A heuristic-based genetic algorithm for the two-machine flowshop scheduling with learning consideration

• We consider a two-machine flowshop problem with a truncated learning to minimize the makespan.
• We propose four dominant properties and four lower bounds to speed up the searching for an optimal solution.
• We propose a branch-and-bound algorithm and four heuristic based genetic algorithms for the problem.

In scheduling problems, the learning phenomenon is often seen in some practical applications such as in the processing of certain chemicals in oil refineries and in the steel plates or bars produced by a foundry. A review of the literature reveals that most researchers paid more attention to the scheduling with both the single-machine settings and the learning without a bound. This is at odds with reality and thereby highlights the importance of addressing the issue by different approaches. This paper tackles the issue by considering a two-machine flowshop problem with a truncated learning consideration where the objective function is to minimize the makespan. In order to solve the proposed model, a branch-and-bound algorithm is first developed for the optimal solution. Then four genetic heuristic-based algorithms are proposed for the near-optimal solution. In addition, the experimental results of all proposed algorithms are also provided.