Predicting short-term urban water demand is essential for water resource management and directly impacts urban water resource planning and supply–demand balance. As numerous factors impact the prediction of short-term urban water demand and present complex nonlinear dynamic characteristics, the current water demand prediction methods mainly focus on the time dimension characteristics of the variables, while ignoring the potential influence of spatial characteristics on the temporal characteristics of the variables. This leads to low prediction accuracy. To address this problem, a short-term urban water demand prediction model which integrates both spatial and temporal characteristics is proposed in this paper. Firstly, anomaly detection and correction are conducted using the Prophet model. Secondly, the maximum information coefficient (MIC) is used to construct an adjacency matrix among variables, which is combined with a graph convolutional neural network (GCN) to extract spatial characteristics among variables, while a multi-head attention mechanism is applied to enhance key features related to water use data, reducing the influence of unnecessary factors. Finally, the prediction of short-term urban water demand is made through a three-layer long short-term memory (LSTM) network. Compared with existing prediction models, the hybrid model proposed in this study reduces the average absolute percentage error by 1.868–2.718%, showing better prediction accuracy and prediction effectiveness. This study can assist cities in rationally allocating water resources and lay a foundation for future research.

The imbalance between water supply and demand (WSD) has been growing noticeable as a result of the economy’s fast expansion which can be effectively alleviated using optimal allocation of water resources. An urban water resources allocation (WRA) model based on the innovative Multi-Objective Nutcracker Optimization Algorithm (MONOA) is proposed in this study. Taking into account economic, social and ecological benefits, a comprehensive multi-objective optimization (MOO) model is established. By introducing the opposite learning strategy, non-dominated sorting approach and crowding distance mechanism to a recently reported intelligent optimization algorithm called the Nutcracker Optimization Algorithm (NOA), the novel nature-inspired metaheuristic algorithm MONOA is proposed to solve the multi-objective optimization model. The MONOA is evaluated on ten benchmark test functions, and it exhibits superior distribution and convergence by comparing with some highly cited algorithms. The proposed model is applied to Handan, China, in order to obtain a reasonable water allocation scheme in the planning year. The simulation results reveal that the economic benefit is in the range CNY [1.36, 1.44] × 10¹¹, water shortage is in the range [0.66, 0.98] × 10⁸ m³ and COD emission is in the range [3.70, 3.91] × 10⁴ t in all the obtained Pareto solutions. The water resources management departments might create customized water allocation plans by balancing different goals and taking preferences into account. Moreover, the proposed method is a general approach that can be applied to many other cities. Hence, it is of great significance to the sustainable development and utilization of urban water resources.

Urban water usage spans diverse sectors, requiring effective management strategies to address increasing demand, limited supplies, and sector-specific needs. In this study, a multi-objective urban water resource allocation model is proposed to balance economic, ecological, and social benefits, focusing on social fairness. The model considers water availability, demand diversity, and environmental factors for optimized resource allocation. An improved zebra optimization algorithm-based multi-objective evolutionary algorithm (ZOA-MOEA/D) is developed, integrating zebra optimization with a decomposition-based approach to overcome the traditional methods’ limitations, improving solution diversity and convergence. ZOA-MOEA/D consistently outperforms the NSGA-II, MOPSO, and MOEA/D algorithms in solution distribution, convergence, quality, and diversity across multiple test scenarios. By applying the model to Ningbo, China, key trade-offs between economic growth, social fairness, living standards, and ecological protection are revealed. These findings provide useful insights into urban water resource management, offering a flexible framework for balancing multiple objectives and supporting sustainable development. Despite some limitations, the approach can contribute to the ongoing development of urban water resources.

With the rapid development of the social economy, the importance of water resources is becoming increasingly prominent. Urban water demand in Beijing has been growing rapidly. Accurate water consumption forecasting is of utmost importance for reasonable allocation and optimization of water supply systems. In this study, an innovative multi-variable grey prediction model with adjacent accumulation (AOGM(1,N)) is proposed to predict Beijing's annual water consumption for four different water usage scenarios (domestic water, agricultural water, industrial water, and environmental water) by incorporating the adjacent accumulation into the optimized grey model. Grey relational analysis is used to select the key influence factors. The adjustable parameter of the prediction model is chosen by using the particle swarm optimization algorithm. By comparing with other models in the existing literature, the proposed AOGM(1,N) model has evidently superior prediction performance based on the error indicators, which supports the novel method's merits and validity. This study could help us better understand water usage and be applied to the planning and management problems of urban water supply systems.