scholarly journals A data structure for spanning tree optimization problems

2019 ◽  
Author(s):  
Marco Aurélio Lopes Barbosa
Keyword(s):  
Data Structure ◽  
Spanning Tree ◽  
Optimization Problems ◽  
Tree Optimization

A Geometry Based Method of Integrated Engineering Analysis and Optimization

1991 ◽  
Author(s):  
Ronald M. Dolin ◽  
Robert J. Bernhard
Keyword(s):  
Data Structure ◽  
Optimization Problems ◽  
Optimization Methods ◽  
Engineering Analysis ◽  
Design Variables ◽  
Engineering Environment ◽  
Specification Analysis

Abstract An integrated geometry based method of analysis and optimization is presented. The significance of geometry based analysis and optimization methods are discussed. A hierarchical integer based data structure, used to define and manipulate geometry, is presented. Many features of the integer based data structure are given. Shapes are shown to represent the fundamental geometry. Variables of shapes are constrained and related to each other so that a reduced set of design variables result. These design variables are used to pose both analysis and optimization problems. Heuristics are used to simplify the integrated geometry specification, analysis and optimization procedures. The resulting engineering environment concurrently poses analysis and optimization problems during geometry generation, leading to an integrated geometry based method of analysis and optimization.

A simulation-based quantitative analysis on the topological heritability of Dandelion-encoded meta-heuristics for tree optimization problems

2016 ◽  
Vol 21 (17) ◽  
pp. 4939-4952
Author(s):  
Cristina Perfecto ◽  
Miren Nekane Bilbao ◽  
Javier Del Ser ◽  
Armando Ferro
Keyword(s):  
Quantitative Analysis ◽  
Optimization Problems ◽  
Simulation Based ◽  
Tree Optimization

Board Game Supporting Learning Prim’s Algorithm and Dijkstra’s Algorithm

2012 ◽  
pp. 256-270
Author(s):  
Wen-Chih Chang ◽  
Te-Hua Wang ◽  
Yan-Da Chiu
Keyword(s):  
Data Structure ◽  
Spanning Tree ◽  
Spanning Trees ◽  
Minimum Spanning Tree ◽  
Experimental Results ◽  
Dijkstra’S Algorithm ◽  
Board Game ◽  
Tree Algorithm ◽  
Dijkstra's Algorithm ◽  
Tree Algorithms

The concept of minimum spanning tree algorithms in data structure is difficult for students to learn and to imagine without practice. Usually, learners need to diagram the spanning trees with pen to realize how the minimum spanning tree algorithm works. In this paper, the authors introduce a competitive board game to motivate students to learn the concept of minimum spanning tree algorithms. They discuss the reasons why it is beneficial to combine graph theories and board game for the Dijkstra and Prim minimum spanning tree theories. In the experimental results, this paper demonstrates the board game and examines the learning feedback for the mentioned two graph theories. Advantages summarizing the benefits of combining the graph theories with board game are discussed.

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.

THREE TECHNIQUES FOR PARALLEL MAINTENANCE OF A MINIMUM SPANNING TREE UNDER BATCH OF UPDATES

1996 ◽  
Vol 06 (02) ◽  
pp. 213-222 ◽  
Author(s):  
PAOLO FERRAGINA ◽  
FABRIZIO LUCCIO
Keyword(s):  
Data Structure ◽  
Parallel Algorithms ◽  
Spanning Tree ◽  
Minimum Spanning Tree ◽  
Undirected Graph ◽  
Batch Size ◽  
Insertions And Deletions ◽  
Erew Pram ◽  
Pram Model ◽  
Proper Values

In this paper we provide three simple techniques to maintain in parallel the minimum spanning tree of an undirected graph under single or batch of edge updates (i.e., insertions and deletions). Our results extend the use of the sparsification data structure to the EREW PRAM model. For proper values of the batch size, our algorithms require less time and work than the best known dynamic parallel algorithms.

