Improved discrete cuckoo-search algorithm for mixed no-idle permutation flow shop scheduling with consideration of energy consumption

The increasing number and types of industrial tasks require factories to be more flexible in production. An improved discrete cuckoo search algorithm (CSA) is proposed and used to optimise the mixed no-idle permutation flow shop scheduling problem (MNPFSP). This problem considers MNPFSP energy consumption (MNPFSP_EC) an optimisation objective. Firstly, according to the characteristics of the individual update formula in the two stages of the standard CSA, the paper replaces the real number calculation or vector calculation in the original update formula with a discrete operation to keep the update mechanism of each stage unchanged. The change allows the algorithm to directly find a feasible solution in the discrete solution space that significantly improves the global search capability of cuckoo search. Secondly, an adaptive-starting local search based on quasi-entropy (QE) is constructed using swap, insert and 2-OPT operations with an exploitation that is adaptively executed based on QE, and QE is used to represent the diversity of population and control individuals in deciding whether to execute local search, thereby reducing computational complexity. Simulation experiments and comparisons of different instances demonstrate that the proposed algorithm can effectively solve MNPFSP_EC.