Iterated-greedy-based algorithms with beam search initialization for the permutation flowshop to minimise total tardiness.

•We address the permutation flow shop to minimise total tardiness.•We propose an efficient constructive heuristic using a beam-search-based approach.•We propose an iterated greedy algorithm for the problem.•We compare several types of destruction-construction phases.•We conduct a comprehensive evaluation of a total of 23 algorithms.