Abstract
This study investigates constrained group formation in intelligent group-buying platforms where users may express interest in multiple offers while remaining subject to individual budgets, product capacities, minimum group-size thresholds, and participation limits. A Hybrid Combinatorial Group Optimization (HCGO) framework is proposed that combines feasibility-preserving candidate filtering, exact binary integer optimization when the reduced candidate-set size satisfies , and activation-oriented heuristic construction with bounded local refinement when . The evaluation uses three reproducible synthetic scenarios and 30 paired seeded realizations per scenario. HCGO achieved group-completion rates of 93.92%, 90.63%, and 56.86% under low-demand, high-diversity, and high-load conditions, respectively, with zero final hard-constraint violations in all runs. In Scenario B, where exact optimality was proven for all 30 ILP runs, HCGO achieved a mean total utility of 508.32 compared with 532.14 for exact ILP, corresponding to a mean optimality gap of 4.48% (BCa 95% CI: 4.13–4.90%), while reducing mean runtime from 201.63 to 28.86 ms. The framework integrates controlled multi-group participation with a reproducible exact–heuristic dispatch mechanism and demonstrates a measurable quality–runtime trade-off suitable for intelligent group-buying platform design.