BRKGA-VNS for Parallel-Batching Scheduling on a Single Machine with Step-Deteriorating Jobs and Release Times

摘要

This paper investigates the problem of scheduling step-deteriorating jobs with release times on a single parallel-batching machine. The processing time of each job can be represented as a simple non-linear step function of its starting time. The machine can process up to c jobs simultaneously as a batch. The objective is to minimize the makespan, and we show that the problem is strongly NP-hard. Then, a hybrid meta-heuristic algorithm BRKGA-VNS combining biased random-key genetic algorithm (BRKGA) and variable neighborhood search (VNS) is proposed to solve this problem. A heuristic algorithm H is developed based on the structural properties of the problem, and it is applied in the decoding procedure of the proposed algorithm. A series of computational experiments are conducted and the results show that the proposed hybrid algorithm can yield better solutions compared with BRKGA, PSO (Particle Swarm Optismization), and VNS.