Modified artificial fish swarm algorithm to solve unrelated parallel machine scheduling problem under fuzzy environment
Unrelated parallel machine scheduling problem (UPMSP) in a fuzzy environment is an active research area due to the fuzzy nature of most real-world problems. UPMSP is an NP-hard problem; thus, finding optimal solutions is challenging, particularly when multiple objectives need to be considered. Hence...
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AIMS Press
2024-12-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20241679 |
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| author | Azhar Mahdi Ibadi Rosshairy Abd Rahman |
| author_facet | Azhar Mahdi Ibadi Rosshairy Abd Rahman |
| author_sort | Azhar Mahdi Ibadi |
| collection | DOAJ |
| description | Unrelated parallel machine scheduling problem (UPMSP) in a fuzzy environment is an active research area due to the fuzzy nature of most real-world problems. UPMSP is an NP-hard problem; thus, finding optimal solutions is challenging, particularly when multiple objectives need to be considered. Hence, a metaheuristic algorithm based on a modified artificial fish swarm algorithm (AFSA) is presented in this study to minimize the multi-objective makespan and total tardiness. Three modifications were made to the proposed algorithm. First, aspiration behavior was added to AFSA behaviors to increase effectiveness. Second, improved parameters such as step and visual were used to balance global search capability and convergence rate. Finally, a transformation method was injected to make the algorithm suitable for discrete optimization problems such as UPMSP. The proposed algorithm was compared with AFSA and five modified versions of AFSA to verify and measure the algorithm's effectiveness by conducting three different sizes of problems. Afterward, the Wilcoxon signed-rank test was used to statistically evaluate the algorithm's performance. The results indicate that the proposed algorithm significantly outperformed the other algorithms, especially for medium and large-sized problems. |
| format | Article |
| id | doaj-art-9ddd282ee4724bcaa68fccfff9ce6e95 |
| institution | Kabale University |
| issn | 2473-6988 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-9ddd282ee4724bcaa68fccfff9ce6e952025-01-23T07:53:25ZengAIMS PressAIMS Mathematics2473-69882024-12-01912353263535410.3934/math.20241679Modified artificial fish swarm algorithm to solve unrelated parallel machine scheduling problem under fuzzy environmentAzhar Mahdi Ibadi0Rosshairy Abd Rahman1School of Quantitative Sciences, Universiti Utara Malaysia, Sintok, Kedah 06010, MalaysiaSchool of Quantitative Sciences, Universiti Utara Malaysia, Sintok, Kedah 06010, MalaysiaUnrelated parallel machine scheduling problem (UPMSP) in a fuzzy environment is an active research area due to the fuzzy nature of most real-world problems. UPMSP is an NP-hard problem; thus, finding optimal solutions is challenging, particularly when multiple objectives need to be considered. Hence, a metaheuristic algorithm based on a modified artificial fish swarm algorithm (AFSA) is presented in this study to minimize the multi-objective makespan and total tardiness. Three modifications were made to the proposed algorithm. First, aspiration behavior was added to AFSA behaviors to increase effectiveness. Second, improved parameters such as step and visual were used to balance global search capability and convergence rate. Finally, a transformation method was injected to make the algorithm suitable for discrete optimization problems such as UPMSP. The proposed algorithm was compared with AFSA and five modified versions of AFSA to verify and measure the algorithm's effectiveness by conducting three different sizes of problems. Afterward, the Wilcoxon signed-rank test was used to statistically evaluate the algorithm's performance. The results indicate that the proposed algorithm significantly outperformed the other algorithms, especially for medium and large-sized problems.https://www.aimspress.com/article/doi/10.3934/math.20241679unrelated parallel machine scheduling problemfuzzy setsmulti-objectiveartificial fish swarm algorithmmodified algorithm |
| spellingShingle | Azhar Mahdi Ibadi Rosshairy Abd Rahman Modified artificial fish swarm algorithm to solve unrelated parallel machine scheduling problem under fuzzy environment AIMS Mathematics unrelated parallel machine scheduling problem fuzzy sets multi-objective artificial fish swarm algorithm modified algorithm |
| title | Modified artificial fish swarm algorithm to solve unrelated parallel machine scheduling problem under fuzzy environment |
| title_full | Modified artificial fish swarm algorithm to solve unrelated parallel machine scheduling problem under fuzzy environment |
| title_fullStr | Modified artificial fish swarm algorithm to solve unrelated parallel machine scheduling problem under fuzzy environment |
| title_full_unstemmed | Modified artificial fish swarm algorithm to solve unrelated parallel machine scheduling problem under fuzzy environment |
| title_short | Modified artificial fish swarm algorithm to solve unrelated parallel machine scheduling problem under fuzzy environment |
| title_sort | modified artificial fish swarm algorithm to solve unrelated parallel machine scheduling problem under fuzzy environment |
| topic | unrelated parallel machine scheduling problem fuzzy sets multi-objective artificial fish swarm algorithm modified algorithm |
| url | https://www.aimspress.com/article/doi/10.3934/math.20241679 |
| work_keys_str_mv | AT azharmahdiibadi modifiedartificialfishswarmalgorithmtosolveunrelatedparallelmachineschedulingproblemunderfuzzyenvironment AT rosshairyabdrahman modifiedartificialfishswarmalgorithmtosolveunrelatedparallelmachineschedulingproblemunderfuzzyenvironment |