The pickup and delivery problem (PDP) is a very common and important problem, which has a large number of real-world applications in logistics and transportation. In PDP, customers send transportation requests to pick up an object from one place and deliver it to another place. This problem is under the focus of researchers since the last two decades with multiple variations. In the literature, different variations of PDP with different number of objectives and constraints have been considered. Depending on the number of objectives, multi and many-objective evolutionary algorithms have been applied to solve the problem and to study the conflicts between objectives. In this paper, PDP is formulated as a many-objective pickup and delivery problem (MaOPDP) with delay time of vehicle having six criteria to be optimized. To the best of our knowledge, this variation of PDP has not been considered in the literature. To solve the problem, this paper proposes a memetic I-DBEA (Improved Decomposition Based Evolutionary Algorithm), which is basically the modification of an existing many-objective evolutionary algorithm called I-DBEA. To demonstrate the superiority of our approach, a set of experiments have been conducted on a variety of small, medium and large-scale problems. The quality of the results obtained by the proposed approach is compared with five existing multi and many-objective evolutionary algorithms using three different multi-objective evaluation measures such as hypervolume (HV), inverted generational distance (IGD) and generational distance (GD). The experimental results demonstrate that the proposed algorithm has significant advantages over several state-of-the-art algorithms in terms of the quality of the obtained solutions.

中文翻译：

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使用基于模因分解的进化算法优化具有车辆延迟时间的多目标接送问题

取货和配送问题（PDP）是一个非常普遍和重要的问题，在物流运输中有着大量的实际应用。在 PDP 中，客户发送运输请求以从一个地方取件并将其运送到另一个地方。自过去二十年以来，这个问题一直是研究人员关注的焦点，具有多种变化。在文献中，已经考虑了具有不同数量的目标和约束的 PDP 的不同变体。根据目标的数量，已应用多目标和多目标进化算法来解决问题并研究目标之间的冲突。在本文中，PDP 被表述为一个多目标取货和交付问题 (MaOPDP)，其中车辆的延迟时间有六个要优化的标准。据我们所知，文献中没有考虑 PDP 的这种变化。为了解决这个问题，本文提出了一种模因 I-DBEA（改进的基于分解的进化算法），它基本上是对现有的称为 I-DBEA 的多目标进化算法的修改。为了证明我们方法的优越性，我们对各种小型、中型和大型问题进行了一系列实验。将所提出方法获得的结果的质量与现有的五种多目标和多目标进化算法进行比较，使用三种不同的多目标评估措施，如超体积（HV）、反向代距离（IGD）和代距离（GD）。