It has been always critical and inevitable to select and assess the appropriate and efficient vendors for the companies such that all the aspects and factors leading to the importance of the select process should be considered. This paper studies the process of selecting the vendors simultaneously in three aspects of multiple criteria, random factors, and reaching efficient solutions with the objective of improvement. Thus, selecting the vendors is introduced in the form of a mixed integer multiobjective stochastic problem and for the first time it is converted by CCGC (min-max) model to a mixed integer nonlinear single objective deterministic problem. As the converted problem is nonlinear and solving it in large scale will be time-consuming then the artificial bee colony (ABC) algorithm is used to solve it. Also, in order to better understand ABC efficiency, a comparison is performed between this algorithm and the particle swarm optimization (PSO) and the imperialist competitive algorithm (ICA) and Lingo software output. The results obtained from a real example show that ABC offers more efficient solutions to the problem solving in large scale and PSO spends less time to solve the same problem.