Document Type : Original Article


1 Department of Industrial Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran.

2 Department of Structural Mechanics and Analysis, Technische University Berlin, Strasse des 17. Juni 135, 10623 Berlin, Germany.


This paper deals with the single machine scheduling problem with sequence-dependent setup time and learning effect on processing time, where the objective is to minimize total earliness and tardiness of the jobs. A Mixed Integer Linear Programming (MILP) model capable of solving small-sized problems is proposed to formulate this problem. In view of the NP-hard nature of the problem, the Hybrid Particle Swarm Optimization (HPSO) algorithm is proposed to solve the large-sized problems. In order to utilize Particle Swarm Optimization (PSO) to solve the scheduling problems, the proposed HPSO approach uses a random key representation to encode solutions, which can convert the job sequences to continuous position values. Also, the local search procedure is included within the HPSO to enhance the exploitation of the algorithm. The performance of the proposed HPSO is verified for small and medium-sized problems by comparing its results with the best solution obtained by the LINGO. In order to test the applicability of the proposed algorithm to solve large-sized problems, 120 instances are generated, and the results are compared with a Random Key Genetic Algorithm (RKGA). The results show the effectiveness of the proposed model and algorithm.


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