Solving Bi-Criteria and Bi-Objectives of Total Tardiness Jobs Times and Range of Lateness Problems Using New Techniques
DOI:
https://doi.org/10.23851/mjs.v33i3.1135Keywords:
Bicritera and Multiobjective machine scheduling problems, Branch and Bound, Tardiness Time, Lateness, Range of Lateness.Abstract
In this paper, we proposed new techniques to solve one of the important fields of the Combinatorial Optimization Problem, which is the problem of machine scheduling. The problem which wants to be solved in this paper is the total tardiness times and range of lateness. For bi-criteria we have (1//(∑Tj,RL)) while for bi-objective we have (1//(∑Tj+RL)). In order to solve the suggested two problems, some new exact and approximation methods are suggested which are produced good results. The results which are obtained from applying the newly proposed methods are compared with the exact method; like Complete Enumeration Method (CEM), then compared results of the heuristics with each other's to obtain the most efficient method.
Downloads
References
F. H. Ali, "Improving exact and local search algorithms for solving some combinatorial optimization problems", Ph. D., Thesis, Mustansiriyah University, College of Science, Dept. of Mathematics, 2015.
T. S. Abdul-Razaq and F. H. Ali, "Constructing of an artificial neural network to minimize total completion time and total tardiness", IOSR Journal of Mathematics (IOSR-JM) e-ISSN: 2278-3008, p-ISSN:2319-7676. Volume 10, Issue 2 Ver. VI (Mar-Apr. 2014), PP 25-37.
T. S. Abdul-Razaq and S. A. Ali, "A comparison of local search algorithm for multicriteria scheduling problems", M.Sc. thesis, University of Al-Mustansiriyah Univ, College of Science, Dept. of Mathematics, 2016.
S. B. Abdulkareem, "Improving exact and local search algorithms for solving some combinatorial optimization problems", M. Sc., Thesis, Mustansiriyah University, College of Science, Dept. of Mathematics, 2017.
H. A. Chachan and A. S. Hameed, "Exact methods for solving multi-objective problem on single machine scheduling", Iraqi Journal of Science, 2019, Vol. 60, No.8, pp:1802-1813.
F. H. Ali and M. G. Ahmed, "Efficient algorithms to solve tricriteria machine scheduling problem", (15th and the second International) Conference of Statistical Applications (ICSA2020), Irbil, Kurdistan Region-Iraq, 12-13/Feb./2020, Journal of Al Rafidain University College, Volume, Issue 46, pp: 485-493, 2020.
F. H. Ali and M. G. Ahmed, "Optimal and near optimal solutions for multi objective function on a single machine", 1st International Conference on Computer Science and Software Engineering (CSASE2020), Duhok, Kurdistan Region-Iraq, Sponsored by IEEE Iraq section, 16-17/Apr./2020.
F. H. Ali and M. G. Ahmed, "Local search methods for solving total completion times, range of lateness and maximum tardiness problem", 6th International Engineering Conference (IEC2020), Irbil, Kurdistan Region-Iraq, Sponsored by IEEE Iraq section, 26-27/Feb./2020.
W. S. Khalaf, "Ensemble bat algorithm based on hyper heuristic approach for solving unconstrained optimization problems", Turkish Journal of Computer and Mathematics EducationVol.12 No.10, pp:5466-5478, 2021,
M. H. Ibrahim, F. A. Ali and H. A. Chachan, "Solving multi-objectives function problem using branch and bound and local search methods", International Journal of Nonlinear and Applications (IJNAA), (Scopus) ISSN 2008-6822, 13 (2022) No. 1, 1649-1658.
J. A. Hoogeveen, "Minimizing maximum earliness and maximum lateness on a single machine", Center for Mathematics and Computer science, P.O. Box 4079, 1009 AB Amsterdam, The Netherland, https://dl.acm.org/doi/10.5555/645585.659304
J. A. Hoogeveen, "Single machine scheduling to minimize a function of two or three maximum cost criteria", Journal of Algorithms, 21, 415-433, 1996.
B. Kolman, Introductory linear algebra with applications, Macmillan Publishing company, 1988.
W. S. Khalaf, M. M. Shakir and N. Y. Abd-Alredaa "Maximizing the performance of the Iraqi Armed Forces and determining the optimal path for them using the dynamic programming", Int. J. Nonlinear Anal. Appl. Volume 12, Special Issue, Winter and Spring 2021, pp: 847-860 ISSN: 2008-6822 (electronic)
C. R. Reeves, Modern Heuristic Techniques for Combinatorial Problems, John Wiley and sons, New York, 1993.
Downloads
Key Dates
Published
Issue
Section
License
Copyright (c) 2022 Al-Mustansiriyah Journal of Science
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
Articles accepted for publication in Al-Mustansiriyah Journal of Science (MJS) are protected under the Creative Commons Attribution 4.0 International License (CC BY-NC). Authors of accepted articles are requested to sign a copyright release form prior to their article being published. All authors must agree to the submission, sign copyright release forms, and agree to be included in any correspondence between MJS and the authors before submitting a work to MJS. For personal or educational use, permission is given without charge to print or create digital copies of all or portions of a MJS article. However, copies must not be produced or distributed for monetary gain. It is necessary to respect the copyright of any parts of this work that are not owned by MJS.
How to Cite
