Adaptive simulated annealing for autonomous labour market delimitation

Labour market areas (LMAs) are functional regions where job workers and employers interact to exchange labour services, playing a crucial role in regional economic analysis and policy-making. Accurate LMA definitions help ensure that regional boundaries reflect actual labour market dynamics. However, most existing methods for defining LMAs are susceptible to threshold values, which can vary significantly across regions due to differences in spatial and commuting interaction patterns. When region-specific thresholds are not well aligned with local commuting patterns, existing methods tend to generate unstable solutions, reflected in large variation in fitness values across algorithm repetitions and misallocations in which regions would perform better if placed in a neighbouring LMA, through stronger cohesion without a substantial loss in self-containment. This undermines the reliable identification of labour market structures. To address these challenges, we developed the Adaptive Simulated Annealing for Autonomous Labour Market Delimitation (AdSA-ALMD) algorithm. The method preserves labour market boundaries by using soft constraints to guide threshold selection, thereby reducing solution variance and minimising misallocations. Our method integrates simulated annealing with an adaptive cooling schedule, allowing efficient exploration of the solution space. Additionally, a penalty-based fitness function guides threshold adjustments, ensuring the resulting thresholds reflect the underlying commuting patterns. We validated our methodology using simulated data and micro-level journey-to-work data from the 2016 Census provided by the Australian Bureau of Statistics. Across both simulated and empirical applications, the method produced regionalisations with stronger cohesion without a substantial loss in self-containment, and fewer misallocations, relative to the Travel-to-Work Area algorithm, the Grouping Evolutionary Algorithm, and a recent Multi-step Approach. The use of soft constraints enables the approach to accommodate varying commuting structures without requiring region-specific tuning. Overall, the results demonstrate that AdSA-ALMD yields reproducible labour market delineations that reduce sensitivity to threshold specification while preserving alignment with observed commuting interactions.