A Max-min Ant System to Minimize Total Tardiness on a Single Machine with Sequence Dependent Setup times Implementing a Limited Budget Local Search

Given the anticipated benefits of better solutions, the scheduling problem of minimizing the total tardiness for single machine with sequence dependent setup times continues to represent a challenge for researchers to resolve. This research presents a novel Max-Min Ant System (MMAS) algorithm for solving this problem. The MMAS algorithm adopts a new local search technique where, a position is randomly chosen from the jobs' sequence and the job located at this position is either interchanged with other jobs or another job from the sequence is inserted in this position. The best move is chosen and the algorithm is repeated. The new algorithm has been tested on a number of benchmark problems for both the weighted and the unweighted tardiness and the experimental results show that the algorithm can reach better results on most of the cases.