A pareto-based discrete harmony search algorithm for bi-objective reentrant hybrid flowshop scheduling problem

Abstract

In this paper, a Pareto-based discrete harmony search (P-DHS) algorithm is proposed to solve the reentrant hybrid flowshop scheduling problem (RHFSP) with the makespan and the total tardiness criteria. For each job, the operation set of each pass is regarded as a sub-job. To adopt the harmony search algorithm to solve the RHFSP, each harmony vector is represented by a discrete sub-job sequence, which determines the priority to allocate all the operations. To handle the discrete representation, a novel improvisation scheme is designed. During the search process, the explored non-dominated solutions are stored in the harmony memory with a dynamic size. The influence of the parameter setting is investigated, and numerical tests are carried out based on some benchmarking instances. The comparisons to some existing algorithms in terms of several performance metrics demonstrate the effectiveness of the P-DHS algorithm.