Press, Menlo Park, California.
- Carnegie Group Inc. (1994). Knowledge-based logistics planning system. Internal Documentation.
- Cheng, C. C. and Smith, S. F. (1997). Applying constraint satisfaction techniques to job shop scheduling. Annals of Operations Research, Special Volume on Scheduling: Theory and Practice, 70:327–378. Forthcoming.
- Cohen, P. R. (1995). Empirical Methods for Artificial Intelligence. The MIT Press, Cambridge, Mass.
- Davenport, A. J., Beck, J. C., and Fox, M. S. (1999). An investigation into two approaches for resource allocation and scheduling. Technical report, Enterprise Integration Laboratory, Department of Mechanical and Industrial Engineering, University of Toronto.
- Fox, M. (1986). Observations on the role of constraints in problem solving. In Proceedings of the Sixth Canadian Conference on Artificial Intelligence.
- Fox, M. S. (1983). Constraint-Directed Search: A Case Study of Job-Shop Scheduling. PhD thesis, Carnegie Mellon University, Intelligent Systems Laboratory, The Robotics Institute, Pittsburgh, PA. CMU-RI-TR-85-7.
- Kott, A. and Saks, V. (1998). A multi-decompositional approach to integration of planning and scheduling – an applied perspective. In Proceedings of the Workshop on Integrating Planning, Scheduling and Execution in Dynamic and Uncertain Environments, Pittsburgh, USA.
- Le Pape, C. (1994). Using a constraint-based scheduling library to solve a specific scheduling problem. In Proceedings of the AAAISIGMAN Workshop on Artificial Intelligence Approaches to Modelling and Scheduling Manufacturing Processes.
- Nuijten, W. P. M. (1994). Time and resource constrained scheduling: a constraint satisfaction approach. PhD thesis, Department of Mathematics and Computing Science, Eindhoven University of Technology.
- Saks, V., Johnson, I., and Fox, M. (1993). Distribution planning: A constrained heuristic search approach. In Proceedings of the Knowledge-based System and Robotics Workshop, pages 13–19. Industry Canada.
- Smith, S. F. and Cheng, C. C. (1993). Slack-based heuristics for constraint satisfaction scheduling. In Proceedings AAAI-93, pages 139–144.