关键词: 洪涝灾害, 应急响应, 应急物资配送, 车辆路径问题, 禁忌搜索算法

Abstract: Floods have become a major type of disaster threatening human life and socio-economic development. According to data from the Ministry of Emergency Management of China, between 2021 and 2023, floods accounted for over 50% of global natural disasters, causing substantial casualties and economic losses. Catastrophic events such as the “7.20” Henan rainstorm flood in 2021 and the Pakistan floods in 2022 highlight the urgency of flood emergency response. Rescue of trapped individuals and relief distribution are the two core tasks; however, previous studies often optimize these decisions separately, ignoring their interdependence. Moreover, existing approaches often fail to consider the priority levels of trapped individuals, lack multi-vehicle integrated coordination mechanisms, or exhibit insufficient algorithmic performance. Focusing on flood emergency scenarios, this study develops an air–ground–water multi-modal multi-vehicle routing optimization model. The core problem can be described as follows: in a network where roads are partitioned into truck-accessible routes, assault-boat-accessible waterways, and flight routes for helicopters/unmanned aerial vehicles (UAVs), rescue operations are coordinated using trucks, assault boats, and helicopters, while relief distribution is dynamically managed via truck–drone collaboration, achieving an integrated optimization of rescue and distribution tasks that accounts for priority levels and task divisibility. Trapped individuals are classified into three priority levels based on the severity of entrapment and health status. Task-splitting strategies allow multiple vehicles to cooperate on the same rescue node, and relief distribution adopts a soft time-window mechanism. The model adopts a lexicographic multi-objective optimization strategy: the primary objective minimizes the weighted rescue time of trapped individuals, and the secondary objective maximizes relief distribution satisfaction. Constraints are formulated as a mixed-integer nonlinear programming model, covering vehicle capacity, travel time, and cooperative scheduling requirements. Methodologically, the study first constructs an integrated multi-objective optimization framework that overcomes the limitations of traditional separate decision-making approaches by deeply integrating rescue priority mechanisms, task-splitting strategies, and multi-vehicle coordination. An Improved Tabu Search (ITS) algorithm is then designed to address the characteristics of truck–boat–helicopter and truck–drone coordination modes. The algorithm incorporates differentiated encoding–decoding mechanisms and optimizes three types of neighborhood operators (intra-route reversal, single-node exchange, and inter-route single-node exchange), integrated with lexicographic optimization logic to first prioritize the primary objective and subsequently optimize the secondary objective. Finally, both a real case and multiple simulated instances of varying scales are used to validate the model and algorithm performance, with comparative analyses of different strategies and algorithms. Key results include: (1) the priority-based task-splitting mechanism significantly improves the rescue efficiency of trapped individuals; (2) dynamic collaborative distribution strategies outperform static strategies, showing advantages in timeliness and flexibility; (3) the ITS algorithm outperforms Genetic Algorithm (GA), Simulated Annealing Algorithm (SAA), Hierarchical Adaptive Large Neighborhood Search (HALNS), and Ant Colony Optimization (ACO), with average improvements on the primary objective of 8.95%, 7.44%, 13.54%, and 6.97%, respectively. In terms of case data, a real instance based on the “7.20” Henan flood is constructed, with a rescue network comprising 25 disaster nodes and 192 trapped individuals. Nodes are partitioned into truck stops, assault-boat rescue points, and helicopter rescue points in a 1:3:1 ratio. Additionally, twelve simulated instances with varying scales (25/50/100/200 nodes) and distribution types (clustered, random, hybrid) are generated based on Solomon and Gehring–Homberger benchmark instances, incorporating vehicle speed, capacity, and rescue time parameters, with algorithm implementation in Matlab. This study explores the integrated multi-objective lexicographic optimization of rescue and relief distribution under flood conditions. The proposed priority mechanism and multi-vehicle coordination strategies provide a quantitative decision-support tool for emergency management, enriching the theory and methods for flood emergency scheduling. The improved ITS algorithm offers an efficient solution approach for complex constrained routing problems. The results can assist emergency management agencies in optimizing scheduling practices, enabling rescue teams to implement “priority to high-risk individuals and precise resource allocation”, and ultimately support decision-making to reduce casualties in flood disasters.

Key words: flood rescue, emergency response, emergency supplies distribution, vehicle routing problem, tabu search algorithm