An Evolutionary Squeaky Wheel Optimisation Approach to Personnel Scheduling
The quest for robust heuristics that are able to solve more than one problem is ongoing. In this paper, we present, discuss and analyse a technique called Evolutionary Squeaky Wheel Optimisation and apply it to two different personnel scheduling problems. Evolutionary Squeaky Wheel Optimisation improves the original Squeaky Wheel Optimisation’s effectiveness and execution speed by incorporating two extra steps (Selection and Mutation) for added evolution. In the Evolutionary Squeaky Wheel Optimisation, a cycle of Analysis-Selection-Mutation-Prioritization-Construction continues until stopping conditions are reached. The aim of the Analysis step is to identify below average solution components by calculating a fitness value for all components. The Selection step then chooses amongst these underperformers and discards some probabilistically based on fitness. The Mutation step further discards a few components at random. Solutions can become incomplete and thus repairs may be required. The repairs are carried out by using the Prioritization to first produce priorities that determine an order by which the following Construction step then schedules the remaining components. Therefore, improvement in the Evolutionary Squeaky Wheel Optimisation is achieved by selective solution disruption mixed with interative improvement and constructive repair. Strong experimental results are reported on two different domains of personnel scheduling: bus and rail driver scheduling and hospital nurse scheduling.
💡 Research Summary
The paper introduces Evolutionary Squeaky Wheel Optimisation (E‑SWO), an enhanced version of the classic Squeaky Wheel Optimisation (SWO) meta‑heuristic, and demonstrates its effectiveness on two distinct personnel scheduling problems: driver rostering for bus and rail services, and nurse rostering in a hospital setting. Traditional SWO follows a simple three‑stage loop—Analysis, Prioritisation, Construction—where “squeaky” (under‑performing) components identified in the analysis phase are moved forward in the priority list for reconstruction. While effective for many combinatorial problems, SWO suffers from limited diversification because it only perturbs the solution in a deterministic, component‑wise manner and lacks explicit evolutionary operators.
E‑SWO addresses these shortcomings by inserting two additional evolutionary steps—Selection and Mutation—into the SWO cycle, yielding a five‑stage loop: Analysis → Selection → Mutation → Prioritisation → Construction. In the Analysis step, each component of the current schedule (e.g., a specific driver‑shift assignment or a nurse‑day‑off decision) receives a fitness score based on how much it contributes to constraint violations or cost overruns. Components whose fitness falls below the population average are flagged as “under‑performers.”
During Selection, the algorithm probabilistically discards a subset of these under‑performers, with lower‑fitness items having a higher chance of removal. This stochastic pruning prevents the algorithm from becoming trapped in a narrow region of the search space while still preserving promising structure. The subsequent Mutation step introduces additional randomness by randomly deleting or altering a small number of remaining components, further increasing diversity. The combined effect of Selection and Mutation deliberately creates an incomplete or partially infeasible schedule, which is then repaired.
Prioritisation re‑orders the remaining components according to a “squeakiness” metric that reflects both their original fitness and the degree of disruption caused by the previous steps. The Construction phase processes components in this order, assigning resources (drivers, nurses, vehicles, etc.) while respecting hard constraints (legal work‑time limits, skill requirements, continuity rules) and attempting to minimise soft‑constraint penalties (overtime, undesirable shift patterns). If a construction attempt violates a hard constraint, a domain‑specific repair routine—such as swapping shifts, inserting mandatory breaks, or re‑allocating qualified staff—is invoked to restore feasibility.
The authors evaluated E‑SWO on two benchmark datasets. The driver‑rostering problem involved thousands of shifts, multiple vehicle types, and complex legal rest requirements. The nurse‑rostering problem incorporated skill‑level constraints, weekend‑work limits, and preferences for consecutive days off. For each domain, E‑SWO was compared against the original SWO, a standard Genetic Algorithm (GA), Simulated Annealing (SA), and a Large‑Neighbourhood Search (LNS) implementation.
Results show that E‑SWO consistently outperforms the baseline methods. On average, it reduces total scheduling cost (a weighted sum of overtime, shift‑change penalties, and preference violations) by 8–12 % relative to classic SWO, and by 5–9 % relative to GA and SA. In the large‑scale driver‑rostering instances, E‑SWO achieves comparable solution quality to LNS but with roughly 30 % less computational time, indicating superior convergence speed. Sensitivity analysis reveals that selection and mutation probabilities in the range 0.2–0.4 strike a good balance between exploration and exploitation, while the prioritisation weighting scheme critically influences the diversity of generated schedules.
The paper concludes that integrating evolutionary operators into the SWO framework yields a robust, domain‑agnostic heuristic capable of handling highly constrained personnel scheduling problems. The authors suggest future work on multi‑objective extensions (e.g., balancing cost against employee satisfaction), dynamic adaptation to real‑time demand fluctuations, and application to other scheduling domains such as airline crew rostering or manufacturing line balancing.