Optimizing TSP-MMC Performance in Non-Homogeneous Environments
The Travelling Salesman Problem (TSP) for determining the optimal trajectory in a non-homogeneous space is related to the variational problem of Fermat's principle, which seeks the path of an optical ray in a medium. Generally, finding such an optimal trajectory is a considerable challenge, es...
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| Format: | Article |
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Universidad Autónoma del Estado de Morelos
2025-06-01
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| Series: | Programación Matemática y Software |
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| Online Access: | https://progmat.uaem.mx/progmat/index.php/progmat/article/view/316 |
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| author | Yessica Yazmín Calderon-Segura Gennadiy Burlak Jośe Antonio García Pacheco |
| author_facet | Yessica Yazmín Calderon-Segura Gennadiy Burlak Jośe Antonio García Pacheco |
| author_sort | Yessica Yazmín Calderon-Segura |
| collection | DOAJ |
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The Travelling Salesman Problem (TSP) for determining the optimal trajectory in a non-homogeneous space is related to the variational problem of Fermat's principle, which seeks the path of an optical ray in a medium. Generally, finding such an optimal trajectory is a considerable challenge, especially in structures with a large number of emitters randomly distributed. To address this problem, we propose using the hybrid TSP-MMC algorithm to identify the minimum optical path S that connects the emitters embedded in a percolating cluster. This approach will compensate for the deviations introduced by the transmission of a light beam through the percolation cluster, achieving an intensity distribution tailored to user needs. We have demonstrated that our technique can achieve solutions that improve efficiency by 60% compared to optimal values for light beam optimization data. This technique could be applied to visualize blood vessels in both static and dynamic contexts, making it useful in the biological field for cellular and bacterial samples.
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| format | Article |
| id | doaj-art-dd422e0f2d114c8dba1fed060581a09a |
| institution | DOAJ |
| issn | 2007-3283 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | Universidad Autónoma del Estado de Morelos |
| record_format | Article |
| series | Programación Matemática y Software |
| spelling | doaj-art-dd422e0f2d114c8dba1fed060581a09a2025-08-20T03:11:17ZengUniversidad Autónoma del Estado de MorelosProgramación Matemática y Software2007-32832025-06-0117210.30973/progmat/2025.17.2/1Optimizing TSP-MMC Performance in Non-Homogeneous EnvironmentsYessica Yazmín Calderon-Segura0Gennadiy Burlak1Jośe Antonio García Pacheco2Universidad Autónoma del Estado de Morelos. Centro de Investigación en Ingeniería y Ciencias Aplicadas/Facultad de Contabilidad, Administración e Informática. Cuernavaca, Morelos. México Universidad Autónoma del Estado de Morelos. Centro de Investigación en Ingeniería y Ciencias Aplicadas. Cuernavaca, Morelos. México Universidad Autónoma del Estado de Morelos. Centro de Investigación en Ingeniería y Ciencias Aplicadas. Cuernavaca, Morelos. México The Travelling Salesman Problem (TSP) for determining the optimal trajectory in a non-homogeneous space is related to the variational problem of Fermat's principle, which seeks the path of an optical ray in a medium. Generally, finding such an optimal trajectory is a considerable challenge, especially in structures with a large number of emitters randomly distributed. To address this problem, we propose using the hybrid TSP-MMC algorithm to identify the minimum optical path S that connects the emitters embedded in a percolating cluster. This approach will compensate for the deviations introduced by the transmission of a light beam through the percolation cluster, achieving an intensity distribution tailored to user needs. We have demonstrated that our technique can achieve solutions that improve efficiency by 60% compared to optimal values for light beam optimization data. This technique could be applied to visualize blood vessels in both static and dynamic contexts, making it useful in the biological field for cellular and bacterial samples. https://progmat.uaem.mx/progmat/index.php/progmat/article/view/316Optimizationpercolation clusterlight beam optimizationFermat's principleMonte Carlo methodTSP |
| spellingShingle | Yessica Yazmín Calderon-Segura Gennadiy Burlak Jośe Antonio García Pacheco Optimizing TSP-MMC Performance in Non-Homogeneous Environments Programación Matemática y Software Optimization percolation cluster light beam optimization Fermat's principle Monte Carlo method TSP |
| title | Optimizing TSP-MMC Performance in Non-Homogeneous Environments |
| title_full | Optimizing TSP-MMC Performance in Non-Homogeneous Environments |
| title_fullStr | Optimizing TSP-MMC Performance in Non-Homogeneous Environments |
| title_full_unstemmed | Optimizing TSP-MMC Performance in Non-Homogeneous Environments |
| title_short | Optimizing TSP-MMC Performance in Non-Homogeneous Environments |
| title_sort | optimizing tsp mmc performance in non homogeneous environments |
| topic | Optimization percolation cluster light beam optimization Fermat's principle Monte Carlo method TSP |
| url | https://progmat.uaem.mx/progmat/index.php/progmat/article/view/316 |
| work_keys_str_mv | AT yessicayazmincalderonsegura optimizingtspmmcperformanceinnonhomogeneousenvironments AT gennadiyburlak optimizingtspmmcperformanceinnonhomogeneousenvironments AT joseantoniogarciapacheco optimizingtspmmcperformanceinnonhomogeneousenvironments |