A modified migrating birds optimization for solving the steelmaking-continuous casting problem with variable processing times

In this paper, the steelmaking-continuous casting problem with variable processing times is addressed. We present a modified migrating birds optimization (MMBO) to deal with this problem within a reasonable time. For the addressed problem, we use the job permutation to represent the solution and give a detailed decoding process. For the employed algorithm, we introduce a various neighborhood strategy to explore the solution space more widely. And the benefit mechanism is modified to take full advantage of the promising solutions. To evaluate the performance of our proposed algorithm, the other three meta-heuristics are compared and the computational results demonstrate the effectiveness of the MMBO.