# Vehicle Route Planning for Relief Item Distribution under Flood Uncertainty
## 1 Introduction
[16] presented an Emergency Logistics Scheduling (ELS) approach with a Multi-Agent Genetic Algorithm (MA-GA), where each agent has specific roles in optimizing the transportation schedule. However, the mentioned researchs do not consider the uncertainty factors of road conditions resulting from disasters. Moreover, real-time data may not be acceptable if there are issues with communication infrastructure. Research has demonstrated strategies to handle uncertainty using various transportation modes. [PERSON] and [PERSON] [17] developed an emergency transportation planning method that integrates air, rail, and road transport to manage uncertainties effectively. They segment the overall problem into sub-components, applying Multi-Objective Tabu Search (MOTS) for task allocation and Multi-Objective Genetic Algorithms (MOGAs) for optimizing delivery schedules and vehicle routes. [PERSON] et al. [18] introduced a method for planning emergency medical supply deliveries using intermodal transportation, including helicopters and vehicles. They employ a balanced Fuzzy C-Means algorithm to select distribution points and standard Fuzzy C-Means to plan routes, aiming to minimize transportation time. Additionally, the research integrates multiple specific issues into a single model, focusing on uncertainty. [PERSON] and [PERSON] [19] developed a stochastic optimization model for relief supply chain decision making, addressing uncertainties such as demand for relief goods, weather conditions, and transportation delays. The model includes inventory management, allocation of goods, and transportation planning. [PERSON] et al. [20] introduced a mixed-integer linear programming (MILP) model for evacuation and relief distribution planning to minimize vehicle arrival times in affected areas. This model accountsfor distance, time, vehicle capacity, and segmented delivery at distribution centers, employing a Memetic Algorithm (MA) for efficiency in large-scale applications. [PERSON] et al. [21] tackled the routing problem within the supply chain to minimize blockages and operational costs using a simulated annealing algorithm for vehicle routing and CPLEX for subproblem evaluation. However, the mentioned research requires extensive data and involves complex calculations applied to small-scale problems. Nonetheless, it also introduces metaheuristic algorithms and search operators to address larger-scale issues. This is crucial because disaster relief operations need to be conducted urgently [22]. Genetic Algorithms (GAs) are frequently used in disaster relief to manage environmental uncertainties due to their flexibility in enhancing response quality and low computation requirements [23]. GAs utilize a mechanism known as crossover to explore the search space and maintain solution diversity, which has been adapted across various fields to improve problem-solving efficiency [24]. However, the literature needs a comprehensive exploration of route planning under dynamic road conditions caused by flooding. Additionally, the distribution patterns of disaster-affected nodes add complexity to the routing process, which requires further study [9; 25; 26; 27]. This paper introduces the VRP-RIDFU model, a vehicle routing plan designed to distribute disaster relief effectively amidst flood-related uncertainties. A Genetic Algorithm (GA), specifically tailored to manage road condition uncertainties, is the primary tool for determining optimal routes. This adjustment includes a risk-based expected value method to part-generate the GA's initial population, integrating flood data and waiting times into this value calculation. The expected values across all routes define the fitness function. The Population Sizing Module (PSM) customizes this population size based on the distribution of disaster-affected nodes, creating a grid that reflects node distribution and uses standard deviation for evaluation.