The research and improvement of hidden-line elimination algorithm for convex polyhedron

Abstract This paper studies the data-based polyhedron model and its application in uncertain linear optimization of engineering structures, especially in the absence of information either on probabilistic properties or about membership functions in the fussy sets-based approach, in which situation it is more appropriate to quantify the uncertainties by convex polyhedra. Firstly, we introduce the uncertainty quantification method of the convex polyhedron approach and the model modification method by Chebyshev inequality. Secondly, the characteristics of the optimal solution of convex polyhedron linear programming are investigated. Then the vertex solution of convex polyhedron linear programming is presented and proven. Next, the application of convex polyhedron linear programming in the static load-bearing capacity problem is introduced. Finally, the effectiveness of the vertex solution is verified by an example of the plane truss bearing problem, and the efficiency is verified by a load-bearing problem of stiffened composite plates.

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A Note on Algorithms for Genotype and Allele Elimination in Complex Pedigrees With Incomplete Genotype Data

Genetics ◽

10.1093/genetics/156.4.2051 ◽

2000 ◽

Vol 156 (4) ◽

pp. 2051-2062

Author(s):

F-X Du ◽

I Hoeschele

Keyword(s):

Markov Chains ◽

Computational Efficiency ◽

Genotype Data ◽

Genetic Analyses ◽

Cpu Time ◽

Elimination Algorithm

Abstract Elimination of genotypes or alleles for each individual or meiosis, which are inconsistent with observed genotypes, is a component of various genetic analyses of complex pedigrees. Computational efficiency of the elimination algorithm is critical in some applications such as genotype sampling via descent graph Markov chains. We present an allele elimination algorithm and two genotype elimination algorithms for complex pedigrees with incomplete genotype data. We modify all three algorithms to incorporate inheritance restrictions imposed by a complete or incomplete descent graph such that every inconsistent complete descent graph is detected in any pedigree, and every inconsistent incomplete descent graph is detected in any pedigree without loops with the genotype elimination algorithms. Allele elimination requires less CPU time and memory, but does not always eliminate all inconsistent alleles, even in pedigrees without loops. The first genotype algorithm produces genotype lists for each individual, which are identical to those obtained from the Lange-Goradia algorithm, but exploits the half-sib structure of some populations and reduces CPU time. The second genotype elimination algorithm deletes more inconsistent genotypes in pedigrees with loops and detects more illegal, incomplete descent graphs in such pedigrees.

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Converting MST to TSP Path by Branch Elimination

Applied Sciences ◽

10.3390/app11010177 ◽

2020 ◽

Vol 11 (1) ◽

pp. 177

Author(s):

Pasi Fränti ◽

Teemu Nenonen ◽

Mingchuan Yuan

Keyword(s):

Spanning Tree ◽

Closed Loop ◽

Minimum Spanning Tree ◽

Travelling Salesman Problem ◽

Open Loop ◽

Travelling Salesman ◽

Elimination Algorithm ◽

Number Of Iterations ◽

Number Of Branches

Travelling salesman problem (TSP) has been widely studied for the classical closed loop variant but less attention has been paid to the open loop variant. Open loop solution has property of being also a spanning tree, although not necessarily the minimum spanning tree (MST). In this paper, we present a simple branch elimination algorithm that removes the branches from MST by cutting one link and then reconnecting the resulting subtrees via selected leaf nodes. The number of iterations equals to the number of branches (b) in the MST. Typically, b << n where n is the number of nodes. With O-Mopsi and Dots datasets, the algorithm reaches gap of 1.69% and 0.61 %, respectively. The algorithm is suitable especially for educational purposes by showing the connection between MST and TSP, but it can also serve as a quick approximation for more complex metaheuristics whose efficiency relies on quality of the initial solution.

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