A Cooperated Imperialist Competitive Algorithm for Unrelated Parallel Batch Machine Scheduling Problem

This study focuses on the scheduling problem of unrelated parallel batch processing machines (BPM) with release times, a scenario derived from the moulding process in a foundry. In this process, a batch is initially formed, placed in a sandbox, and then the sandbox is positioned on a BPM for moulding. The complexity of the scheduling problem increases due to the consideration of BPM capacity and sandbox volume. To minimize the makespan, a new cooperated imperialist competitive algorithm (CICA) is introduced. In CICA, the number of empires is not a parameter, and four empires are maintained throughout the search process. Two types of assimilations are achieved: The strongest and weakest empires cooperate in their assimilation, while the remaining two empires, having a close normalization total cost, combine in their assimilation. A new form of imperialist competition is proposed to prevent insufficient competition, and the unique features of the problem are effectively utilized. Computational experiments are conducted across several instances, and a significant amount of experimental results show that the new strategies of CICA are effective, indicating promising advantages for the considered BPM scheduling problems.