Iterative Flattening: A Scalable Method for Solving Multi-Capacity Scheduling Problems

Amedeo Cesta and Angelo Oddi, IP-CNR, National Research Council of Italy; Stephen F. Smith, Carnegie Mellon University

One challenge for research in constraint-based scheduling has been to produce scalable solution procedures under fairly general representational assumptions. Quite often, the computational burden of techniques for reasoning about more complex types of temporal and resource capacity constraints places fairly restrictive limits on the size of problems that can be effectively addressed. In this paper, we focus on developing a scalable heuristic procedure to an extended, multi-capacity resource version of the job shop scheduling problem (MCJSSP). Our starting point is a previously developed procedure for generating feasible solutions to more complex, multi-capacity scheduling problems with maximum time lags. Adapting the procedure to exploit the simpler temporal structure of MCJSSP, we are able to produce a quite efficient solution generator. However, the procedure only indirectly attends to MCJSSP’s objective criteria and produces sub-optimal solutions. To provide a scalable, optimizing procedure, we propose a simple, local-search procedure called {\em iterative flattening}, which utilizes the core solution generator to perform an extended iterative improvement search. Despite its simplicity, experimental analysis shows the iterative improvement search to be quite effective. On a set of reference problems ranging in size from 100 to 900 activities, the iterative flattening procedure efficiently and consistently produces solutions within 10\% of computed upper bounds. Overall, the concept of iterative flattening is quite general and provides an interesting new basis for designing more sophisticated local search procedures.

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