This paper presents a new extension of SALBP-2, so called assembly line resource assignment and balancing problem of type 2 (ALRABP-2). Two main differences from the existing literature are revealed in this work. The first is on the objective function which is a multiple one. It is aimed here to minimize both the cycle time and the cost per time unit (hour) of a line for a fixed number of stations to satisfy the constraints of precedence between tasks and compatibility between resources. The second difference lies in the proposed method to solve this problem. A new version of multi-objective genetic algorithm (MOGA) called hybrid MOGA (HMOGA) is elaborated. Full experiment design is used to obtain a better MOGA parameters combination. The effectiveness of the HMOGA was assessed through a set of literature problems. The performance of HMOGA shows a good quality of the fronts generated and a better problem-solving capacity for two optimisations.