An adaptive penalty guided genetic algorithm for scheduling parallel batch processing machines

We study the problem of scheduling a set of jobs with non-identical capacity requirements on parallel non-identical batch processing machines to minimise the makespan. We formulate the problem as a nonlinear integer programming model. Given that this problem is NP-hard, we propose a genetic algorithm to heuristically solve it. An adaptive penalty is combined to guide the search process to explore promising feasible and infeasible regions. Random problem instances were generated to test the approach with respect to solution quality and run time. Computational results demonstrate the effectiveness of the proposed algorithm.