Genetic algorithm for the single machine earliness and tardiness scheduling problem with fuzzy processing times

This paper studies the earliness and tardiness scheduling problem on the single machine with fuzzy processing times. A new membership function of the fuzzy processing times is established. Under some assumptions, the E/T scheduling model with fuzzy processing time is formulated, and a criterion to rank the different fuzzy schemes is also presented. Since the problem is a NP-hard problem, Genetic algorithms are used to search the near optimal solutions. Five different crossover operators are used to construct five genetic algorithms. The last crossover operator is a new crossover ---- Hybrid Crossover (HX) which simultaneously use the other four crossover operators at a generation. By the computation results, the genetic algorithm with the new crossover operator is best of all genetic algorithms.