Effective Data Structure for the Multidimensional Orthogonal Bin Packing Problems

2014 ◽  
Vol 962-965 ◽  
pp. 2868-2871 ◽  
Author(s):  
Alexander V. Chekanin ◽  
Vladislav A. Chekanin
Keyword(s):  
Data Structure ◽  
Linked Data ◽  
Bin Packing ◽  
High Efficiency ◽  
Optimization Problems ◽  
Packing Problem ◽  
Strong Sense ◽  
Np Hard ◽  
Packing Problems ◽  
Orthogonal Packing Problem

The actual in industry multidimensional orthogonal packing problem is considered in the article. Solution of a large number of different practical optimization problems, including resources saving problem, optimization problems in logistics, scheduling and planning comes down to the orthogonal packing problem which is NP-hard in strong sense. One of the indicators characterizing the efficiency of packing constructing algorithm is the efficiency of the used data structure. In the article a multilevel linked data structure that increases the speed of constructing of a packing is proposed. The carried out computational experiments show the high efficiency of the new data structure. Multilevel linked data structure is applicable for multidimensional orthogonal bin packing problems any kind.

PARALLEL REAL-TIME OPTIMIZATION: BEYOND SPEEDUP

1999 ◽  
Vol 09 (04) ◽  
pp. 499-509 ◽  
Author(s):  
SELIM G. AKL ◽  
Stefan D. Bruda
Keyword(s):  
Parallel Algorithm ◽  
Real Time ◽  
Spanning Tree ◽  
Optimization Problems ◽  
Minimum Weight ◽  
Parallel Computer ◽  
Worst Case ◽  
Time Optimization ◽  
Minimum Weight Spanning Tree ◽  
Real Time Optimization

Traditionally, interest in parallel computation centered around the speedup provided by parallel algorithms over their sequential counterparts. In this paper, we ask a different type of question: Can parallel computers, due to their speed, do more than simply speed up the solution to a problem? We show that for real-time optimization problems, a parallel computer can obtain a solution that is better than that obtained by a sequential one. Specifically, a sequential and a parallel algorithm are exhibited for the problem of computing the best-possible approximation to the minimum-weight spanning tree of a connected, undirected and weighted graph whose vertices and edges are not all available at the outset, but instead arrive in real time. While the parallel algorithm succeeds in computing the exact minimum-weight spanning tree, the sequential algorithm can only manage to obtain an approximate solution. In the worst case, the ratio of the weight of the solution obtained sequentially to that of the solution computed in parallel can be arbitrarily large.

scholarly journals Genetic algorithm for binary and functional decision diagrams optimization

2018 ◽  
Vol 31 (2) ◽  
pp. 169-187
Author(s):  
Stojkovic Suzana ◽  
Velickovic Darko ◽  
Moraga Claudio
Keyword(s):  
Genetic Algorithm ◽  
Genetic Algorithms ◽  
Data Structure ◽  
Optimization Problems ◽  
Binary Decision Diagrams ◽  
Size Optimization ◽  
Decision Diagrams ◽  
Crossover Operator ◽  
Binary Decision ◽  
Discrete Functions

Decision diagrams (DD) are a widely used data structure for discrete functions representation. The major problem in DD-based applications is the DD size minimization (reduction of the number of nodes), because their size is dependent on the variables order. Genetic algorithms are often used in different optimization problems including the DD size optimization. In this paper, we apply the genetic algorithm to minimize the size of both Binary Decision Diagrams (BDDs) and Functional Decision Diagrams (FDDs). In both cases, in the proposed algorithm, a Bottom-Up Partially Matched Crossover (BU-PMX) is used as the crossover operator. In the case of BDDs, mutation is done in the standard way by variables exchanging. In the case of FDDs, the mutation by changing the polarity of variables is additionally used. Experimental results of optimization of the BDDs and FDDs of the set of benchmark functions are also presented.

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