A meta-heuristic for minimizing total weighted flow time on parallel batch machines

To address the problem of minimizing the total weighted completion time on parallel batch processing machines with identical machine capacities, non-identical job sizes and unequal weights, an effective meta-heuristic based on ant colony optimization is proposed. After presenting a mathematic model of the problem, we provide an algorithm to calculate the lower bound. Then, a meta-heuristic is proposed to solve the problem. The heuristic information is defined with consideration of job weights and job sizes. Meanwhile, a candidate set for constructing the solution is used to narrow the search space. Additionally, to improve the solution quality, a local optimization strategy is incorporated. Simulation results show that the proposed algorithm is able to obtain a high-quality solution within a reasonable time, and outperforms the compared algorithms.