The Just-In-Time (JIT) concept is of great importance in many manufacturing processes. JIT scheduling problems affects the performance of the whole production procedure, because early in job completion causes inventory cost while delay in job completion raises penalties paid to customers. In this paper, a memorial self evolution algorithm is proposed to solve the problem of total earliness and tardiness penalties on a machine unit with a common due date. Up to now, researches on this problem have paid no specific attention to straddling V-shaped schedules, which may be better than pure V-shaped schedules for early due date cases; and no specific discussions have been made on the start time setting of the first job in a schedule. Thus, efforts have been made on searching good straddling V-shaped schedules, and optimizing start time setting of schedules. A GHRM approach is proposed to create the initial solution for memorial self evolution. Meanwhile a database which keeps the memories of the elite solutions is introduced to deliver better initial solutions for similar problems. The performance of the proposed algorithm has been tested on 280 benchmark instances ranging from 10 to 1000 jobs. The results show that the proposed memorial self evolution algorithm delivers better results in in finding optimal or near-optimal solutions than previous researches.