MULTI-OBJECTIVE OPTIMIZATION OF REGIONAL BUDGET ALLOCATION BASED ON NSGA-II WITH FAIRNESS CONSTRAINTS

Abstract

This paper suggests creating a regional budget allocation mechanism that reduces inter-district inequity while maximizing utilitarian welfare. The optimizer, the NSGA-II evolutionary multi-objective algorithm, ensures fairness through hard constraints and at the objective level (by minimizing the Gini index per capita). In order to eliminate inter-district inequality with little loss of utility, the authors show that their NSGA-II-based methodology with fairness constraints creates a solid Pareto front and offers three workable alternatives (efficiency, equality, and knee). It is demonstrated that the NSGA-II-based methodology with fairness restrictions produces a stable and interpretable Pareto front with three main solution options: an equality-oriented solution, an efficiency-oriented solution, and a compromise solution (the knee point). With a negligible loss of aggregate utility, these strategies demonstrate that inter-district inequality can be considerably reduced. In particular, the incorporation of «hard» constraints like G(x)≤τ, a max/min-ratio, and a per-capita floor guarantees that regulatory thresholds (such τ=0.21–0.22) are fulfilled, avoiding the exclusion of minor districts. Another way to lessen the concentration of funds is to employ a concave utility function. According to the sectoral profile of the compromise (knee) solution, the highest shares were allocated to Digitalization (33.49%), Transportation (31.98%), and Culture (24.08%), while Healthcare and Ecology received only about 0.19% and 0.13% respectively. In this case, the Gini index decreases from 0.1586 (efficiency) to 0.0469 (knee), i.e. by 70.44%, whereas total utility drops by only 4.44%, which quantitatively confirms the efficiency–equality balance.

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