In this paper, we propose an algorithm (CLLE) to find efficient solutions for multi-objective sequencing problem on one machine. The objectives are total completion time ($\sum C_j$), total lateness ($\sum L_j$), maximum lateness ($L_{\max}$) and maximum earliness ($E_{\max}$). A collection of dependent jobs (tasks) has to be sequenced on one machine, jobs $j$ ($j=1,2,3,\dots,n$) required processing time $p_j$ and due date $d_j$. Conclusions are formulated from the (CLLE) algorithm based on results of computational experiments.