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CMU-CS-05-162
Computer Science Department
School of Computer Science, Carnegie Mellon University
CMU-CS-05-162
How the Landscape of Random Job Shop Scheduling Instances
Depends on the Ratio of Jobs to Machines
Matthew J. Streeter, Stephen F. Smith
August 2005
CMU-CS-05-162.ps
CMU-CS-05-162.pdf
Keywords: Job shop scheduling, big valley, easy-hard-easy pattern
We characterize the search landscape of random instances of the job
shop scheduling problem (JSSP). Specifically, we investigate how
the expected values of (1) backbone size, (2) distance between
near-optimal schedules, and (3) makespan of random schedules vary as
a function of the job to machine ratio (N/M). For the limiting
cases N/M approaching 0 and N/M approaching infinity we provide
analytical results, while for intermediate values of N/M we
perform experiments. We prove that as N/M approaches 0, backbone
size approaches 100%, while as N/M approaches infinity the backbone
vanishes. In the process we show that as N/M approaches 0
(resp. N/M approaches infinity), simple priority rules almost surely gene
rate an optimal schedule, suggesting a theoretical account of the
"easy-hard-easy" pattern of typical-case instance difficulty in job
shop scheduling. We also draw connections between our theoretical
results and the "big valley" picture of JSSP landscapes.
34 pages
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