An effective discrete differential evolution algorithm for scheduling uniform parallel batch processing machines with non-identical capacities and arbitrary job sizes

Batch processing machines (BPMs) simultaneously process multiple jobs in a batch, which are commonly used in many industrial systems. This paper studies the scheduling problem of uniform parallel batch processing machines with arbitrary job sizes. These batch processing machines have non-identical capacities and different speeds. The objective is to minimize the makespan (or maximize the machine utilization). We formulate this problem as a mixed integer programming model. Since the problem is strongly NP-hard, an effective differential evolution-based hybrid algorithm is proposed for solving large-scale problems. Firstly, in this algorithm, individuals in the population are represented as discrete job sequences, and novel mutation and crossover operators are designed based on this representation. Next, a heuristic is developed to form batches and schedule the resulting batches on the uniform parallel machines. Then, the performance of the proposed algorithm is evaluated by comparing its results to a commercial solver (CPLEX), a random keys genetic algorithm (RKGA) and a particle swarm optimization (PSO) algorithm. Experimental results demonstrate the superiority of the proposed algorithm in terms of solution quality and robustness, especially for large-scale instances.