Multi-objective Optimization for the Degree-Constrained Minimum Spanning Tree

2008 ◽  
Author(s):  
Fangguo He ◽  
Huan Qi
Keyword(s):  
Spanning Tree ◽  
Minimum Spanning Tree ◽  
Multi Objective Optimization ◽  
Multi Objective

scholarly journals ETEA: A Euclidean Minimum Spanning Tree-Based Evolutionary Algorithm for Multi-Objective Optimization

2014 ◽  
Vol 22 (2) ◽  
pp. 189-230 ◽  
Author(s):  
Miqing Li ◽  
Shengxiang Yang ◽  
Jinhua Zheng ◽  
Xiaohui Liu
Keyword(s):  
Evolutionary Algorithm ◽  
Spanning Tree ◽  
Euclidean Distance ◽  
Minimum Spanning Tree ◽  
Optimization Problems ◽  
Multi Objective Optimization ◽  
Position Information ◽  
Multi Objective ◽  
Environmental Selection ◽  
Fitness Value

The Euclidean minimum spanning tree (EMST), widely used in a variety of domains, is a minimum spanning tree of a set of points in space where the edge weight between each pair of points is their Euclidean distance. Since the generation of an EMST is entirely determined by the Euclidean distance between solutions (points), the properties of EMSTs have a close relation with the distribution and position information of solutions. This paper explores the properties of EMSTs and proposes an EMST-based evolutionary algorithm (ETEA) to solve multi-objective optimization problems (MOPs). Unlike most EMO algorithms that focus on the Pareto dominance relation, the proposed algorithm mainly considers distance-based measures to evaluate and compare individuals during the evolutionary search. Specifically, in ETEA, four strategies are introduced: (1) An EMST-based crowding distance (ETCD) is presented to estimate the density of individuals in the population; (2) A distance comparison approach incorporating ETCD is used to assign the fitness value for individuals; (3) A fitness adjustment technique is designed to avoid the partial overcrowding in environmental selection; (4) Three diversity indicators—the minimum edge, degree, and ETCD—with regard to EMSTs are applied to determine the survival of individuals in archive truncation. From a series of extensive experiments on 32 test instances with different characteristics, ETEA is found to be competitive against five state-of-the-art algorithms and its predecessor in providing a good balance among convergence, uniformity, and spread.

scholarly journals On Multi-Objective Minimum Spanning Tree Problem under Uncertain Paradigm

Symmetry ◽  
2022 ◽  
Vol 14 (1) ◽  
pp. 106
Author(s):  
Saibal Majumder ◽  
Partha Sarathi Barma ◽  
Arindam Biswas ◽  
Pradip Banerjee ◽  
Bijoy Kumar Mandal ◽  
...  
Keyword(s):  
Spanning Tree ◽  
Uncertainty Theory ◽  
Minimum Spanning Tree ◽  
Transportation Cost ◽  
Petroleum Products ◽  
Solution Technique ◽  
Multi Objective ◽  
Varied Range ◽  
Minimum Spanning Tree Problem ◽  
Constraint Method

Minimum spanning tree problem (MSTP) has allured many researchers and practitioners due to its varied range of applications in real world scenarios. Modelling these applications involves the incorporation of indeterminate phenomena based on their subjective estimations. Such phenomena can be represented rationally using uncertainty theory. Being a more realistic variant of MSTP, in this article, based on the principles of the uncertainty theory, we have studied a multi-objective minimum spanning tree problem (MMSTP) with indeterminate problem parameters. Subsequently, two uncertain programming models of the proposed uncertain multi-objective minimum spanning tree problem (UMMSTP) are developed and their corresponding crisp equivalence models are investigated, and eventually solved using a classical multi-objective solution technique, the epsilon-constraint method. Additionally, two multi-objective evolutionary algorithms (MOEAs), non-dominated sorting genetic algorithm II (NSGAII) and duplicate elimination non-dominated sorting evolutionary algorithm (DENSEA) are also employed as solution methodologies. With the help of the proposed UMMSTP models, the practical problem of optimizing the distribution of petroleum products was solved, consisting in the search for symmetry (balance) between the transportation cost and the transportation time. Thereafter, the performance of the MOEAs is analyzed on five randomly developed instances of the proposed problem.

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