In the setting of a single machine, this study suggests approximation local search strategies to identify approximate solutions to the multi-objective sequencing problem, where the problem is the total of the four objectives: total completion time ∑Cj j= 1,….,n, total lateness ∑Lj, maximum lateness Lmax and maximum earliness Emax. Descent Method (DM), Simulated Annealing (SA), and genetic algorithm (GA) are three approximate local search techniques that are computer-implemented Matlab programs. On the basis of the outcomes of computing tests, conclusions are modeled on the effectiveness of the local search techniques.