## 3 Algorithm Improvement and Scheme Evaluation
### Improvement Strategy for the NSGA-III Algorithm
#### 3.1.4 Algorithm Implementation Process:
However, this study further quantifies the trade-off relationships between different objectives through the design of water-saving scenario. Additionally, the high proportion of agricultural water shortages is closely related to the high demand for agricultural water in Jinzhong City and its low supply priority. This phenomenon echoes the findings of [PERSON] et al. [36] in Yangquan City, underscoring the importance of optimizing the agricultural water use structure. It is recommended to adopt more scientific irrigation methods and promote water-saving renovations to improve irrigation water use efficiency and reduce agricultural water losses. (5) Despite the contributions of this study, certain limitations remain. This research establishes a water resource optimization model and improves the algorithm specifically for water-scarce regions, with the primary goal of alleviating the regional water supply and demand conflict. In contrast, in regions with more abundant water resources, the aim of water resource optimization is typically to achieve high-quality development. Therefore, different water conditions and objectives pose challenges to the improved algorithm presented in this study. In the future, we will collect data from corresponding regions to conduct water resource optimization studies to validate the algorithm's performance. Additionally, the water demand forecasting in this study relies on current water usage data. In future research, we will employ other forecasting methods: 1. Introducing socio-economic scenario analysis: Designing multiple scenarios based on Shared Socio-economic Pathways (SSPs), such as high growth-high water consumption and low carbon-water-saving societies, to quantify water demand under different development paths. 2. Using uncertainty modeling methods, such as Stochastic Programming: Treating climate change and socio-economic variables as random parameters to construct a two-stage optimization model. (6) Our current research focuses on improving the effectiveness of the algorithm and the quality of the solutions, without analyzing the potential increase in computational overhead introduced by the improved algorithm. In future research, we can evaluate computational overhead by comparing the average runtime per generation for DTLZ series problems. Additionally, we can explore adaptive triggering mechanisms--activating reference point updates only when population diversity falls below a certain threshold--to balance solution quality with computational efficiency. ## 7 Conclusions

This study addresses the water supply-demand conflict in Jinzhong City by establishing a multi-objective optimization model encompassing economic, social, and ecological objectives. An improved I-NSGA-III algorithm is proposed, integrating adaptive reference point generation, dynamic solution retention mechanisms, and optimized selection strategies to enhance algorithmic performance and achieve scientifically sound regional water resource allocation. The main conclusions are as follows:

(1) The I-NSGA-III algorithm overcomes the limitations of NSGA-III's predefined fixed reference points by dynamically adjusting reference point distributions. Combined with an early-stage high-quality solution retention strategy, it significantly improves solution set convergence and diversity. Experimental results demonstrate reductions of 5.17-50.22% in the IGD metric and increases of 2.71-25.51% in the HV metric across the DTLZ test functions, validating its effectiveness for complex constrained multi-objective optimization problems. (2) The coupled coordination degree evaluation model innovatively incorporates system synergy theory into water resource allocation assessment, quantifying interactions among economic, social, and ecological objectives. Results show coordination degrees of 0.8556-0.8701 for 2035 scenarios (compared to 0.7847-0.8358 in 2030), confirming that the optimized schemes effectively mitigate multi-system conflicts in Jinzhong City.