An enhanced estimation of distribution algorithm for solving hybrid flow-shop scheduling problem with identical parallel machines

In this paper, an enhanced estimation of distribution algorithm (EEDA) is proposed to solve the hybrid flow-shop scheduling problem with identical parallel machines to minimize makespan. To evaluate the individuals, some decoding rules including the improved permutation scheduling rule, the improved list scheduling rule and the backward scheduling rule are designed for the permutation-based encoding scheme, and then a hybrid decoding method is proposed. To describe the distribution of the solution space for the EEDA, a probability model is built and used to generate new individuals by sampling. To well trace the region with promising solutions, a mechanism is provided to update the model with the superior sub-population. To enhance the exploitation capability, multiple local search operators are incorporated in the framework of the EEDA. The influence of the parameter setting is investigated based on the Taguchi method of design-of-experiment. Extensive numerical testing results based on sets of the well-known benchmarks and the comparisons with some existing algorithms demonstrate the effectiveness of the proposed algorithm.