To minimize the makespan for scheduling the jobs with non-identical sizes and dynamic arrivals on the parallel batch process machines with non-identical capacities, an effective meta-heuristic is proposed.A lower bound is presented to measure the performance of algorithm.Based on the weak restriction for the first jobs of the batches under construction, two selection strategies are proposed and used to improve the ant colony optimization(ACO) algorithm.The proposed algorithm is compared with several up-to-date algorithms and the ACO algorithm using usual selection method by simulations.The results demonstrate the effectiveness of selecting the first jobs used in the proposed ACO algorithm, the weak restriction where the jobs with larger sizes have larger probability to be selected, and the proposed algorithm has obvious superiority in search performance than the others.