# A Hybrid Brain Storm Optimization Algorithm to Solve the Emergency Relief Routing Model
###### Abstract  
Due to the inappropriate or untimely distribution of post-disaster goods, many regions did not receive timely and efficient relief for infected people in the coronavirus disease outbreak that began in 2019. This study develops a model for the emergency relief routing problem (ERRP) to distribute post-disaster relief more reasonably. Unlike general route optimizations, patients' suffering is taken into account in the model, allowing patients in more urgent situations to receive relief operations first. A new metaheuristic algorithm, the hybrid brain storm optimization (HBSO) algorithm, is proposed to deal with the model. The hybrid algorithm adds the ideas of the simulated annealing (SA) algorithm and large neighborhood search (LNS) algorithm into the BSO algorithm, improving its ability to escape from the local optimum trap and speeding up the convergence. In simulation experiments, the BSO algorithm, BSO+LNS algorithm (combining the BSO with the LNS), and HBSO algorithm (combining the BSO with the LNS and SA) are compared. The results of simulation experiments show the following: (1) The HBSO algorithm outperforms its rivals, obtaining a smaller total cost and providing a more stable ability to discover the best solution for the ERRP; (2) the ERRP model can greatly reduce the level of patient suffering and can prioritize patients in more urgent situations. relief routing; BSO algorithm; hybrid algorithms; route optimization 20232023158187. 20232023158187.  
location can speed up the efficiency of rescue vehicles to a certain extent [3]. In the specific context of emergencies, the time sensitivity of the post-disaster routing problem can be high [4]. By dispatching assessment vehicles, establishing an assessment and response system [5], and validating the needs identified by social media [6], rescue needs can be predicted more accurately. The emergency repair of the damaged road network after a disaster [7] is highly important in the implementation of relief operations. Mobile Internet networks can be applied to disaster relief scenarios to ensure communication between rescuers and casualties, and to achieve improved connectivity in small-scale disaster areas [8]. The emergency relief problem has been examined from many perspectives by the academics described above, and several feasible optimization strategies for emergency relief have been proposed. There are only some optimizations that have been made to models, which have not made the solutions for the ERRP faster or more accurate. Furthermore, the relief distribution problem in emergencies has received little attention. ERRP is a complex optimization problem that arises in emergency management scenarios, such as natural disasters or humanitarian crises. The objective of ERRP is to minimize rescue time, maximize the number of people whose probability of survival exceeds a marginal level, or minimize loss of life and human suffering under various constraints, such as capacity constraints and time windows [9; 10; 11]. Post-disaster emergency relief and material distribution can be viewed as a specific type of vehicle routing problem (VRP) with time windows, which has garnered considerable attention in the field of path selection. VRP with time windows plays a crucial role in various aspects of our daily lives, ranging from small delivery arrangements for take-away and express delivery to large-scale deployment of materials across different regions. While traditional VRP models can be adapted for scheduling emergency supplies, such models have significant limitations when it comes to emergency relief and material distribution. In contrast to solving VRPs, where minimizing total cost and time is typically the main objective, solving the ERRP requires more consideration of the degree of suffering of the patients or casualties. Priority must be given to patients in more critical conditions. Consequently, a realistic gap exists between traditional VRP models and ERRP models.