Abstract: In recent years, the frequent occurrence of sudden disasters has not only caused huge economic losses but also seriously endangered people's physical and mental health. Accelerating the rapid distribution of emergency materials after a disaster can effectively reduce the harm done to personnel in the affected areas due to the lack of emergency services. As an important part of the emergency relief system, the location of the emergency material distribution center determines the efficiency of material distribution for the entire relief system. Currently, there are studies on facility location models divided into three categories: (1)The p-center problem, which selects p facilities that minimize the maximum distance between the demand point and the nearest used candidate emergency facility. (2)The p-median problem, which selects the p facilities that minimize the demand-weighted average distance between the demand point and the nearest candidate emergency facility. (3)The maximum coverage problem, minimizing the number of selected emergency facilities while covering all demand points, or maximizing the number of covered demand points by locating the number of emergency p facilities.
However, the simple location model of the emergency material distribution center does not fit well with the real post-disaster rescue scenario, due to the inherent abruptness, uncertainty, and great destructiveness of disasters. Post-disaster demand data are difficult to collect accurately, whereas an accurate emergency material demand assessment can not only help decision-makers arrange suitable emergency material distribution center services for demand points in the face of limited materials but also improve the utilization rate of emergency materials while reducing the distribution cost of emergency materials. The main ways to deal with the uncertainty of emergency location demands are robust optimization, fuzzy theory, stochastic programming, and connection number. Although the robust method can optimize uncertain problems, it considers only the worst-case scenario and obtains relatively conservative results. In addition, demand in affected areas changes over time, so it is difficult to obtain the reliable prior data needed for stochastic programming.
In conclusion, this paper proposes a model for the location of emergency material distribution centers based on uncertain demand and service utility. The research of the model focuses on how demand points can select emergency material distribution centers at the same construction cost. We propose ROLNSWOA to solve the problem in the paper to overcome the shortcomings of the basic non-dominated sorting whale optimization algorithm (NSWOA), such as slow convergence, low accuracy, and falling into local optimization, and also better fit the model in this paper. A series of improvements have been made to the algorithm. ROLNSWOA is compared to NSWOA, Non-dominated Sorting Genetic Algorithm II(NSGA-II), Strength Pareto Evolutionary Algorithm 2(SPEA2), Multi-objective Evolutionary Decomposition Algorithm(MOEA/D), and Multi-objective Particle Swarm Optimization Algorithm(MOPSO), by performing the real case data in the context of Shanghai, China. From the experimental results, it can be seen that the ROLNSWOA algorithm proposed in this paper significantly outperforms the other algorithms in all the evaluation metrics, although this requires more computational time, which is within the acceptable range. The results of this experiment further validate the effectiveness and accuracy of the model and algorithm.
Although the proposed model for the location of emergency material distribution centers based on uncertain demand and service utility, along with the ROLNSWOA, has demonstrated strong performance in the experiments, there is still room for further research. First, the current study does not fully account for the dynamic path constraints caused by post-disaster damage to the transportation network. Future work could integrate dynamic traffic recovery models to jointly optimize distribution routing. Second, in real-world scenarios, demand points may exhibit multi-level and multi-type demand characteristics. Therefore, subsequent research could extend the model to incorporate hierarchical collaborative distribution and multi-type material classification and scheduling mechanisms. Furthermore, although ROLNSWOA shows excellent performance in terms of precision and convergence, its computational efficiency may decrease when handling large-scale data. Future studies may explore the integration of distributed computing and deep learning-assisted optimization strategies to enhance the practicality and intelligence of the algorithm.

Key words: fuzzy demand, location of emergency material distribution center, service utility, refracted opposition-based learning for non-dominated sorting whale optimization algorithm

摘要： 为加快灾后应急物资的快速分配,减少受灾地区人员因未得到服务而产生的伤害,本文提出了一种基于不确定需求和服务效用的应急物资配送中心选址多目标优化模型。该模型以最大化受灾区域各需求点的整体服务效用、最小化救援行动的总成本为目标,力求在复杂多变的灾后环境中提升应急响应效率与资源配置公平性。此外,考虑到灾后实际需求常具有模糊性和不确定性,本文引入模糊数对各需求点的物资需求进行建模,使模型更贴近现实决策场景。为求解该多目标优化问题,提出了基于折射反向学习的非支配排序鲸鱼优化算法(Refracted Opposition-based Learning for Non-dominated Sorting Whale Optimization Algorithm, ROLNSWOA)。并通过中国上海为背景的真实案例,与非支配排序鲸鱼优化算法、非支配排序遗传算法II、强度帕累托进化算法Ⅱ、基于分解的多目标进化算法和多目标粒子群算法进行比较,验证了ROLNSWOA算法的性能和应用价值。

关键词: 模糊需求, 应急物资配送中心选址, 服务效用, 基于折射反向学习的非支配排序鲸鱼优化算法