In our previous researches, we proposed the artificial chromosomes with genetic algorithm (ACGA) which combines the concept of the Estimation of Distribution Algorithms (EDAs) with genetic algorithms (GAs). The probabilistic model used in the ACGA is the univariate probabilistic model. We showed that ACGA is effective in solving the scheduling problems. In this paper, a new probabilistic model is proposed to capture the variable linkages together with the univariate probabilistic model where most EDAs could use only one statistic information. This proposed algorithm is named extended artificial chromosomes with genetic algorithm (eACGA). We investigate the usefulness of the probabilistic models and to compare eACGA with several famous permutation-oriented EDAs on the benchmark instances of the permutation flowshop scheduling problems (PFSPs). eACGA yields better solution quality for makespan criterion when we use the average error ratio metric as their performance measures. In addition, eACGA is further integrated with well-known heuristic algorithms, such as NEH and variable neighborhood search (VNS) and it is denoted as eACGAhybrid to solve the considered problems. No matter the solution quality and the computation efficiency, the experimental results indicate that eACGAhybrid outperforms other known algorithms in literature. As a result, the proposed algorithms are very competitive in solving the PFSPs.
