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

Abstract

The decline of the working-age population is a major challenge for regional sustainability, particularly in ageing societies such as Japan. We present a 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 discretized social indicators. The resulting quadratic surrogate model showed reasonable predictive performance, with a test-set correlation coefficient of 0.84 and an average R-squared value of 0.76. Its coefficient matrix provides an interpretable representation of individual indicator-level contributions and pairwise associations. We converted the fitted model into a QUBO formulation with one-hot constraints and optimized it using quantum annealing, simulated annealing, and Gurobi. All three methods identified the same optimal feasible configuration, while the annealing-based samplers also generated feasible suboptimal configurations with different predicted growth rates. Municipality-level single-indicator analyses showed that changing one indicator can increase or decrease the predicted growth rate depending on the other indicators. The framework provides an interpretable and optimization-ready approach for connecting municipal social statistics, nonlinear interactions, and model-based scenario generation. It should be regarded as an exploratory tool for policy discussion rather than as a causal estimate of policy interventions.