改进野马算法求解低碳开放式送取货选址路径问题

目的 针对当前物流背景下普遍出现的送货公司外包、退换货频繁等问题，结合现有的碳排放政策，提出低碳背景下开放式同时送取货选址−路径模型(Low-Carbon Open Location-routing Problem with Simultaneous Pickup and Delivery Problem，LOLRPSPD)，并通过改进野马算法进行求解。方法 首先设计一种新的解码方式，使得原离散问题可以采用连续算法求解。之后，运用哈尔顿序列生成初始解，改进非线性进化概率因子，使用模拟二进制交叉，增加变异操作，以及精英保留、设置连续失败重新初始化等步骤，改进野马算法。最后，通过6组不同大小的算例将改进野马算法与原始野马算法、模拟退火算法、粒子群算法、遗传算法进行对比。结果 针对中大型算例，改进野马算法远超原始野马算法。针对小型算例，在确保准确率的同时，改进野马算法对比各经典算法也在速度上具有优势。结论 提出的LOLRPSD模型具备合理性，改进的野马算法针对选址路径问题具有较好的搜索能力。

Improved Wild Horse Optimizer for Solving Low-carbon Open Location-routing Problem with Simultaneous Pickup and Delivery Problem

The work aims to propose an Open Location-Routing Problem with Simultaneous Pickup and Delivery (LOLRPSPD) model under the low-carbon background to solve the common problems of outsourcing, frequent return and exchange of goods in delivery companies and solve the problem through the Wild Horse Optimizer. Firstly, a new decoding mode was designed so that the discrete problems could be solved by continuous algorithms. Then, the initial solutions were generated through the Halton sequence to improve the nonlinear evolution probability factor TDR; The simulated binary crossover was used. Polynomial mutation operators were added. Elite preservation, and setting of consecutive failed reinitialization steps were completed. Finally, the effectiveness of the improved algorithm was verified through the comparison results between Improved Wild Horse Optimizer (IWHO), Wild Horse Optimizer (WHO), Simulated Annealing (SA), Particle Swarm Optimization (PSO), and genetic algorithm (GA). The experimental results showed that IWHO in this paper had better optimization ability than normal WHO in terms of large and medium-sized examples, and had a good advantage in the processing of small examples whiling ensuring accuracy. The proposed LOLRPSD model is reasonable, and the Improved Wild Horse Optimizer has better searching ability for LRP problems.