Memetic algorithm with node and edge histogram for no-idle flow shop scheduling problem to minimize the makespan criterion

Abstract

This paper presents a memetic algorithm with hybrid node and edge histogram (MANEH) to solve no-idle permutation flow shop scheduling problem (NIPFSP) with the criterion to minimize the maximum completion time (the makespan criterion). The MANEH mainly composes of two components: population-based global search and local refinements for individuals. At the initialization stage, a modified speed-up NEH method and the random initialization are utilized to generate more promising solutions with a reasonable running time. At the population-based global search stage, a random sample crossover is first proposed to construct a hybrid node and edge histogram matrix (NEHM) with superior solutions in the population, and then a new sequence is generated by sampling the NEHM or selecting jobs from a template sequence. At the local refinements stage, an improved general variable neighborhood search with the simulated annealing acceptance (GVNS-SA) is developed to improve the current best individual. The GVNS-SA adopts a random referenced local search in the inner loop and the probability of SA to decide whether accept the incumbent solution for the next iteration. Moreover, the influence of key parameters in the MANEH is investigated based on the approach of a design of experiments (DOE). Finally, numerical simulation based on the benchmark of Ruiz and thorough statistical analysis are provided. The comparisons between MANEH and some existing algorithms as well as MA-based algorithms demonstrate the effectiveness and superiority of the proposed MANEH in solving the NIPFSP. Furthermore, the MANEH improves 89 out of the 250 current best solutions reported in the literature.