引入启发信息的粒子群算法在低碳TSP中的应用

建立低碳旅行商问题的数学模型LCTSP，并验证了模型的有效性。提出一种基于问题启发信息的离散粒子群算法。根据距离和载重信息设计一种新型离散个体生成算子，该算子对个体自身采用多元变异策略，保持个体的“惯性”，同时采用贪婪交叉策略实现个体与个体极值和全局极值之间的信息交互；基于优先卸货信息对个体极值进行局部搜索，调整种群跟踪对象，以快速跳出局部最优；度量种群同化程度，利用点插法和2-Opt算子对全局极值进行精细化搜索，增强挖掘能力，提高搜索精度，降低种群同化速度。将所提算法与6种代表性算法应用于一组不同规模的低碳旅行商问题中，结果表明，所提算法具有更高的求解精度。

Application of particle swarm optimizationwith heuristic information in low-carbon TSP

A mathematical model (LCTSP) of the low-carbon traveling salesman problem is established and its validity is verified. A discrete particle swarm optimization algorithm based on heuristic information is proposed. Firstly, according to the distance and load information, a novel discrete individual generation operator is designed, which adopts the multi-mutation strategy for the individual itself to maintain the “inertia” of the individual, and adopts the greedy crossover strategy to realize the information interaction between the personal best and the global best. Secondly, the personal best is searched locally based on the priority unloading information, and the population tracking object is adjusted to jump out of the local optimum quickly. Thirdly, according to the degree of population assimilation, the point insertion method and the 2-Opt operator are used to search the global best in a refined way, in order to enhance the mining ability, improve the search accuracy and reduce the rate of population assimilation. Experimental results in a group of low-carbon traveling salesman problems with different scales show that the proposed algorithm has higher accuracy than six state-of-the-art algorithms.