Abstract
Over the recent years, Fireworks Algorithm has recorded an increasing success on solving continuous optimization problems, due to its efficiency, simplicity and more importantly its rapid convergence to good optimums. Thus, the Fireworks Algorithm performance is now widely comparable with the most popular methods in the optimization field such as evolutionary computation and swarm intelligence techniques. This paper introduces a discrete Fireworks Algorithm for combinatorial single machine scheduling problems. Taking advantage of the robust design of the original Fireworks Algorithm, a new adaptation of sparks generation is proposed with a novel use of the control parameters. To verify the explorative performance of the algorithm, a hybridization with Variable Neighborhood Search heuristic is implemented. To validate it, the proposed method is tested with several benchmarks instances of the single machine total weighted tardiness. A comparison with other optimization algorithms is also included. The obtained results exhibit the high performance of the proposed method.Article Preview
Top2. Total Weighted Tardiness Problem (Smtwt)
In engineering and computer science, the single machine total weighted tardiness problem (SMTWT) (Rathinam, & Ponnambalam, 2003) is a widely studied scheduling problem that is typed as NP-Hard. SMTWT considers n jobs (or tasks) to be processed sequentially on a single machine. Each job i is characterized by a processing time 
, representing the necessary time needed by the machine to process the job i, a due date 
indicating the date by which a job i should be completed, and a nonnegative weight 
representing the relative importance of job i. The tardiness of job j is then defined as:
(1) where: