[Paper Review] Bayesian Optimisation Algorithm for Nurse Scheduling

Jingpeng Li, Uwe Aickelin|arXiv (Cornell University)|Apr 3, 2008

Scheduling and Timetabling Solutions42 references15 citations

TL;DR

This paper proposes a Bayesian Optimization Algorithm (BOA) for nurse scheduling that dynamically selects optimal shift patterns using probabilistic modeling. By constructing a Bayesian network from high-quality solutions and iteratively sampling conditional probabilities, the BOA evolves rule-based schedules that achieve 100% feasibility and mean cost of 39.8 across 52 real-world instances, outperforming most metaheuristics in solution reliability while running in under 30 seconds.

ABSTRACT

Our research has shown that schedules can be built mimicking a human scheduler by using a set of rules that involve domain knowledge. This chapter presents a Bayesian Optimization Algorithm (BOA) for the nurse scheduling problem that chooses such suitable scheduling rules from a set for each nurses assignment. Based on the idea of using probabilistic models, the BOA builds a Bayesian network for the set of promising solutions and samples these networks to generate new candidate solutions. Computational results from 52 real data instances demonstrate the success of this approach. It is also suggested that the learning mechanism in the proposed algorithm may be suitable for other scheduling problems.

Motivation & Objective

• To address the complexity of real-world nurse scheduling problems that are too large and constrained for exact mathematical programming methods.
• To develop a flexible, rule-based scheduling approach that mimics human decision-making by selecting from a set of domain-specific rules.
• To improve solution quality and feasibility over existing metaheuristics like genetic algorithms and learning classifier systems.
• To demonstrate the effectiveness of Bayesian optimization in scheduling by modeling dependencies between nurse-shift pattern assignments.

Proposed method

• The BOA uses a Bayesian network where each node represents a nurse/rule pair, and directed edges encode probabilistic dependencies between assignments.
• Conditional probabilities for each nurse/rule pair are learned from a population of high-quality rule strings, representing promising solutions.
• New rule strings are generated by stochastic sampling from the Bayesian network, preserving high-probability building blocks.
• The algorithm uses roulette-wheel selection to update the population, replacing lower-quality solutions with newly sampled ones.
• The network is iteratively retrained using the best solutions from each generation to refine the probabilistic model.
• The approach incorporates four rule types: 'Overall Cover', 'Contribution', 'Highest Cover', and 'Enhanced Contribution', each guiding rule selection based on coverage and cost metrics.

Experimental results

Research questions

• RQ1 Can a Bayesian Optimization Algorithm effectively model and evolve rule-based schedules for complex nurse scheduling problems?
• RQ2 How does the BOA's probabilistic learning mechanism compare to traditional metaheuristics in terms of solution quality and feasibility?
• RQ3 To what extent can the BOA learn and exploit structural patterns (building blocks) in nurse scheduling solutions?
• RQ4 Can the BOA achieve high-quality solutions within a practical runtime, even without local search or complex parameter tuning?

Key findings

• The BOA achieved a mean cost of 39.8 across 52 real-world nurse scheduling instances, outperforming most metaheuristics in solution quality and feasibility.
• The algorithm achieved 100% feasibility across all 52 instances, significantly outperforming other metaheuristics like basic GA (33% feasibility) and multi-population GA (75% feasibility).
• The BOA ran in an average of 23.0 seconds per instance, achieving near-optimal results in under half a minute, while exact integer programming required over 24 hours.
• The graphical visualization of the Bayesian network showed convergence to high-probability paths, indicating effective learning of optimal building blocks such as the segment from node 10 to node 21 in the final generation.
• The 'Enhanced Contribution' and 'Highest Cover' rules showed promise in experimental evaluations, improving rule selection accuracy.
• The BOA's performance was competitive with advanced methods like the hill-climbing GA and indirect GA, despite not using local search or solution-space mapping.