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.