Harmony search algorithm to enhance approach to permutation flow shop scheduling problem

The permutation flow-shop scheduling problem (PFSP) is one of the widely analysed and investigated problems within the general field of scheduling, as its major focus is on the allocation and sequencing of a set of jobs across a set of machines in order to minimize the makespan or satisfy other criteria. This paper further generalizes the problem to the distributed permutation flow-shop scheduling problem (DPFSP), namely in a manufacturing system with multiple factories, where every factory employs identical machines; with the objective of achieving the least makespan at the worst factory in terms of processing time. We resolve the issue through a Harmony Search Algorithm (HSA), a metaheuristic model developed from the musical harmonisation concept, together with constraint programming techniques, including interval variables and non-adjacent constraints. The problemsolving algorithm incorporates a lower bound estimation heuristic for efficiently directing the search in the right possible solution zone. Performance evaluation on both the small benchmark and the large benchmark data set showed the ability of the HSA to perform the different assignment in various problem scenarios that include the different number of jobs, machines and factories to support them. Comparisons with the best-known values established the performance of the HSA algorithm in identifying high quality solutions for the PFSP in less computation time.