Inventory cost and delay penalty are two kinds of annoying spendings in manufactory industry. Accordingly, earliness and tardiness penalties are proposed to simulate such scheduling problems where the popular just-in-time (JIT) concept is considered to be of significant importance. In this paper, a self evolution algorithm is proposed to solve the problem of single machine total earliness and tardiness penalties with a common due date. Up to now, such problem has been solved without specific consideration of straddling V-shaped schedules, which may be better than pure V-shaped schedules for early due date problems; without specific discussions on g improving, where g refers to the idle time before the start of the first job; and the many individuals in all so far proposed GA-like algorithms become the bottleneck of execution time reduction. Therefore, in this research, efforts have been made on digging out the straddling V-shaped schedules, improving the efficiency of g improving, and reducing the execution time. In addition, a new RHRM approach is proposed to create the initial solution for evolution, which helps achieve the fast contingency of the algorithm. The performance of the proposed algorithm has been tested on 280 benchmark instances ranging from 10 to 1000 jobs from the OR Library, the results showing that the proposed self evolution algorithm delivers much higher efficiency in finding optimal or near-optimal solutions with both better results in total penalties and significant execution time reduction.