A multi-population, multi-objective memetic algorithm for energy-efficient job-shop scheduling with deteriorating machines

This paper focuses on an energy-efficient job-shop scheduling problem within a machine speed scaling framework, where productivity is affected by deterioration. To alleviate the deterioration effect, necessary maintenance activities must be put in place during the scheduling process. In addition to sequencing operations on machines, the problem at hand aims to determine the appropriate speeds of machines and positions of maintenance activities for the schedule, in order to minimise the total weighted tardiness and total energy consumption simultaneously. To deal with this problem, a multi-population, multiobjective memetic algorithm is proposed, in which the solutions are distributed into sub-populations. Besides a general local search, an advanced objective-oriented local search is also executed periodically on a portion of the population. These local search methods are designed based on a new disjunctive graph introduced to cover the solution space. Furthermore, an efficient non-dominated sorting method for bi-objective optimisation is developed. The performance of the memetic algorithm is evaluated via a series of comprehensive computational experiments, comparing it with state-of-the-art algorithms presented for job-shop scheduling problems with/without considering energy efficiency. Experimental results confirm that the proposed algorithm can outperform other algorithms being compared across a range of performance metrics.