A memetic algorithm with a variable block insertion heuristic for single machine total weighted tardiness problem with sequence dependent setup times

In this paper, a memetic algorithm with a variable block insertion heuristic is presented to solve the single machine total weighted tardiness problem with sequence dependent setup times. Together with the traditional insertion neighborhood structure, the memetic algorithm is combined with a variable block insertion heuristic in which a block of jobs are removed from a sequence and then inserted into all possible positions of the partial sequence. For this purpose, we devise a variable neighborhood descent algorithm to incorporate different block insertion heuristics having different block sizes. We also employ a simulated annealing type of acceptance criterion to diversify the population. To evaluate its performance, the memetic algorithm is tested on a set of benchmark instances from the literature. The analyses of experimental results have shown highly effective performance of the memetic algorithm against the best performing algorithms from the literature. The proposed memetic algorithm was able to find 98 out 120 optimal solutions within reasonable CPU times.