Recently, deep reinforcement learning has gained attention for solving routing problems due to its ability to learn complex patterns and optimize sequential decision-making. Despite their success in various routing problems, the applicability of learning-based methods on pickup and delivery problems (PDPs) is limited and only addresses one-to-one PDPs and their variants. However, the many-to-many PDP addressed in this paper is a practical variant of the routing problems and finds several applications in logistics and supply chains. We propose a novel reinforcement learning framework empowered by a multi-head heterogeneous attention mechanism (MHHA) and a decoder capable of exploring a diverse set of solutions, namely HAP, to generate efficient solutions for many-to-many PDP. The proposed framework incorporates an encoder-decoder structure designed explicitly for many-to-many PDP. In particular, the encoder consists of the MHHA mechanism to capture the many-to-many relationships and effectively model the flow constraints. Moreover, it is integrated with the multi-solution generator, polynet and masking scheme to generate high-quality diverse solutions. Additionally, we improve the solution quality of HAP using a warm starting variable neighbourhood search. As extensive experimental results demonstrate, the proposed method outperforms state-of-the-art metaheuristic and learning-based approaches. Additionally, in bi-objective (time and gap) comparison, the HAP lies on the Pareto efficient frontier, proving its effectiveness. Moreover, the HAP effectively generalizes to diverse problem sizes, unseen data distributions, benchmark datasets, and also solves one-to-one PDP more effectively than baseline methods, showing its adaptability and robustness. Finally, we conduct ablation studies to justify the proposed design.

A major challenge in machine learning is the accurate categorization of data in the presence of noise, outliers, and imbalanced class distributions. Fuzzy support vector machines and their variants have demonstrated potential in handling noise and outliers but struggle to address the challenge of imbalanced datasets. To deal with this problem, in this article, we propose a novel relative density and non-membership-based intuitionistic fuzzy twin support vector machine for class imbalance learning. The method utilizes a$k$-nearest neighbor-based probability density estimation to assess the significance of each training pattern. Furthermore, a novel relative density and non-membership (RDNM) based membership function is employed to effectively distinguish noise and outliers from support vectors. To address the class imbalance problem, majority class training patterns are assigned a score function incorporating the imbalance ratio, while minority class patterns are given a higher membership degree of unity. To validate the superiority of the proposed method, comprehensive experiments, and statistical analyses are conducted over 30 imbalanced benchmark datasets, employing linear and non-linear kernels, and compare the outcomes with the existing approaches. Additionally, the proposed model is applied to the HAM10000 dataset, which consists of dermatoscopic images for skin lesion classification, showcasing its effectiveness in medical applications. The experimental results demonstrate that the proposed model surpasses the baseline models, underscoring its capability for addressing classification challenges in real-world applications with imbalanced class distributions.