Abstract
The paper considers the problem of forming user groups in intelligent group shopping systems in conditions of heterogeneous preferences and the possibility of multiple user participation. Unlike traditional group purchase models, in which each user can only be part of one active group, the proposed approach allows simultaneous user participation in several groups, which significantly increases the flexibility of the system and expands the space of acceptable solutions. The task of forming groups is formalized as a combinatorial optimization problem and presented as an integer linear programming model with binary variables. The model considers practical constraints, including minimum group size, user participation limits, budget constraints, and user compatibility with products. To overcome the computational complexity typical of high-dimensional problems, a hybrid algorithmic approach is proposed that combines combinatorial filtering, greedy heuristics, and precise integer programming methods applied to reduced sets of candidates. The mechanism of incremental updating of solutions is also considered, ensuring the adaptability of the system in a dynamic environment. An illustrative example demonstrates the correctness and interpretability of the proposed model and algorithm. The results show that the assumption of multiple user participation makes it possible to increase the total usefulness of the system and increase the effectiveness of group activation compared to classical approaches, which confirms the practical applicability of the proposed solution in intelligent e-commerce platforms.