Artificial chromosomes with genetic algorithm (ACGA) is one of the latest versions of the estimation of distribution algorithms (EDAs). This algorithm has already been applied successfully to solve different kinds of scheduling problems. However, due to the fact that its probabilistic model does not consider variable interactions, ACGA may not perform well in some scheduling problems, particularly if sequence-dependent setup times are considered. This is due to the fact that the previous job will influence the processing time of the next job. Simply capturing ordinal information from the parental distribution is not sufficient for a probabilistic model. As a result, this paper proposes a bi-variate probabilistic model to add into the ACGA. This new algorithm is called the ACGA2 and is used to solve single machine scheduling problems with sequence-dependent setup times in a common due-date environment. A theoretical analysis is given in this paper. Some heuristics and local search algorithm variable neighborhood search (VNS) are also employed in the ACGA2. The results indicate that the average error ratio of this ACGA2 is half the error ratio of the ACGA. In addition, when ACGA2 is applied in combination with other heuristic methods and VNS, the hybrid algorithm achieves optimal solution quality in comparison with other algorithms in the literature. Thus, the proposed algorithms are effective for solving the scheduling problems. 
Artificial chromosomes with genetic algorithm 2 (ACGA2) for single machine scheduling problems with sequence-dependent setup times