A Trajectory-Based Immigration Strategy Genetic Algorithm to Solve a Single-Machine Scheduling Problem with Job Release Times and Flexible Preventive Maintenance

This paper considers the single-machine problem with job release times and flexible preventive maintenance activities to minimize total weighted tardiness, a complicated scheduling problem for which many algorithms have been proposed in the literature. However, the considered problems are rarely solved by genetic algorithms (GAs), even though it has successfully solved various complicated combinatorial optimization problems. For the problem, we propose a trajectory-based immigration strategy, where immigrant generation is based on the given information of solution extraction knowledge matrices. We embed the immigration strategy into the GA method to improve the population’s diversification process. To examine the performance of the proposed GA method, two versions of GA methods (the GA without immigration and the GA method with random immigration) and a mixed integer programming (MIP) model are also developed. Comprehensive experiments demonstrate the effectiveness of the proposed GA method by comparing the MIP model with two versions of GA methods. Overall, the proposed GA method significantly outperforms the other GA methods regarding solution quality due to the trajectory-based immigration strategy

Single-Machine Scheduling with Fixed Periodic Preventive Maintenance to Minimise the Total Weighted Completion Times

The single-machine scheduling problem with fixed periodic preventive maintenance, in which preventive maintenance is implemented periodically to maintain good machine operational status and decrease the cost caused by sudden machine failure, is studied in this paper. The adopted objective function is to minimise the total weighted completion time, which is representative of the minimisation of the global holding/inventory cost in the system. This problem is proven to be NP-hard; a position-based mixed integer programming model and an efficient heuristic algorithm with local improvement strategy are developed for the total weighted completion time problem. To evaluate the performances of the proposed heuristic algorithms, two new lower bounds are further developed. Computational experiments show that the proposed heuristic can rapidly achieve optimal results for small-sized problems and obtain near-optimal solutions with tight average relative percentage deviation for large-sized problems