<p>Collaborative robots (cobots) are increasingly utilized in assembly lines to assist the human workers or complete assembly tasks independently to reduce human worker cost. Two mixed-integer programming models are formulated to optimize the cycle time in assembly lines with multi-type cobots, parallel collaboration, and considering limited worker numbers. These two models are capable of solving the small-size instances optimally utilizing the CPLEX solver. An improved artificial bee colony algorithm (IABC) and an improved migrating bird optimization algorithm (IMBO) are developed to solve large-size problems. The proposed algorithms propose two vectors (task assignment vector and process alternative vector) for encoding and employ a decoding procedure with a mathematical programming approach to obtain a feasible scheduling scheme. Specifically, IABC proposes an improved onlooker phase to accelerate the evolution of the whole population, improved scout phase to achieve new high-quality solutions, and a local search phase to enhance the exploitation capability. IMBO utilizes an improved leader improvement phase and population improvement phase to accelerate the evolution of the whole swarm and avoid being trapped in local optimum, and a restart mechanism to enhance the algorithm's exploration ability. To evaluate the proposed methods, they are compared with several well-known algorithms such as simulated annealing algorithm, late acceptance hill-climbing algorithm, genetic algorithm, particle swarm optimization algorithm, bee algorithm, original artificial bee colony algorithm, and original migrating bird optimization algorithm. The computational study demonstrates that the proposed methods outperform the original ones and achieve promising performance compared to other methods.</p>