Machine scheduling problems have become increasingly complex and dynamic. The complexity and size of the problems require the development of methods and solutions whose efficiency is measured by their ability to find acceptable results within a reasonable amount of time. Therefore, this paper addresses to propose a new mathematical model for multi objective function based on Single-machine scheduling problems  by minimizing  the discounted total weighted completion time the number of tardy jobs the maximum earliness and the maximum weighted tardiness  with release date denoted   +  which are an NP-hard. To achieve efficient solutions, a metaheuristic method (Meerkat clan algorithm (MCA)) is used to solve the mathematical model and compare it with branch and bound (BAB) method. Computational results show that MCA provides efficient solutions in terms of accuracy and calculation speed compared to BAB. In addition, the BAB can solve up to 10 problems, while MCA can resolve problems up to 1000 for multi objective.