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We characterize the search landscape of random instances of the job shopscheduling problem (JSP). Specifically, we investigate how the expected valuesof (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 approaches 0 and N/M approaches infinity weprovide analytical results, while for intermediate values of N/M we performexperiments. 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 showthat as N/M approaches 0 (resp. N/M approaches infinity), simple priority rulesalmost surely generate an optimal schedule, providing theoretical evidence ofan "easy-hard-easy" pattern of typical-case instance difficulty in job shopscheduling. We also draw connections between our theoretical results and the"big valley" picture of JSP landscapes.

How the Landscape of Random Job Shop Scheduling Instances Depends on the Ratio of Jobs to Machines