Surrogate Objective based Search Heuristics to Minimize the Number of Tardy Jobs for Multi-Stage Hybrid Flow Shop Scheduling

This paper considers the hybrid flow shop scheduling problem for the objective of minimizing the number of tardy jobs. In hybrid flow shops, each job is processed through multiple production stages in series, each of which has multiple identical parallel machines. The problem is to determine the allocation of jobs to the parallel machines at each stage as well as the sequence of the jobs assigned to each machine. Due to the complexity of the problem, we suggest search heuristics, tabu search and simulated annealing algorithms with a new method to generate neighborhood solutions. In particular, to evaluate and select neighborhood solutions, three surrogate objectives are additionally suggested because not much difference in the number of tardy jobs can be found among the neighborhoods. To test the performances of the surrogate objective based search heuristics, computational experiments were performed on a number of test instances and the results show that the surrogate objective based search heuristics were better than the original ones. Also, they gave the optimal solutions for most small-size test instances