Solving pickup and drop-off problem using hybrid pointer networks with deep reinforcement learning.

In this study, we propose a general method for tackling the Pickup and Drop-off Problem (PDP) using Hybrid Pointer Networks (HPNs) and Deep Reinforcement Learning (DRL). Our aim is to reduce the overall tour length traveled by an agent while remaining within the truck's capacity restrictions and adhering to the node-to-node relationship. In such instances, the agent does not allow any drop-off points to be serviced if the truck is empty; conversely, if the vehicle is full, the agent does not allow any products to be picked up from pickup points. In our approach, this challenge is solved using machine learning-based models. Using HPNs as our primary model allows us to gain insight and tackle more complicated node interactions, which simplified our objective to obtaining state-of-art outcomes. Our experimental results demonstrate the effectiveness of the proposed neural network, as we achieve the state-of-art results for this problem as compared with the existing models. We deal with two types of demand patterns in a single type commodity problem. In the first pattern, all demands are assumed to sum up to zero (i.e., we have an equal number of backup and drop-off items). In the second pattern, we have an unequal number of backup and drop-off items, which is close to practical application, such as bike sharing system rebalancing. Our data, models, and code are publicly available at Solving Pickup and Dropoff Problem Using Hybrid Pointer Networks with Deep Reinforcement Learning.

Clustering algorithm with strength of connectedness for m-polar fuzzy network models.

In this research study, we first define the strong degree of a vertex in an m-polar fuzzy graph. Then we present various useful properties and prove some results concerning this new concept, in the case of complete m-polar fuzzy graphs. Further, we introduce the concept of m-polar fuzzy strength sequence of vertices, and we also investigate it in the particular instance of complete m-polar fuzzy graphs. We discuss connectivity parameters in m-polar fuzzy graphs with precise examples, and we investigate the m-polar fuzzy analogue of Whitney's theorem. Furthermore, we present a clustering method for vertices in an m-polar fuzzy graph based on the strength of connectedness between pairs of vertices. In order to formulate this method, we introduce terminologies such as ϵA-reachable vertices in m-polar fuzzy graphs, ϵA-connected m-polar fuzzy graphs, or ϵA-connected m-polar fuzzy subgraphs (in case the m-polar fuzzy graph itself is not ϵA-connected). Moreover, we discuss an application for clustering different companies in consideration of their multi-polar uncertain information. We then provide an algorithm to clearly understand the clustering methodology that we use in our application. Finally, we present a comparative analysis of our research work with existing techniques to prove its applicability and effectiveness.