An Indirect Genetic Algorithm for a Nurse Scheduling Problem (0803.2969v1)

Abstract: This paper describes a Genetic Algorithms approach to a manpower-scheduling problem arising at a major UK hospital. Although Genetic Algorithms have been successfully used for similar problems in the past, they always had to overcome the limitations of the classical Genetic Algorithms paradigm in handling the conflict between objectives and constraints. The approach taken here is to use an indirect coding based on permutations of the nurses, and a heuristic decoder that builds schedules from these permutations. Computational experiments based on 52 weeks of live data are used to evaluate three different decoders with varying levels of intelligence, and four well-known crossover operators. Results are further enhanced by introducing a hybrid crossover operator and by making use of simple bounds to reduce the size of the solution space. The results reveal that the proposed algorithm is able to find high quality solutions and is both faster and more flexible than a recently published Tabu Search approach.

• The paper introduces an indirect GA that transforms nurse permutations into feasible schedules using specialized heuristic decoders.
• It demonstrates that the PUX crossover paired with a combined decoder achieves solutions within 2% of optimal performance.
• The research highlights a flexible approach that effectively manages real-world scheduling constraints, suggesting broader applicability in optimization.

Assessing the Efficacy of an Indirect Genetic Algorithm for Nurse Scheduling

The paper "An Indirect Genetic Algorithm for a Nurse Scheduling Problem," authored by Uwe Aickelin and Kathryn A. Dowsland, delineates a sophisticated approach to address the complexities of nurse scheduling in a hospital environment using Genetic Algorithms (GAs). This research critically addresses the insufficiencies of traditional GAs when dealing with constraints intrinsic to real-world optimization scenarios, specifically within the domain of manpower scheduling.

Problem Complexity and Methodological Approaches

Nurse scheduling, a NP-hard optimization task, involves intricacies such as multiple constraints related to shift patterns, preferences, and varying levels of nurse qualifications. Traditional methods like penalty and repair functions commonly fail to effectively handle such constraints. The paper proposes an alternative: utilizing indirect coding via permutations of nurses and a heuristic-based decoder designed to construct feasible schedules while respecting imposed constraints.

Algorithmic Design and Experimental Framework

The researchers devised an indirect GA where the GA's operators work on an unconstrained solution space, represented as permutations of nurses. A heuristic decoder translates these permutations into actual schedules. The paper leveraged data from 52 weeks of scheduling scenarios from a UK hospital to evaluate three heuristic decoders of varying sophistication alongside four crossover operators.

• Decoders:
  • Cover Decoder: Focuses on achieving feasibility through ensuring adequate coverage for the most understaffed shifts.
  • Contribution Decoder: Attempts to incorporate nurse preferences into scheduling decisions, aiming at cost-effectiveness without guaranteeing feasibility.
  • Combined Decoder: Synthesizes elements of the former two techniques, balancing between feasibility and cost-effectiveness.
• Crossover Operators: PMX, uniform order-based crossover, C1 crossover, and order-based crossover were explored, demonstrating varying efficacies, with PMX yielding superior performance.

The research identifies the hybridization approach—particularly the "Combined Decoder" paired with a novel crossover, PUX (Parameterized Uniform Crossover)—as producing solutions robustly and consistently proximate to optimal, often within 2% of it. The use of PUX assured high feasibility and low-cost solutions by intelligently combining order and position information transmitted from parent solutions.

Comparative Analysis and Practical Impact

A significant aspect of this paper is its empirical comparison against other optimization methods, such as Tabu Search and Integer Programming. Results show the indirect GA to provide competitive, if not superior, outcomes while allowing for a flexibility in adapting to problem specifications. This flexibility is particularly advantageous as it decouples GA operations from the meticulous problem-specific adjustments that traditional implementations necessitate.

Implications and Future Directions

The findings underscore the potential application of indirect GAs beyond nurse scheduling, suggesting broader applicability to other similarly structured, constraint-laden optimization problems. The hierarchical incorporation of active constraints directly into the heuristic decoder, as opposed to merely modifying the objective function, might inspire future AI research to explore richer, more adaptive heuristic designs.

Moreover, the paper opens avenues for further research into optimizing decoder heuristics and crossover strategies to handle dynamically evolving constraint sets, fostering development in evolutionary computation beyond fixed problem boundaries. Future investigations may explore adaptive mechanisms within the GAs to autonomously adjust heuristic parameters for optimal performance across different constraint environments.

In conclusion, this paper provides a substantive contribution to both evolutionary algorithm research and practical personnel scheduling, demonstrating a refined approach to incorporating constraints through bespoke algorithmic architecture.