Scheduling is one of the very important tools for treating a complex combinatorial optimization problem (COP) model, where it can have a major impact on the productivity of a manufacturing process. The most well known models of scheduling are confirmed as NP-hard or NP-complete problems. The aim of scheduling is to find a schedule with the best performance through selecting resources for each operation, the sequence for each resource and the beginning time. Genetic algorithm is one of the most efficient methods among metaheuristics for solving the real-world manufacturing problems. In this paper we firstly survey the literature on genetic algorithms (GAs) with GPU acceleration. A parallel multiobjective GA (MoGA) acceleration with CUDA (Compute Unified Device Architecture) will be introduced. A parallel hybrid multiobjective GA with learning is introduced through a real-world case study of the train scheduling problem and numerical experiments on GPU for multiobjective GA approaches are also demonstrated.