Tahani Jabbar Khraibet1,*, Nagham Muosa Neamah2
1 Department of Mathematics Thi-Qar Directorate of Education, Ministry of Education, Thi-Qar, Iraq
2 Department of Mathematics, College of Science for Women, University of Baghdad, Baghdad, Iraq
*Corresponding Author: tahani@utq.edu.iq
Received 3 Nov. 2025, Accepted 12 Dec. 2025, published 30 Dec. 2025.
AbstractKey wordsDOI
The present paper addresses the problem of scheduling jobs on single machines to minimize the total weight of completion times and late work, considering release dates. This problem, denoted by 1∕r_j∕∑_(j=1)^n▒〖〖(w〗_j c_j 〗+V_j) , is NP-hard and, as far as we know, unstudied. In view of the NP-hardness of the problem, an Artificial Fish Swarm Algorithm approach is proposed to solve it. The Computational results indicate that the proposed algorithm is capable of finding near optimal solutions (approximate solutions) to the problems up to 4000 jobs. These results establish the AFSA as a revolutionary instrument for addressing intricate scheduling challenges in both theoretical and practical contexts. Arithmetic results are calculated computational results were obtained using MATLAB 2023a.
Scheduling; Single machines; the total weighted of completion times; the late work with release date; Artificial Fish Swarm Algorithm
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