Modification of Algorithm of Directed Graph Paths Decomposition with Schedule

2021 ◽  
Vol 11 (2) ◽  
pp. 51-58
Author(s):  
I.A. Zolotarev ◽  
V.A. Rasskazova
Keyword(s):  
Directed Graph ◽  
Original Problem ◽  
Oriented Graph ◽  
Additional Constraint ◽  
Decomposition Algorithm ◽  
Transport Networks ◽  
Complex Topology ◽  
Balance Parameter

This study aims to refinement of the oriented graph paths decomposition algorithm. An additional constraint on the balance parameter is considered to take into account the locomotive departure schedule. Also new rule to compute Ns parameters is given. An example of the operation of the oriented graph paths decomposition algorithm with the schedule is given. The scientific and practical novelty of the work lies in a significant reduction in the dimension of the original problem, which is especially important in the conditions of transport networks of complex topology.

Practical Realization of Algorithm of Oriented Graph Paths Decomposition

2020 ◽  
Vol 10 (3) ◽  
pp. 60-68
Author(s):  
I.A. Zolotarev ◽  
V.A. Rasskazova
Keyword(s):  
Original Problem ◽  
Oriented Graph ◽  
Decomposition Algorithms ◽  
Rail Transportation ◽  
Transport Networks ◽  
Matrix Formulation ◽  
Original Algorithm ◽  
Complex Topology ◽  
Graph Size ◽  
Methodological Status

This study aims to clarify the methodological status program realization of oriented graph paths decomposition. Algorithms of matrix formulation of decomposition table M from multitude of paths, table sorting by NΣ and balance computing explored. On the basis of those algorithms and original algorithm of oriented graph paths decomposition realized Python 3 program. Results for random-generated graph size of 100 vertices computed and time measured. The results obtained can be used to solve the problem of organizing freight rail transportation at the stage of assignment and movement of locomotives. The scientifi c and practical novelty of the work lies in a signifi cant reduction in the dimension of the original problem, which is especially important in the conditions of transport networks of complex topology.

A Regularized Inexact Penalty Decomposition Algorithm for Multidisciplinary Design Optimization Problems With Complementarity Constraints

2010 ◽  
Vol 132 (4) ◽  
Author(s):  
Shen Lu ◽  
Harrison M. Kim
Keyword(s):  
Design Optimization ◽  
Multidisciplinary Design Optimization ◽  
Original Problem ◽  
Equilibrium Problems ◽  
Optimization Problems ◽  
Decomposition Algorithm ◽  
Multidisciplinary Design ◽  
Stationary Points ◽  
Complementarity Constraints ◽  
Regularization Technique

Economic and physical considerations often lead to equilibrium problems in multidisciplinary design optimization (MDO), which can be captured by MDO problems with complementarity constraints (MDO-CC)—a newly emerging class of problem. Due to the ill-posedness associated with the complementarity constraints, many existing MDO methods may have numerical difficulties solving this class of problem. In this paper, we propose a new decomposition algorithm for the MDO-CC based on the regularization technique and inexact penalty decomposition. The algorithm is presented such that existing proofs can be extended, under certain assumptions, to show that it converges to stationary points of the original problem and that it converges locally at a superlinear rate. Numerical computation with an engineering design example and several analytical example problems shows promising results with convergence to the all-in-one solution.

scholarly journals Skew Spectra of Oriented Graphs

10.37236/270 ◽  
2009 ◽  
Vol 16 (1) ◽  
Author(s):  
Bryan Shader ◽  
Wasin So
Keyword(s):  
Directed Graph ◽  
Adjacency Matrix ◽  
Undirected Graph ◽  
Oriented Graph ◽  
Oriented Graphs ◽  
Underlying Graph ◽  
Adjacency Spectrum ◽  
The Relationship ◽  
Skew Adjacency Matrix

An oriented graph $G^{\sigma}$ is a simple undirected graph $G$ with an orientation $\sigma$, which assigns to each edge a direction so that $G^{\sigma}$ becomes a directed graph. $G$ is called the underlying graph of $G^{\sigma}$, and we denote by $Sp(G)$ the adjacency spectrum of $G$. Skew-adjacency matrix $S( G^{\sigma} )$ of $G^{\sigma}$ is introduced, and its spectrum $Sp_S( G^{\sigma} )$ is called the skew-spectrum of $G^{\sigma}$. The relationship between $Sp_S( G^{\sigma} )$ and $Sp(G)$ is studied. In particular, we prove that (i) $Sp_S( G^{\sigma} ) = {\bf i} Sp(G)$ for some orientation $\sigma$ if and only if $G$ is bipartite, (ii) $Sp_S(G^{\sigma}) = {\bf i} Sp(G)$ for any orientation $\sigma$ if and only if $G$ is a forest, where ${\bf i}=\sqrt{-1}$.

Study on Parameter Transfer Structure of Generalized Modular Based Graph Theory

2012 ◽  
Vol 562-564 ◽  
pp. 1323-1326 ◽  
Author(s):  
Chao Zhou ◽  
Yan Ping Liu
Keyword(s):  
Graph Theory ◽  
Directed Graph ◽  
Mathematical Description ◽  
Theoretical Basis ◽  
Product Structure ◽  
Decomposition Algorithm ◽  
Modular Structure ◽  
Directed Edge ◽  
Transfer Structure ◽  
Transfer Chain

