Journal ArticleDOI
Models for inverse minimum spanning tree problem with fuzzy edge weights
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TLDR
A fuzzy α-minimum spanning tree model and a credibility maximization model are presented to formulate the problem according to different decision criteria, and a fuzzy simulation for computing credibility is designed and embedded into a genetic algorithm to produce some hybrid intelligent algorithms.Abstract:
An inverse minimum spanning tree problem is to make the least modification on the edge weights such that a predetermined spanning tree is a minimum spanning tree with respect to the new edge weights In this paper, a type of fuzzy inverse minimum spanning tree problem is introduced from a LAN reconstruction problem, where the weights of edges are assumed to be fuzzy variables The concept of fuzzy α-minimum spanning tree is initialized, and subsequently a fuzzy α-minimum spanning tree model and a credibility maximization model are presented to formulate the problem according to different decision criteria In order to solve the two fuzzy models, a fuzzy simulation for computing credibility is designed and then embedded into a genetic algorithm to produce some hybrid intelligent algorithms Finally, some computational examples are given to illustrate the effectiveness of the proposed algorithmsread more
Citations
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Journal ArticleDOI
Improved similarity measure in neutrosophic environment and its application in finding minimum spanning tree
Kanika Mandal,Kajla Basu +1 more
TL;DR: The weight of each network edge using single valued neutro- sophic set (SVNS) is defined and a new approach using similarity measure to find minimum spanning tree in neutrosophic environment is introduced and two formulas for the entropy measure proving a fundamental relation between similarity measure and entropy measure are developed.
Journal ArticleDOI
Uncertain Distribution-Minimum Spanning Tree Problem
TL;DR: This paper studies the minimum spanning tree problem on a graph with uncertain edge weights, which are formulated as uncertain variables and shows that this problem can be effectively solved via the proposed deterministic graph transformation-based approach with the aid of the β-distribution-path optimality condition.
Journal ArticleDOI
The Inverse Spanning Tree of a Fuzzy Graph Based on Credibility Measure
Jian Zhou,Qina Wang,Xiang Zhang +2 more
TL;DR: It is shown that when all the edge weights are assumed to be independent fuzzy variables with regular credibility distributions, the proposed model can be reformulated into a traditional nonlinear programming according to the equivalent condition of fuzzy α-minimum spanning tree characterized by a set of constraints on non-tree edges and their tree paths.
Journal ArticleDOI
A Chance-Constrained Programming Model for Inverse Spanning Tree Problem with Uncertain Edge Weights
Xiang Zhang,Qina Wang,Jian Zhou +2 more
TL;DR: A chance-constrained programming model is proposed to handle the inverse spanning tree problem where the edge weights are assumed to be uncertain variables and it is shown that such an uncertain minimum spanning tree can be characterized by some constraints on the paths of the graph.
Journal ArticleDOI
Optimization of Regional City Economic Gravity Network Based on Optimal Tree Theory
TL;DR: The research method was applied to build and optimize the economic gravity network of the cities in the Yangtze River Delta, based on the key indices of these cities in 2018, and lay a solid theoretic basis for regional planning and national development.
References
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Fuzzy sets
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TL;DR: In-depth, self-contained treatments of shortest path, maximum flow, and minimum cost flow problems, including descriptions of polynomial-time algorithms for these core models are presented.
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Genetic algorithms and engineering optimization
Mitsuo Gen,Runwei Cheng +1 more
TL;DR: This paper presents a meta-modelling framework that automates the very labor-intensive and therefore time-heavy and therefore expensive and labor-heavy process of designing and solving optimization problems.
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