## 1 Introduction
[24] improved the inertia weight and learning factors of the Particle Swarm Optimization (PSO) algorithm and applied it to the optimal allocation of water resources in Yangquan City. The resulting water-saving scheme not only mitigated water shortages across administrative districts but also reduced COD emissions, thereby easing ecological and environmental pressures. When solving multi-objective optimization allocation models for water resources using multi-objective optimization algorithms (MOAs), a series of non-dominated solution sets are obtained instead of a single optimal solution, due to the characteristics of multi-objective optimization problems. Therefore, to ensure the scientific and rational allocation of water resources, evaluation methods are needed to filter the non-dominated solution sets in order to find the optimal solution that maximizes overall benefits. Common evaluation methods include the analytical hierarchy process (AHP) [25], the entropy weight method [26], and the technique for order preference by similarity to ideal solution (TOPSIS) [27]. The AHP relies heavily on expert experience for weighting, making it quite subjective. The Entropy Weight Method calculates weights based on data distribution, offering more objectivity, yet it fails to reflect decision-makers' preferences and is highly sensitive to the distribution of the indicators' data. TOPSIS is a ranking method based on distance measurement, but it lacks the ability to evaluate the synergy between multiple systems, making it difficult to fully reflect the comprehensive effects of water resource allocation. The coupled coordination degree evaluation model [28] is constructed based on system theory and synergy theory. Its advantages lie in quantifying the feasibility of comprehensive benefit evaluation schemes on the one hand and analyzing the interactive coupling relationships between multiple systems to determine whether the schemes meet the requirements for coordinated development on the other. Compared to traditional evaluation methods, this model overcomes the shortcomings of single evaluation dimensions and insufficient representation of dynamic correlations. It can quantitatively represent the overall coordination of water resource allocation schemes under multi-objective constraints, making it suitable for indicator evaluation in water resource optimization allocation. Furthermore, as mentioned above, NSGA-III, as a representative algorithm in the field of multi-objective optimization, demonstrates excellent convergence and distribution, showing significant advantages in solving multi-objective optimization problems [29]. However, the NSGA-III algorithm can only generate a series of reference points through pre-definition and, in actual multi-objective optimization problems, the true Pareto front (PF) is often unknown in advance, so the preset reference points may not reflect the development trend of the PF. To address this issue, this study proposes three improvements: reference point improvement strategy, adaptive solution retention mechanism, and Pareto front screening strategy, to construct an improved NSGA-III (I-NSGA-III) algorithm. The improved I-NSGA-III is applied to the southern water supply zone of Jinzhong City, providing a diverse set of alternative solutions for water resource optimization and offering theoretical support and methodological innovation for water resource optimization in water-scarce northern regions.