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En el instante 11 de octubre de 2025, 1:23:57 UTC,
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Añadido recurso On the selection of the optimal topology for particle swarm optimization: a study of the tree as the universal topology a On the selection of the optimal topology for particle swarm optimization: a study of the tree as the universal topology
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2 | "author": "\u00c1A Rojas-Garc\u00eda, A Hern\u00e1ndez-Aguirre, SI | 2 | "author": "\u00c1A Rojas-Garc\u00eda, A Hern\u00e1ndez-Aguirre, SI | ||
3 | Valdez", | 3 | Valdez", | ||
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43 | topology-for-particle-swarm-optimization-a-study-of-the-3d640e518955", | 43 | topology-for-particle-swarm-optimization-a-study-of-the-3d640e518955", | ||
44 | "notes": "In this paper, we deal with the problem of selecting the | 44 | "notes": "In this paper, we deal with the problem of selecting the | ||
45 | best topology in Particle Swarm Optimization. Unlike most | 45 | best topology in Particle Swarm Optimization. Unlike most | ||
46 | state-of-the-art papers, where statistical analysis of a large number | 46 | state-of-the-art papers, where statistical analysis of a large number | ||
47 | of topologies is carried out, in this work we formalize mathematically | 47 | of topologies is carried out, in this work we formalize mathematically | ||
48 | the problem. In this way, the problem is to find the best topology in | 48 | the problem. In this way, the problem is to find the best topology in | ||
49 | the set of all simple connected graphs of n nodes. To determine which | 49 | the set of all simple connected graphs of n nodes. To determine which | ||
50 | is the best topology, each graph in this set must be measured with a | 50 | is the best topology, each graph in this set must be measured with a | ||
51 | function that evaluates its quality. We introduce the concepts of | 51 | function that evaluates its quality. We introduce the concepts of | ||
52 | equivalent neighborhood and equivalent topology to prove that for any | 52 | equivalent neighborhood and equivalent topology to prove that for any | ||
53 | simple connected graph there is an equivalent tree. The equivalence | 53 | simple connected graph there is an equivalent tree. The equivalence | ||
54 | between two topologies means that each particle belonging to these has | 54 | between two topologies means that each particle belonging to these has | ||
55 | the same local best in both. Therefore, the problem can be simplified | 55 | the same local best in both. Therefore, the problem can be simplified | ||
56 | in complexity to find the best tree in the set of all trees with n | 56 | in complexity to find the best tree in the set of all trees with n | ||
57 | nodes. Finally, we give some examples of equivalent topologies, as | 57 | nodes. Finally, we give some examples of equivalent topologies, as | ||
58 | well as the applicability of the obtained result.", | 58 | well as the applicability of the obtained result.", | ||
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86 | most state-of-the-art papers, where statistical analysis of a large | ||||
87 | number of topologies is carried out, in this work we formalize | ||||
88 | mathematically the problem. In this way, the problem is to find the | ||||
89 | best topology in the set of all simple connected graphs of n nodes. To | ||||
90 | determine which is the best topology, each graph in this set must be | ||||
91 | measured with a function that evaluates its quality. We introduce the | ||||
92 | concepts of equivalent neighborhood and equivalent topology to prove | ||||
93 | that for any simple connected graph there is an equivalent tree. The | ||||
94 | equivalence between two topologies means that each particle belonging | ||||
95 | to these has the same local best in both. Therefore, the problem can | ||||
96 | be simplified in complexity to find the best tree in the set of all | ||||
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