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En el instante 21 de octubre de 2025, 9:01:54 UTC,
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Añadido recurso Computation of the improvement directions of the Pareto front and its application to MOEAs a Computation of the improvement directions of the Pareto front and its application to MOEAs
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| 2 | "author": "S Botello-Aceves, A Hernandez-Aguirre, SI Valdez", | 2 | "author": "S Botello-Aceves, A Hernandez-Aguirre, SI Valdez", | ||
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| 25 | "value": "Proceedings of the 2020 Genetic and Evolutionary | 25 | "value": "Proceedings of the 2020 Genetic and Evolutionary | ||
| 26 | Computation Conference, 480-488, 2020" | 26 | Computation Conference, 480-488, 2020" | ||
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| 39 | ement-directions-of-the-Pareto-front-and-its-application-to-MOEAs.pdf" | 39 | ement-directions-of-the-Pareto-front-and-its-application-to-MOEAs.pdf" | ||
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| 61 | "notes": "This paper introduces the mathematical development and | 61 | "notes": "This paper introduces the mathematical development and | ||
| 62 | algorithm of the Improvement-Directions Mapping (IDM) method, which | 62 | algorithm of the Improvement-Directions Mapping (IDM) method, which | ||
| 63 | computes improvement directions to \"push\" the current solutions | 63 | computes improvement directions to \"push\" the current solutions | ||
| 64 | toward the true Pareto front. The main idea is to compute normal | 64 | toward the true Pareto front. The main idea is to compute normal | ||
| 65 | vectors to the front, as improvement directions in the objective | 65 | vectors to the front, as improvement directions in the objective | ||
| 66 | space, to be then transformed into search directions in the variable | 66 | space, to be then transformed into search directions in the variable | ||
| 67 | space through a transformation tensor. The main contributions of the | 67 | space through a transformation tensor. The main contributions of the | ||
| 68 | IDM as a local search operator versus previous approaches are the | 68 | IDM as a local search operator versus previous approaches are the | ||
| 69 | following: 1) It does not require of a priori information about | 69 | following: 1) It does not require of a priori information about | ||
| 70 | improvement directions or location of the true Pareto front, 2) It | 70 | improvement directions or location of the true Pareto front, 2) It | ||
| 71 | uses a local quadratic approximation of the Pareto front to compute | 71 | uses a local quadratic approximation of the Pareto front to compute | ||
| 72 | the transformation tensor, thus, reducing numerical problems and | 72 | the transformation tensor, thus, reducing numerical problems and | ||
| 73 | avoiding abrupt changes in the search direction which could lead to | 73 | avoiding abrupt changes in the search direction which could lead to | ||
| 74 | erratic searches. These features allow the IDM to be implemented as a | 74 | erratic searches. These features allow the IDM to be implemented as a | ||
| 75 | local search operator within any Multi-objective Evolutionary | 75 | local search operator within any Multi-objective Evolutionary | ||
| 76 | Algorithm (MOEA). The potential of the IDM is shown by hybridizing two | 76 | Algorithm (MOEA). The potential of the IDM is shown by hybridizing two | ||
| 77 | well-known multi-objective algorithms: a) MOEA/D + IDM; b) NSGA-II + | 77 | well-known multi-objective algorithms: a) MOEA/D + IDM; b) NSGA-II + | ||
| 78 | IDM. In the first approach, IDM \"pushes\" the offspring population in | 78 | IDM. In the first approach, IDM \"pushes\" the offspring population in | ||
| 79 | each iteration. A similar experiment is performed with the second | 79 | each iteration. A similar experiment is performed with the second | ||
| 80 | approach. Furthermore, one more experiment evaluates the IDM as a | 80 | approach. Furthermore, one more experiment evaluates the IDM as a | ||
| 81 | refinement step that is applied to the last Pareto front delivered by | 81 | refinement step that is applied to the last Pareto front delivered by | ||
| 82 | NSGA-II.", | 82 | NSGA-II.", | ||
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| 109 | development and algorithm of the Improvement-Directions Mapping (IDM) | ||||
| 110 | method, which computes improvement directions to \"push\" the current | ||||
| 111 | solutions toward the true Pareto front. The main idea is to compute | ||||
| 112 | normal vectors to the front, as improvement directions in the | ||||
| 113 | objective space, to be then transformed into search directions in the | ||||
| 114 | variable space through a transformation tensor. The main contributions | ||||
| 115 | of the IDM as a local search operator versus previous approaches are | ||||
| 116 | the following: 1) It does not require of a priori information about | ||||
| 117 | improvement directions or location of the true Pareto front, 2) It | ||||
| 118 | uses a local quadratic approximation of the Pareto front to compute | ||||
| 119 | the transformation tensor, thus, reducing numerical problems and | ||||
| 120 | avoiding abrupt changes in the search direction which could lead to | ||||
| 121 | erratic searches. These features allow the IDM to be implemented as a | ||||
| 122 | local search operator within any Multi-objective Evolutionary | ||||
| 123 | Algorithm (MOEA). The potential of the IDM is shown by hybridizing two | ||||
| 124 | well-known multi-objective algorithms: a) MOEA/D + IDM; b) NSGA-II + | ||||
| 125 | IDM. In the first approach, IDM \"pushes\" the offspring population in | ||||
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| 128 | refinement step that is applied to the last Pareto front delivered by | ||||
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