Two Dimension Coding Algorithm for Single Machine Scheduling with Controllable Processing Times

Based on genetic algorithm and schedule theory, a two dimension coding genetic algorithm is presented for solving the NP-hard single machine total weighted completion time problem with controllable processing times. When the mathematic model is given, the two dimension coding method is proposed to describe the job sequence and actual processing time. Because of the problem´s characters, the new crossover and mutation operations of GA are defined. The two dimension coding GA not only can start with better initial populations, but also can reach the solutions more precise and faster. Applying it to the example, the simulation results show that satisfactory performance is obtained