QUBO-Based Optimization of Social Indicator Configurations for Working-Age Population Growth

<title>Abstract</title> <p>The decline of the working-age population is a major challenge for regional sustainability, particularly in ageing societies such as Japan.Although municipal demographic change is associated with multiple socioeconomic indicators, it remains difficult to translate such associations into interpretable and optimization-ready models.We present the first methodological demonstration of a quadratic unconstrained binary optimization (QUBO)-based framework for exploring social-indicator configurations associated with working-age population growth.Using Japanese municipal data, we regressed the 2010--2020 working-age population growth rate on ten social indicators encoded as discretized one-hot variables.The resulting quadratic surrogate model achieved reasonable predictive performance, with a test-set correlation coefficient of 0.84 and an average coefficient of determination of $R^{2}=0.76$.Because the model is quadratic, its coefficients can be represented as an interpretable matrix whose diagonal elements describe individual indicator-level contributions and whose off-diagonal elements describe pairwise associations between indicator levels.We then converted the fitted surrogate model into a QUBO formulation with one-hot constraints and optimized it using quantum annealing, simulated annealing, and Gurobi.All three approaches identified the same optimal feasible configuration in the present problem setting, while the annealing-based samplers also generated feasible suboptimal configurations with different predicted growth rates.Municipality-level single-indicator flip analyses further showed that modifying one indicator can either increase or decrease the predicted growth rate depending on the configuration of other indicators.These results demonstrate that QUBO-based modelling can provide an interpretable and optimization-ready framework for connecting municipal social statistics, nonlinear indicator interactions, and model-based scenario generation.The proposed framework should be interpreted as an exploratory tool for policy discussion rather than as a causal estimate of policy interventions.</p>