A new history-guided multi-objective evolutionary algorithm based on decomposition for batching scheduling

In this paper, a multi-objective scheduling problem on parallel batching machines is investigated with three objectives, the minimization of the makespan, the total weighted earliness/tardiness penalty and the total energy consumption, simultaneously. It is known that the batch scheduling problem is a type of NP-hard problems and the solutions to this problem have quite valuable structural features that are difficult to be formulated. One of the main issues is to make full use of the structural features of the existing solutions. Aiming at this issue, two effective strategies, local competition and internal replacement, are designed. Firstly, the local competition searches for the competitive neighboring solutions to accelerate convergence, through adjusting job positions based on two structural indicators. Secondly, the internal replacement uniformly retains half of the population as elites by elitist preservation based on decomposition. Thereafter, the other half of the population is replaced by the new solutions generated under the guidance of historical information. Moreover, the historical information is updated with the structural features extracted from the elites. As a result, a history-guided evolutionary algorithm based on decomposition with the above two strategies is proposed. To verify the performance of the proposed algorithm, extensive experiments are conducted on 18 groups of instances, in comparison with four state-of-the-art multi-objective optimization algorithms. Experimental results demonstrate that the proposed algorithm shows considerable competitiveness in addressing the studied multi-objective scheduling problems.