# Transportation and Reserve of Emergency Medical Supplies during Public Health Events
## 3 Materials and Methods
### Allocation and Storage Model of Emergency Medical Materials
#### 3.3.3 Solving the Model  
Since [PERSON] proved that vehicle routing problems with time windows (VRPTW) is a NP-hard problem [35], research on this problem has focused mainly on various heuristic algorithms. In the vehicle distribution problem (VRP), heuristic algorithms have shown great advantages in problem solution selection and algorithm runtime [36]. Metaheuristic algorithms are similar to heuristic algorithms, but metaheuristic algorithms consider more important local optimality problems. Among them, PSO algorithm can be used to solve high uncertainty multi-objective optimization problems [37]. Moreover, PSO algorithm has proved to be a very effective method for solving vehicle path-related problems with more easily configurable parameters and wider applicability [38]. The metaheuristic algorithm is an improved scheme of the heuristic algorithm. Meta-heuristic algorithms mainly include Tabu algorithm, simulated annealing, genetic algorithm, ant colony optimization, particle swarm optimization, hybrid jumping frog algorithm, and artificial neural network algorithm [39]. In 1995, [PERSON] and [PERSON] [40] proposed PSO. Meta-heuristic algorithms are simple, parallel, and adaptive and can effectively solve some combinatorial optimization problems in practical applications. Therefore, more and more researchers attach importance to it. In order to solve the above model, the PSO algorithm can be used for calculation. PSO is based on swarm to achieve the global optimum and then obtain the approximate optimal solution of the model. See Table 3 for an explanation of relevant terms, and use Python code for particle swarm optimization. PSO is used to simulate the behavior of birds in the process of randomly searching for food. It is a globally convergent intelligent search algorithm. In PSO, the potential solution of each optimization problem is regarded as a bird in the search space, which is called \"microparticle\". By updating the position, size, and flying height of particles, the population can reach the optimal solution or approximate optimal solution. The \"flight\" direction and distance of each particle are determined by the fitness value determined by an optimized function, while the speed of each particle determines their flight state. PSO is initialized as a group of random particles that constantly seek the optimal solution in the iterative process to achieve the optimal effect. In this paper, a new adaptive particle swarm optimization method is presented, which uses a fast search strategy to optimize each particle locally in each iteration to improve convergence speed and accuracy. In each iteration, the particle will update itself by tracking two extremes, the first of which is the optimal solution discovered by the particle itself; that is, the individual extreme value. The second is the optimal value of the current particle at a new position found in the previous search area, which is called the group extreme value. The optimal solution found by the current population is called global extremum. In this case, if all the particles can be optimized, it is necessary to add some new parameters, called group extremum. Local extremum is a method that does not use the whole population but takes a part of it as the neighbor of particles to achieve the optimization effect. Not depending on the problem itself, it has high efficiency and good robustness in solving complex optimization problems. The \(i\)-th particle is denoted \(x_{i}=(x_{i1},x_{i2},\ldots,x_{iD})\)