A Variant Iterated Greedy Algorithm Integrating Multiple Decoding Rules for Hybrid Blocking Flow Shop Scheduling Problem

This paper studies the hybrid flow shop scheduling problem with blocking constraints (BHFSP). To better understand the BHFSP, we will construct its mixed integer linear programming (MILP) model and use the Gurobi solver to demonstrate its correctness. Since the BHFSP exists parallel machines in some processing stages, different decoding strategies can obtain different makespan values for a given job sequence and multiple decoding strategies can assist the algorithm to find the optimal value. In view of this, we propose a hybrid decoding strategy that combines both forward decoding and backward decoding to select the minimal objective function value. In addition, a hybrid decoding-assisted variant iterated greedy (VIG) algorithm to solve the above MILP model. The main novelties of VIG are a new reconstruction mechanism based on the hybrid decoding strategy and a swap-based local reinforcement strategy, which can enrich the diversity of solutions and explore local neighborhoods more deeply. This evaluation is conducted against the VIG and six state-of-the-art algorithms from the literature. The 100 tests showed that the average makespan and the relative percentage increase (RPI) values of VIG are 1.00% and 89.6% better than the six comparison algorithms on average, respectively. Therefore, VIG is more suitable to solve the studied BHFSP.