Rough‐fuzzy quadratic minimum spanning tree problem

A quadratic minimum spanning tree problem determines a minimum spanning tree of a network whose edges are associated with linear and quadratic weights. Linear weights represent the edge costs whereas the quadratic weights are the interaction costs between a pair of edges of the graph. In this study,...

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Bibliographic Details
Published in:Expert systems Vol. 36; no. 2
Main Authors: Majumder, Saibal, Kar, Samarjit, Pal, Tandra
Format: Journal Article
Language:English
Published: Oxford Blackwell Publishing Ltd 01.04.2019
Subjects:
chance‐constrained programming
Classification
Confidence intervals
epsilon‐constraint method
Evolutionary algorithms
Genetic algorithms
Graph theory
Graphical representations
Mathematical models
MOCHC
NSGA‐II
quadratic minimum spanning tree
rough‐fuzzy variable
Sensitivity analysis
Sorting algorithms
ISSN:0266-4720, 1468-0394
Online Access:Get full text
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Summary:A quadratic minimum spanning tree problem determines a minimum spanning tree of a network whose edges are associated with linear and quadratic weights. Linear weights represent the edge costs whereas the quadratic weights are the interaction costs between a pair of edges of the graph. In this study, a bi‐objective rough‐fuzzy quadratic minimum spanning tree problem has been proposed for a connected graph, where the linear and the quadratic weights are represented as rough‐fuzzy variables. The proposed model is formulated by using rough‐fuzzy chance‐constrained programming technique. Subsequently, three related theorems are also proposed for the crisp transformation of the proposed model. The crisp equivalent models are solved with a classical multi‐objective solution technique, the epsilon‐constraint method and two multi‐objective evolutionary algorithms: (a) nondominated sorting genetic algorithm II (NSGA‐II) and (b) multi‐objective cross‐generational elitist selection, heterogeneous recombination, and cataclysmic mutation (MOCHC) algorithm. A numerical example is provided to illustrate the proposed model when solved with different methodologies. A sensitivity analysis of the example is also performed at different confidence levels. The performance of NSGA‐II and MOCHC are analysed on five randomly generated instances of the proposed model. Finally, a numerical illustration of an application of the proposed model is also presented in this study.
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ISSN:0266-4720
1468-0394
DOI:10.1111/exsy.12364