摘要：

针对疫苗配送路径优化问题，在同时考虑固定成本、运输成本、制冷成本、碳排放成本和惩罚成本的情况下，提出以疫苗配送成本最小化为目标的车辆路径优化模型。为求解模型，在平衡优化器算法中引入模拟退火算法，改进平衡优化器算法容易陷入局部最优的不足，通过加入可变参数，提升算法平衡全局搜索和局部寻优的能力，得到一个能够稳定求出较高质量解的混合平衡优化算法。对2种不同规模的算例分别进行20次实验，将混合平衡优化算法与并行平衡优化算法、知识型蚁群算法、混合变邻域搜索算法、改进混合粒子群算法和平衡优化器算法进行对比。实验结果表明，混合平衡优化算法在小规模算例和大规模算例下得到的最小配送成本和配送成本的标准差都小于其他5种算法，其中，在小规模算例下进行实验后得到的最小配送成本分别为其他5种算法的73.5%、53.9%、69.1%、64.1%和33.4%。

关键词: 疫苗冷链配送, 车辆路径优化, 资源满意度, 惩罚函数, 混合平衡优化算法

Abstract:

Aiming at the optimization problem of vaccine distribution route, a vehicle routing optimization model aiming at minimizing vaccine distribution cost is proposed in this study, considering the fixed, transportation, refrigeration, carbon emission, and penalty costs. To solve the model, the Simulated Annealing(SA) algorithm is introduced into the Equilibrium Optimizer(EO) algorithm to improve the shortage of the EO algorithm, which is easy to fall into the local optimal. The variable parameters are added to improve the ability of the algorithm to balance the global search and local optimization, and a hybrid EO algorithm that can stably obtain high quality solutions is obtained. By conducting 20 experiments on two examples with different scales, the hybrid EO and parallel balance optimization algorithms, the knowledge based, hybrid variable neighborhood search algorithm, improved hybrid particle swarm optimization, ant colony algorithm, and the EO algorithm are compared. The results demonstrate that the standard deviation of the minimum and minimum distribution costs obtained by the hybrid EO algorithm is smaller than that of the other five algorithms in the case of small or large-scale calculation. For instance, the minimum distribution cost obtained in the case of small-scale calculation is 73.5%, 53.9%, 69.1%, 64.1%, and 33.4% of the other five algorithms, respectively.

Key words: cold chain delivery of vaccine, vehicle route optimization, resource satisfaction, penalty function, hybrid equilibrium optimization algorithm