6 research outputs found
How the landscape of random job shop scheduling instances depends on the ratio of jobs to machines
Abstract: "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 -> 0 and N/M -> [infinity] we provide analytical results, while for intermediate values of N/M we perform experiments. We prove that as N/M -> 0, backbone size approaches 100%, while as N/M -> [infinity] the backbone vanishes. In the process we show that as N/M -> 0 (resp. N/M -> [infinity]), simple priority rules almost surely generate 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.
How the Landscape of Random Job Shop Scheduling Instances Depends on the Ratio of Jobs to Machines
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 N N). For the limiting cases โ 0 and โ โ we provide analytica
Human-Machine Collaborative Optimization via Apprenticeship Scheduling
Coordinating agents to complete a set of tasks with intercoupled temporal and
resource constraints is computationally challenging, yet human domain experts
can solve these difficult scheduling problems using paradigms learned through
years of apprenticeship. A process for manually codifying this domain knowledge
within a computational framework is necessary to scale beyond the
``single-expert, single-trainee" apprenticeship model. However, human domain
experts often have difficulty describing their decision-making processes,
causing the codification of this knowledge to become laborious. We propose a
new approach for capturing domain-expert heuristics through a pairwise ranking
formulation. Our approach is model-free and does not require enumerating or
iterating through a large state space. We empirically demonstrate that this
approach accurately learns multifaceted heuristics on a synthetic data set
incorporating job-shop scheduling and vehicle routing problems, as well as on
two real-world data sets consisting of demonstrations of experts solving a
weapon-to-target assignment problem and a hospital resource allocation problem.
We also demonstrate that policies learned from human scheduling demonstration
via apprenticeship learning can substantially improve the efficiency of a
branch-and-bound search for an optimal schedule. We employ this human-machine
collaborative optimization technique on a variant of the weapon-to-target
assignment problem. We demonstrate that this technique generates solutions
substantially superior to those produced by human domain experts at a rate up
to 9.5 times faster than an optimization approach and can be applied to
optimally solve problems twice as complex as those solved by a human
demonstrator.Comment: Portions of this paper were published in the Proceedings of the
International Joint Conference on Artificial Intelligence (IJCAI) in 2016 and
in the Proceedings of Robotics: Science and Systems (RSS) in 2016. The paper
consists of 50 pages with 11 figures and 4 table
Mixed integer programming and adaptive problem solver learned by landscape analysis for clinical laboratory scheduling
This paper attempts to derive a mathematical formulation for real-practice
clinical laboratory scheduling, and to present an adaptive problem solver by
leveraging landscape structures. After formulating scheduling of medical tests
as a distributed scheduling problem in heterogeneous, flexible job shop
environment, we establish a mixed integer programming model to minimize mean
test turnaround time. Preliminary landscape analysis sustains that these
clinics-orientated scheduling instances are difficult to solve. The search
difficulty motivates the design of an adaptive problem solver to reduce
repetitive algorithm-tuning work, but with a guaranteed convergence. Yet, under
a search strategy, relatedness from exploitation competence to landscape
topology is not transparent. Under strategies that impose different-magnitude
perturbations, we investigate changes in landscape structure and find that
disturbance amplitude, local-global optima connectivity, landscape's ruggedness
and plateau size fairly predict strategies' efficacy. Medium-size instances of
100 tasks are easier under smaller-perturbation strategies that lead to
smoother landscapes with smaller plateaus. For large-size instances of 200-500
tasks, extant strategies at hand, having either larger or smaller
perturbations, face more rugged landscapes with larger plateaus that impede
search. Our hypothesis that medium perturbations may generate smoother
landscapes with smaller plateaus drives our design of this new strategy and its
verification by experiments. Composite neighborhoods managed by meta-Lamarckian
learning show beyond average performance, implying reliability when prior
knowledge of landscape is unknown