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PARETO EFFICIENT SOLUTIONS IN MULTI-OBJECTIVE OPTIMIZATION INVOLVING FORBIDDEN REGIONS
PARETO EFFICIENT SOLUTIONS IN MULTI-OBJECTIVE OPTIMIZATION INVOLVING FORBIDDEN REGIONS
| dc.creator | Gunther, Christian | |
| dc.date | 2023-04-12 | |
| dc.date.accessioned | 2023-06-20T14:02:50Z | |
| dc.date.available | 2023-06-20T14:02:50Z | |
| dc.identifier | https://revistas.uh.cu/invoperacional/article/view/3947 | |
| dc.identifier.uri | https://repositorioslatinoamericanos.uchile.cl/handle/2250/6720767 | |
| dc.description | In this paper, the aim is to compute Pareto efficient solutions of multi-objective optimization prob- lems involving forbidden regions. More precisely, we assume that the vector-valued objective function is componentwise generalized-convex and acts between a real topological linear pre-image space and a finite-dimensional image space, while the feasible set is given by the whole pre-image space excepting some forbidden regions that are defined by convex sets. This leads us to a nonconvex multi-objective optimization problem. Using the recently proposed penalization approach by G ̈unther and Tammer (2017), we show that the solution set of the original problem can be generated by solving a finite family of unconstrained multi-objective optimization problems. We apply our results to a special multi-objective location problem (known as point-objective location problem) where the aim is to locate a new facility in a continuous location space (a finite-dimensional Hilbert space) in the pres- ence of a finite number of demand points. For the choice of the new location point, we are takinginto consideration some forbidden regions that are given by open balls (defined with respect to the underlying norm). For such a nonconvex location problem, under the assumption that the forbid- den regions are pairwise disjoint, we give complete geometrical descriptions for the sets of (strictly, weakly) Pareto efficient solutions by using the approach by G ̈unther and Tammer (2017) and resultsderived by Jourani, Michelot and Ndiaye (2009) | en-US |
| dc.description | El objetivo de este trabajo es el estudio de los puntos eficientes de Pareto en problemas multi- objetivo con regiones prohibidas. O sea, se considera el problema en el que el dominio de la funci ́on objetivo es un espacio lineal topol ́ogico, su imagen es un espacio de dimenci ́on finita, cada una de sus componentes son fuciones convexas generalizadas y el conjunto de soluciones factibles es el complemento de la uni ́on de conjuntos convexos de su diminio. Usando el enfoque de penalizaci ́on propuesto por G ̈unther y Tammer (2017), mostramos que el conjunto de soluciones puede generarse resolviendo una familia finita de problemas multiobjetivo sin restricciones. Estos resultados se aplican al caso particular de ubicar un punto en un espacio Eucl ́ıdeo, donde hay una cantidad finita de clientes y las regiones prohibidas son bolas abiertas con respecto a la norma que se considera. Si las regiones son disjuntas, se obtiene una caracterizaci ́on geom ́etrica completa de los conjuntos de soluciones estricas y d ́ebiles de Pareto. usando el enfoque propuesto en G ̈unther y Tammer (2017) y los resultados que se derivan de Jourani, Michelot y Ndiaye (2009) | es-ES |
| dc.format | application/pdf | |
| dc.language | eng | |
| dc.publisher | Departamento de Matemática Aplicada. Facultad de Matemática y Computación. Universidad de La Habana | en-US |
| dc.relation | https://revistas.uh.cu/invoperacional/article/view/3947/3480 | |
| dc.rights | https://creativecommons.org/licenses/by/4.0 | es-ES |
| dc.source | Investigación Operacional; Vol. 39 No. 3 (2018): SPECIAL ISSUE ON VARIATIONAL ANALYSIS ON HOMAGE TO THE 70TH ANNIVERSARY OF BORIS MURDUKHOVICH | en-US |
| dc.source | Investigación Operacional; Vol. 39 Núm. 3 (2018): SPECIAL ISSUE ON VARIATIONAL ANALYSIS ON HOMAGE TO THE 70TH ANNIVERSARY OF BORIS MURDUKHOVICH | es-ES |
| dc.source | 2224-5405 | |
| dc.subject | Multi-objective optimization | en-US |
| dc.subject | Pareto efficiency | en-US |
| dc.subject | Generalized-convexity | en-US |
| dc.subject | Forbidden regions | en-US |
| dc.subject | Location theory | en-US |
| dc.subject | Euclidean norm | en-US |
| dc.subject | Convexidad Generalizada | es-ES |
| dc.subject | Eficiencia de Pareto | es-ES |
| dc.subject | Norma Euclídeana | es-ES |
| dc.subject | Prob- lema de Optimización Multi-objetivo | es-ES |
| dc.subject | regiones Prohibidas | es-ES |
| dc.subject | Teoría de la Ubicación | es-ES |
| dc.title | PARETO EFFICIENT SOLUTIONS IN MULTI-OBJECTIVE OPTIMIZATION INVOLVING FORBIDDEN REGIONS | en-US |
| dc.title | PARETO EFFICIENT SOLUTIONS IN MULTI-OBJECTIVE OPTIMIZATION INVOLVING FORBIDDEN REGIONS | es-ES |
| dc.type | info:eu-repo/semantics/article | |
| dc.type | info:eu-repo/semantics/publishedVersion | |
| dc.type | Articles | en-US |
| dc.type | Artículo | es-ES |