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

Research Question and Approach

Regional sustainability in ageing societies like Japan is threatened by the decline of the working-age population. While many socioeconomic indicators are correlated with this decline, translating these associations into actionable, locality-specific policy guidance is difficult due to nonlinear interactions and the combinatorial nature of social planning. The authors address this by constructing an interpretable optimization pipeline that links municipal social statistics to working-age population growth.

Using 2010–2020 data from Japanese municipalities, the researchers regressed the working-age population growth rate on ten discretized social indicators. They utilized a quadratic surrogate model to capture both individual indicator contributions and pairwise interactions. This model was then converted into a Quadratic Unconstrained Binary Optimization (QUBO) formulation, allowing the researchers to search for indicator configurations that maximize predicted growth using quantum annealing, simulated annealing, and the Gurobi solver.

The quadratic surrogate model achieved a test-set correlation coefficient of 0.84 and an average R-squared of 0.76, indicating that the model captures the overall trends in population growth effectively. The resulting coefficient matrix provides a transparent representation of how specific indicator levels—such as lower average age—contribute to growth, as well as how different indicators interact (e.g., the positive association between low average age and moderate primary-industry employment).

All three optimization methods (quantum annealing, simulated annealing, and Gurobi) successfully identified the same optimal feasible configuration. Furthermore, the annealing-based samplers were able to generate a set of feasible suboptimal configurations, which the authors argue are valuable for policy discussions where the global optimum may not be immediately attainable. The study also included a sensitivity analysis (single-indicator flip) to demonstrate how modifying one indicator can change the predicted growth rate depending on the existing configuration of other indicators.