With limited budget and inflation rate, the materials acquisition in multi-unit libraries has been a challenging issue all over the world. The materials acquisition for multi-unit libraries can be regarded as a generalized version of the knapsack problem, which was known to be NP-hard, with much more constraints. Thus, it can be computationally expensive to solve the problem. In this paper, the materials acquisition problem in multi-unit libraries is formulated as an integer programming model, and two different constraint-handling mechanisms applied in discrete particle swarm optimization algorithm for obtaining the near optimal solution are presented. It is evident from our computational results that one constraint-handling mechanism can solve the problem effectively and efficiently, while the other one takes more time.