Near-Optimal Solutions for Mold Constraints on Two Parallel Machines

This paper investigates the mold constraints for the two parallel machines problem. The goal is to minimize the makespan. The resource constraint can be defined as a mold. This constraint is also defined as jobs with conflict. Two jobs can't be executed by the two machines simultaneously. The problem is proved to be a non-deterministic polynomial NP-hard one. Different heuristics have been proposed in this paper to solve the studied problem. A novel meta-heuristics algorithm is developed to enhance the proposed heuristics. The computational results and discussions show the performance of the proposed solutions. A different class of instances is implemented to test the proposed heuristics. The results show that the developed heuristics reaches the optimal solution in 96.4% of instances. Therefore, the obtained results represent near-optimal solutions for the studied problem.