A Discrete Artificial Bee Colony Algorithm for the Energy-Efficient No-Wait Flowshop Scheduling Problem

Abstract

No-wait permutation flow shop scheduling problem (NWPFSP) is a variant of permutation flow shop scheduling problem (PFSP), where the processing of each job must be continuous from start to end without any interruption. That is, once a job starts its processing, it has to be processed until the last machine without any interruption. The aim of this study is to propose an energy-efficient NWPFSP for the determination of a trade-off between total flow time and total energy consumption by obtaining the Pareto optimal set that is the non-dominated solution set. A bi-objective mixed-integer programming model is developed where the machines can operate at different speed levels. Since the problem is NP-complete, an energy-efficient discrete artificial bee colony (DABC), and an energy-efficient genetic algorithm (MOGA), also a variant of this algorithm (MOGALS) are developed, as heuristic methods. First, the performance of these algorithms for comparison with the mathematical model is represented in small size instances in the scope of cardinality and quality of the non-dominated solutions, then it is shown that DABC performs better than two other algorithms in larger instances.