物流运输作为经济发展的关键环节，其合理优化不仅能为物流企业降低运输成本，还有利于能源节约和生态保护。文章以降本、低碳节能为导向，在车辆路径问题中引入低碳理念和软时间窗约束，对模型进行改良；同时研究发现传统算法的求解精度较低，在复杂算例中运算速度慢，采用智能优化算法求解该问题是目前研究热点。鲸鱼优化算法目前已被应用于多个领域并验证其性能。因此，文章对于鲸鱼优化算法存在的问题加以改进，并采用改进算法求解车辆路径规划模型以验证其有效性。主要研究成果有：

（1）针对传统鲸鱼优化算法寻优效率低、易陷入局部极值等缺点，提出一种精英混合扰动的改进鲸鱼优化算法（MDWOA）。首先将对立学习策略与Tent 混沌映射相融合来提高初始种群的多样性；其次基于正余弦函数调整收敛因子，并引入分阶段式惯性权重，来兼顾全局搜索和局部开发能力；为避免算法过早收敛，提出一种精英差分变异策略，结合折射反向变异，对候选解进行自适应混合扰动。在不同维度上通过13个测试函数上进行仿真实验，对比结果表明改进算法在寻优精度和鲁棒性方面均显著提升。

（2）采用MDWOA求解有容量限制的车辆路径问题（Capacitated Vehicle Routing Problem，CVRP），在18个CVRP测试集上的运算结果显示：MDWOA的求解精度和运算速度比其他三种对比算法VDWOA、ALNS和AIGA均有所提升，验证了MDWOA在该问题上的适用性；为了更大程度推动“低碳”经济和满足各利益方需求，在原有车辆路径优化模型中引入软时间窗约束和相应惩罚函数，以及碳排放成本函数，构建低碳车辆路径优化模型。利用MDWOA与四种对比算法在Solomon标准测试集上对新模型进行对比实验，数据显示MDWOA较其他算法均有改进，相对平均改进率最大高达52%，进一步验证改进策略的合理性和有效性，同时求得总成本最小的物流配送方案。

（3）引入医疗物流案例做低碳路线规划。基于医疗物流的特点，在求解实际配送路径优化案例时，将重量约束改为车辆体积约束，同时将碳排放成本与违反时间窗的惩罚成本考虑在内，建立适合医疗物流的低碳路径优化数学模型。将MDWOA用于求解该模型得到医疗物流配送总成本最低的解决方案，降低配送成本的同时减少环境污染。

As a key link in economic development, the rational optimization of logistics and transportation can not only reduce transportation costs for logistics enterprises, but also contribute to energy conservation and ecological protection. Guided by cost reduction, low-carbon and energy-saving, this paper introduces the low-carbon concept and the consideration of multiple stakeholders into the model of the standard vehicle path optimization problem, and improves the model. The whale optimization algorithm is not limited by the objective function, and has been applied to many fields and verified its performance. Therefore, the existing problems of the whale optimization algorithm are improved, and the vehicle path planning model is used to verify its effect. The main research achievements are:

(1) In order to solve the shortcomings of traditional whale optimization algorithms, such as low optimization efficiency and easy to fall into local extremum, an improved whale optimization algorithm based on elite hybrid perturbation (MDWOA) was proposed. Firstly, the adversarial learning strategy is fused with the Tent chaos map to improve the diversity of the initial population, and secondly, the convergence factor is adjusted based on the sine and cosine function, and the staged inertia weights are introduced to take into account the global search and local development capabilities. Simulation experiments are carried out on 13 test functions in different dimensions, and the comparison results show that the improved algorithm has significantly improved the optimization accuracy and robustness.

(2) MDWOA is used to solve the Capacitated Vehicle Routing Problem (CVRP), and the results on 18 CVRP test sets show that the solution accuracy and speed of MDWOA are improved compared with the other three comparison algorithms: VDWOA, ALNS and AIGA, which verifies the applicability of MDWOA to this problem. In order to promote the "low-carbon" economy to a greater extent and meet the needs of all stakeholders, a low-carbon vehicle path optimization model is constructed by introducing soft time window constraints, corresponding penalty functions, and carbon emission cost functions into the original vehicle route optimization model. Using MDWOA and four comparison algorithms to compare the new model on the Solomon standard test set, the data show that MDWOA is improved compared with the other algorithms, and the relative average improvement rate is as high as 52%, which further verifies the rationality and effectiveness of the improvement strategy, and at the same time obtains the logistics distribution scheme with the smallest total cost.

(3) Introduce examples to make low-carbon route planning for medical logistics. Based on the characteristics of medical logistics, when solving the actual medical logistics distribution path optimization case, the weight constraint is changed to the vehicle volume constraint, and the carbon emission cost and the penalty cost of violating the time window are considered, and a low-carbon path optimization mathematical model suitable for medical logistics is established. MDWOA is used to solve the model to obtain the solution with the lowest total cost of medical logistics distribution, which reduces the distribution cost and environmental pollution.