Evolutionary algorithms for the bi-objective adjacent only quadratic spanning tree

Maia, Sílvia M. D. M.; Goldbarg, Elizabeth Ferreira Gouvêa; Goldbarg, Marco César

doi:10.1504/ijica.2014.066493

Cited by 7 publications

(1 citation statement)

References 34 publications

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“…All the abovementioned studies on QMST are considered as single objective optimization problem, where the linear weights are added with the quadratic weights. The conflicting nature of the linear and the quadratic weights have been studied by Maia, Goldbarg, and Goldbarg (). Here, the authors have considered the linear and quadratic weights as two separate objectives for the problem.…”

Section: Introductionmentioning

confidence: 99%

Rough‐fuzzy quadratic minimum spanning tree problem

2019

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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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Section: Introductionmentioning

confidence: 99%