Abstract: A single machine n job scheduling problem is examined to minimize the sum of absolute deviations of completion times from a common due date. Simple and hybrid genetic algorithms are developed by investigating basic operators for the application to the job sequencing problems. For the simple genetic algorithm two heuristic crossover schemes: Algorithm VASX and Algorithm VADX are developed based on the important properties of the scheduling problem. Local improvement techniques are considered to enhance the solution quality of the simple genetic algorithms. The performance of the two heuristic crossover methods are compared and the power of the genetic algorithm is illustrated.