Abstract
This research focuses on studying the correlated parallel machine scheduling problem with release dates to minimize the number of tardy jobs and the total weighted completion time to find Pareto optima of all non-dominated solutions for both criteria. First, a mixed integer programming (MIP) model to find the entire efficient frontier for the studied problem has been proposed. Next, a bicriteria heuristic, named UTWC, and three artificial bee colony (ABC) variant algorithms have been proposed to tackle the studied problem. The three ABC variant algorithms are ABC, ABC with variable neighborhood search scheme (ABC_VNS), and ABC with simulated annealing scheme (ABC_SA). For small problem instances, we compare the proposed heuristic UTWC and three ABC variant algorithms with the efficient frontier generated by solving the MIP model. For large problem instances, we compare the UTWC and three ABC variant algorithms with an existing multi-objective tabu search algorithm (TSA). We create a reference set by combining the solutions from the three ABC variant algorithms and the TSA. The computational results indicate that the UTWC heuristic can find a set of non-dominated solutions that are uniformly distributed above the efficient frontier. The proposed ABC_VNS algorithm outperforms all the compared algorithms in both small and large problem instances.
