A bi-objective evolutionary algorithm scheduled on uniform parallel batch processing machines

This paper addresses the problem of minimizing the maximum lateness and the total pollution emission costs by scheduling a group of jobs with different processing times, sizes, release times, and due dates on uniform parallel batch processing machines with non-identical machine capacities and different unit pollution emission costs. We develop a discrete bi-objective evolutionary algorithm C-NSGA-A to solve this problem. On the one hand, we present a method of constructively generating an individual with the first job selection to produce an initial population for improving the convergence of individuals. On the other hand, we propose an angle-based environmental selection strategy to choose individuals to maintain the diversity of individuals. Through extensive simulation experiments, C-NSGA-A is compared with several state-of-the-art algorithms, and experimental results show that the proposed algorithm performs better than those algorithms. Moreover, the proposed algorithm has more obvious advantages on instances with a larger number of jobs.