In supply chain network (SCN) management, multi-objective Pareto optimization means the network can meet the demand for both minimal cost and minimal lead-time in SCN. Due to the compromise between cost and lead-time, it is a non-trivial issue to search for multi-objective Pareto optimal solutions (POS) in SCN. Furthermore, with the wide application of the internet, an increasing number of SCN applications have been based on the internet. As a result, the complexity of SCN increases exponentially with the number of suppliers increasing. It is really a big challenge to find the global multi-objective POS within a limited time in SCN management. In order to solve this problem, first, this paper proposes an artificial bee colony (ABC) optimization algorithm with two improvements: (1) a novel solution framework designed to extend the application field of the SCN based on complex network; (2) the acceleration of search speed by adopting naive Bayes classifier. Second, the paper provides a case example of optimizing a three-echelon SCN with the objective of minimizing both cost and lead-time. After the simulation with this example, it turns out that the enhanced ABC algorithm can satisfy the requirements of: (1) finding the global multi-objective POS; (2) improving the speed of finding optimal solutions in SCN management.