A Hybrid Harmony Search algorithm to minimize total weighted tardiness in the permutation flow shop

We address the permutation flow shop scheduling problem with sequence dependent setup times between jobs. Each job has its weight of importance as well as due date. The goal is to find sequence of jobs such that total weighted tardiness of jobs is minimized. Due to NP-Hard complexity of this problem, a hybrid meta-heuristic algorithm based on Harmony Search Algorithm is developed. In the proposed algorithm, a new acceptance criterion of new improvised harmony is suggested which allows the algorithm to explore the solution space in earlier iterations (diversification), and as algorithm progresses the acceptance criterion leads the algorithm to accept the solutions in neighborhood of the current solution, (intensification). In order to improve the search ability of the algorithm, Variable Neighborhood Search Algorithm is applied to improve the quality of generated harmony. The computational experiments based on well-known benchmark instances are conducted. Results show that the proposed algorithm outperforms other state of the art algorithm used for solving studied problem.