Improved hybrid estimation of distribution algorithm for distributed parallel assembly permutation flow shop scheduling problem

Distributed assembly permutation flow shop scheduling problem is the hot spot of distributed pipeline scheduling research; however, parallel assembly machines are often in the assembly stage. Therefore, we propose and study distributed parallel assembly permutation flow shop scheduling problem (DPAPFSP). This aims to enhance the efficiency of multi-factory collaborative production in a networked environment. Initially, a corresponding mathematical model was established. Then, an improved hybrid distribution estimation algorithm was proposed to minimize the makespan. The algorithm adopts a single-layer permutation encoding and decoding strategy based on the rule of the Earliest Finished Time. A local neighbourhood search based on critical paths is performed for the optimal solution using five types of neighborhood design. A dual sampling strategy based on repetition rates was introduced to ensure the diversity of the population in the later periods of iteration. Simulated annealing searching was applied to accelerate the decline of optimal value. Finally, we conduct simulation experiments using 900 arithmetic cases and compare the simulation experimental data of this algorithm with the other four existing algorithms. The analysis results demonstrate this improved algorithm is very effective and competitive in solving the considered DPAPFSP.