Due to the uneven distribution of water resources in time and space, the problem of water shortage has become increasingly serious in some areas. To optimize use of water resources, it is urgent to establish multi-objective models and apply effective optimization algorithms to guide reservoir management. This study proposed a model of multi-objective optimization for reservoir operation (MORO) with the objectives of maximizing water diversion and power generation. The multi-objective evolutionary algorithm based on decomposition with adaptive weight vector adjustment (MOEA/D-AWA) was applied to solve the MORO problem. In addition, the performance of the MOEA/D-AWA was compared with two other algorithms based on the hyper-volume index. Huangjinxia reservoir, which is located in Shaanxi, China, was selected as the case study. The results show that: (1) the proposed model is effective and reasonable in theory; (2) the optimization results obtained by MOEA/D-AWA demonstrate this algorithm can be applied to the MORO problem, providing a set of evenly distributed non-dominated solutions; and (3) water diversion and power generation are indeed contradictory objectives. The MORO strategy can be used to efficiently utilize water resources, improve the comprehensive benefits of reservoirs, and provide decision support for actual reservoir operation.

A complex interwoven relationship exists between water resources and urbanization, which is of much interest in international water science research. To study the urban development in large cities facing water deficiency problems, it is important to identify rational thresholds of urbanization to achieve optimal utilization of limited water resources, and to promote sustainable economic and population growth and social development. A multi-objective optimization model is proposed to search for the optimal scale of urbanization of large cities with limited water resources. To solve a large-dimensional multi-objective optimization problem, the non-dominated sorting genetic algorithm (NSGA-II) is improved to the OENSGA-II based on the orthogonal generation method and the E-optimality method and applied to a typical arid city, Xi’an of China, which underwent rapid urbanization in recent years. For Xi’an, a statistically significant positive correlation is found between urbanization rate (U_r) and gross domestic product (GDP), domestic water, tertiary industry water, and ecological water. However, U_r is negatively correlated with the primary industry water. If the current urbanization trend continues, the water resources available are far from sufficient to support the future city of Xi’an. In this work, it was found that, by implementing restrictive water resources management and water saving measures, the economic threshold of Xi’an could be raised to 1890.3 and 2403.3 billion yuan, while the population threshold could be raised to 11.0 and 13.9 million, and U_r to 79.9% and 85.9% in 2020 and 2030, respectively. The corresponding maximum urban area to be constructed based on the projected population will be 964.81 and 1197.6 km² in those years. It will be prudent for Xi’an to practice strict water resource management, and to allocate its water resources among various water sectors effectively and equitably to avoid major water shortage problems in the future.