Mixed integer programming and adaptive problem solver learned by landscape analysis for clinical laboratory scheduling

Abstract

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