Bi-criteria ant colony optimization algorithm for minimizing makespan and energy consumption on parallel batch machines

We investigate the problem of minimizing the makespan and the total electric power cost simultaneously on a set of parallel identical batch-processing machines, where the jobs with non-identical sizes dynamically arrive. To address the bi-criteria problem, a Pareto-based ant colony optimization (PACO) algorithm is proposed. Depending on whether the current batch being delayed after the job is added into, two candidate lists are constructed to narrow the search space. Moreover, heuristic information is designed for each candidate list to guide the search. In addition, the objective-oriented local optimization methods are applied to improve the solution quality. Finally, the proposed algorithm is compared with existing multi-objective algorithms through extensive simulation experiments. The experimental results indicate that the proposed algorithm outperforms all of the compared algorithms, especially for large-scale problems.