In the present research, a new variant of the Vehicle Routing Problem (VRP), the Environmental Prize-Collecting Vehicle Routing Problem (E-PCVRP), is introduced. The E-PCVRP is a selective routing problem that focuses on the maximization of the aggregated prize values collected from the visited nodes while minimizing the fixed and variable cost of the formed routes. In terms of variable cost, the CO2 emissions of the vehicles performing the routes are considered as a load-distance function. The presented solution approach is based on the Firefly Algorithm (FA). The FA is an optimization algorithm, designed for the solution of continuous problems, while the proposed E-PCVRP, requires a discrete solution approach. Addressing the above discrepancy, the Firefly Algorithm based on Coordinates (FAC) is introduced, which incorporates the proposed “Coordinates Related” (CR) encoding/decoding process in the original FA scheme. The CR is a novel process that allows for algorithms designed for continuous optimization to by employed in the solution of discrete problems, such as the VRP. Specifically, the CR utilizes auxiliary vectors for solution representation, containing the Cartesian coordinates of each node, that allows for the original movement equation of the FA to be applied directly. The effectiveness of the FAC algorithm is showed over computational experiments and statistical analysis, in comparison to the performance of other bio-inspired algorithms and a mathematical solver.

在本研究中，介绍了车辆路径问题（VRP）的新变体，即“环境奖收集车辆路径问题（E-PCVRP）”。E-PCVRP是一个选择性的路由问题，其重点是最大化从拜访节点收集的汇总奖励值，同时最大程度地减少所形成路线的固定成本和可变成本。就可变成本而言，执行路线的车辆的CO2排放被视为负载-距离函数。提出的解决方案方法基于Firefly算法（FA）。FA是一种优化算法，旨在解决连续问题，而提出的E-PCVRP需要离散解决方案。针对以上差异，介绍了基于坐标的萤火虫算法（FAC），它在原始FA方案中合并了建议的“与坐标有关”（CR）编码/解码过程。CR是一种新颖的过程，它允许设计用于连续优化的算法来解决离散问题（例如VRP）。具体而言，CR利用辅助向量进行解决方案表示，其中包含每个节点的笛卡尔坐标，从而可以直接应用FA的原始运动方程。与其他生物启发算法和数学求解器的性能相比，FAC算法的有效性在计算实验和统计分析中得到了证明。CR是一种新颖的过程，它允许设计用于连续优化的算法来解决离散问题（例如VRP）。具体而言，CR利用辅助向量进行解决方案表示，其中包含每个节点的笛卡尔坐标，从而可以直接应用FA的原始运动方程。与其他生物启发算法和数学求解器的性能相比，FAC算法的有效性在计算实验和统计分析中得到了证明。CR是一种新颖的过程，它允许设计用于连续优化的算法来解决离散问题（例如VRP）。具体而言，CR利用辅助矢量进行解决方案表示，其中包含每个节点的笛卡尔坐标，从而可以直接应用FA的原始运动方程。与其他生物启发算法和数学求解器的性能相比，FAC算法的有效性在计算实验和统计分析中得到了证明。