Exploiting problem structure in a genetic algorithm approach to a nurse rostering problem (0802.2001v3)

Abstract: There is considerable interest in the use of genetic algorithms to solve problems arising in the areas of scheduling and timetabling. However, the classical genetic algorithm paradigm is not well equipped to handle the conflict between objectives and constraints that typically occurs in such problems. In order to overcome this, successful implementations frequently make use of problem specific knowledge. This paper is concerned with the development of a GA for a nurse rostering problem at a major UK hospital. The structure of the constraints is used as the basis for a co-evolutionary strategy using co-operating sub-populations. Problem specific knowledge is also used to define a system of incentives and disincentives, and a complementary mutation operator. Empirical results based on 52 weeks of live data show how these features are able to improve an unsuccessful canonical GA to the point where it is able to provide a practical solution to the problem

• The paper presents a co-evolutionary GA that decomposes the nurse rostering problem by using sub-populations based on nurse grades.
• The study shows that adaptive penalties and intelligent mutation/repair methods significantly enhance convergence and feasibility in complex, NP-hard scheduling challenges.
• Empirical results from 52 real-world datasets demonstrate that the enhanced GA consistently produces feasible solutions within an average of 17 seconds per run.

Overview of Genetic Algorithm for Nurse Rostering

The paper "Exploiting Problem Structure in a Genetic Algorithm Approach to a Nurse Rostering Problem" presents an enhancement of genetic algorithms (GAs) tailored to address the complexities involved in a nurse scheduling problem at a major UK hospital. Classical GAs often struggle with scheduling problems due to conflicts between objectives and constraints. By incorporating problem-specific knowledge through a co-evolutionary strategy, the authors propose modifications that significantly enhance the ability of a GA to produce viable solutions.

Problem Context and Approach

The nurse scheduling problem entails creating weekly schedules for wards with up to 30 nurses. This scheduling must align with contract obligations, accommodate nurse preferences, and ensure shifts are equitably distributed. The underlying optimization is formulated as a multiple-choice set-covering problem, which is NP-hard, involving up to 2000 variables and 70 constraints per instance. Traditional optimization methods, like integer programming, often face difficulty, making this a suitable candidate for heuristic methods like GAs.

The authors outline their development using a canonical GA enhanced with three major modifications:

1. A co-evolutionary strategy with co-operating sub-populations engineered around the different nurse grade levels.
2. An adaptive penalty function to manage constraint violations dynamically.
3. Intelligent mutation and repair strategies to improve convergence quality.

Co-evolutionary Strategy

The haLLMark of the proposed solution is its co-evolutionary approach. By decomposing the problem into several sub-populations based on nurse grades, the approach enables co-operation between these sub-populations. This strategy significantly mitigates the epistatic nature of the problem, where the interdependencies among nurse assignments render the crossover operation less effective. By focusing on sub-populations, the GA maintains higher-quality partial solutions that are then amalgamated to form complete solutions.

Numerical Evaluation and Results

The empirical evaluation, conducted on 52 real-world datasets, demonstrates the efficacy of the proposed enhancements. The canonical GA, without the modifications, found feasible solutions infrequently, with 7 instances yielding no feasible solution after 20 runs. In contrast, the co-evolutionary strategy coupled with intelligent mutation and repair yielded at least one feasible solution in nearly every instance, with computation times averaging at approximately 17 seconds per run.

Implications and Future Directions

This research offers significant practical implications for applying GAs to scheduling problems. The specific modifications proposed — such as the use of sub-populations related to nurse grades — exhibit potential in related scheduling and timetabling domains, particularly where subset constraints naturally exist.

The paper also invites further exploration into applying similar co-evolutionary techniques to other complex combinatorial optimization problems. While the specific enhancements are necessarily tailored to the problem at hand, the underlying strategies of managing interdependencies and dynamically adapting penalty functions could be beneficial in other heuristic optimization contexts.

Moreover, the ongoing development of a GA with a heuristic decoder, as suggested by Davis, constitutes a promising area of future research. This approach could streamline the integration of problem-specific knowledge, reducing the complexity of developing tailored GA solutions.

In conclusion, this work contributes a methodologically solid enhancement to the GA paradigm, making it a viable tool for solving complex rostering problems in environments constrained by multiple-choice conditions. The adaptations presented in this paper not only enhance solution quality but also underline the importance of incorporating domain-specific insights into heuristic optimization frameworks.