Human-robot collaborative assembly is recognized as an essential component of intelligent manufacturing systems, combining human flexibility with machine efficiency, thereby enhancing the effectiveness and adaptability of assembly tasks. However, challenge in adaptability, decision-making, and responsiveness to changing scenarios persist. To address these, this paper propose a digital twin-driven decision-making approach for task allocation, using an Improved Genetic Algorithm with Tabu Search (IGA-TS). First, an assembly task evaluation model and digital twin framework are developed to support dynamic decision-making. Subsequently, the IGA-TS algorithm integrates a custom encoding scheme, fitness function, tabu list, and neighborhood search to avoid local optima, enhancing global optimization and convergence speed. Lastly, a digital twin-assisted system, combining human body modeling and motion recognition, enables real-time optimization feedback, forming a closed-loop for collaboration. Experimental results show that IGA-TS outperforms traditional genetic algorithms and heuristic methods in multi-objective optimization, reducing assembly time, task complexity, and human workload. In addition, the designed digital twin system demonstrates strong adaptability and robustness in responding to dynamic changes during the assembly process, providing a practical and feasible solution for manufacturing workshop assembly. It significantly enhances production efficiency and product quality, offering substantial industrial application value.