For the purpose of reducing product structure levels and shorting transfer chain of parameter, in this paper the product structure levels are expressed with generalized modular. The concept of directed graph of parameter connection structure for generalized modular is proposed with the use of directed graph theory, generalized modular, sub-modular and part represented by vertex, the driven relations of parameter connection represented by directed edge, and the properties of directed graph of parameter connection structure for generalized modular are gained. The directed graph of parameter connection structure for generalized modular is divided into a number of sub-graphs according to the relations of product-level modular structure. And the horizontal edges of sub-graphs among vertexes are decomposed. Therefore, a standardized relation of parameter connection structure is established by given the decomposition algorithm and the mathematical description of parameters connection that are provide the theoretical basis for parameters connection analysis of variant design.

scholarly journals Decomposition algorithm and mathematical models of hierarchical structure of control of the process of primary oil processing

2018 ◽  
pp. 75-82
Author(s):  
E. A. Melikov
Keyword(s):  
Optimal Control ◽  
Original Problem ◽  
Probabilistic Models ◽  
Decomposition Algorithm ◽  
Oil Refining ◽  
Automatic Regulation ◽  
Oil Processing ◽  
System Functioning ◽  
And Control ◽  
Deterministic Analog

The article considers the development of deterministic and probabilistic models and control algorithm for the technological process of primary oil processing, as well as the solution of the problem of optimal control in the form of stochastic programming. To solve the problem of optimization of the researched technological system functioning by means of the Lagrange multiplier method, the decomposition algorithm and a method based on the transformation of the original problem on the principle of a deterministic analog have been developed. The principles of constructing an optimal control system based on the developed models, the optimization algorithm and the elements of automatic regulation of the regime parameters of the primary oil refining unit are proposed.

scholarly journals A Decomposition Algorithm for the Oriented Adjacency Graph of the Triangulations of a Bordered Surface with Marked Points

10.37236/578 ◽  
2011 ◽  
Vol 18 (1) ◽  
Author(s):  
Weiwen Gu
Keyword(s):  
Oriented Graph ◽  
Decomposition Algorithm ◽  
Adjacency Graph ◽  
Connected Graphs ◽  
Marked Points ◽  
Adjacency Graphs ◽  
Mutation Type

In this paper we consider an oriented version of adjacency graphs of triangulations of bordered surfaces with marked points. We develop an algorithm that determines whether a given oriented graph is an oriented adjacency graph of a triangulation. If a given oriented graph corresponds to many triangulations, our algorithm finds all of them. As a corollary we find out that there are only finitely many oriented connected graphs with non-unique associated triangulations. We also discuss a new algorithm which determines whether a given quiver is of finite mutation type. This algorithm is linear in the number of nodes and is more effective than the previously known one.

A Regularized Inexact Penalty Decomposition Algorithm for Multidisciplinary Design Optimization Problem With Complementarity Constraints

2009 ◽  
Author(s):  
Shen Lu ◽  
Harrison M. Kim
Keyword(s):  
Design Optimization ◽  
Multidisciplinary Design Optimization ◽  
Optimization Problem ◽  
Original Problem ◽  
Equilibrium Problems ◽  
Decomposition Algorithm ◽  
Multidisciplinary Design ◽  
Stationary Points ◽  
Complementarity Constraints ◽  
Regularization Technique

Economic and physical considerations often lead to equilibrium problems in multidisciplinary design optimization (MDO), which can be captured by MDO problems with complementarity constraints (MDO-CC) — a newly emerging class of problem. Due to the ill-posedness associated with the complementarity constraints, many existing MDO methods may have numerical difficulties solving the MDO-CC. In this paper, we propose a new decomposition algorithm for MDO-CC based on the regularization technique and inexact penalty decomposition. The algorithm is presented such that existing proofs can be extended, under certain assumptions, to show that it converges to stationary points of the original problem and that it converges locally at a superlinear rate. Numerical computation with an engineering design example and several analytical example problems shows promising results with convergence to the all-in-one (AIO) solution.

scholarly journals Multi-directed Graph Complexes and Quasi-isomorphisms Between Them II: Sourced Graphs

2019 ◽  
Author(s):  
Marko Živković
Keyword(s):  
Directed Graph ◽  
Deformation Theory ◽  
Vector Fields ◽  
Oriented Graph ◽  
Rational Homotopy ◽  
Graph Complexes ◽  
Graph Complex

Abstract We prove that the projection from graph complex with at least one source to oriented graph complex is a quasi-isomorphism, showing that homology of the “sourced” graph complex is also equal to the homology of standard Kontsevich’s graph complex. This result may have applications in theory of multi-vector fields $T_{\textrm{poly}}^{\geq 1}$ of degree at least one, and to the hairy graph complex that computes the rational homotopy of the space of long knots. The result is generalized to multi-directed graph complexes, showing that all such graph complexes are quasi-isomorphic. These complexes play a key role in the deformation theory of multi-oriented props recently invented by Sergei Merkulov. We also develop a theory of graph complexes with arbitrary edge types.

scholarly journals Characteristic Polynomials of Skew-Adjacency Matrices of Oriented Graphs

10.37236/643 ◽  
2011 ◽  
Vol 18 (1) ◽  
Author(s):  
Yaoping Hou ◽  
Tiangang Lei
Keyword(s):  
Characteristic Polynomial ◽  
Directed Graph ◽  
Adjacency Matrix ◽  
Undirected Graph ◽  
Oriented Graph ◽  
Bipartite Graphs ◽  
Characteristic Polynomials ◽  
Oriented Graphs ◽  
Underlying Graph ◽  
Skew Adjacency Matrix

An oriented graph $\overleftarrow{G}$ is a simple undirected graph $G$ with an orientation, which assigns to each edge a direction so that $\overleftarrow{G}$ becomes a directed graph. $G$ is called the underlying graph of $\overleftarrow{G}$ and we denote by $S(\overleftarrow{G})$ the skew-adjacency matrix of $\overleftarrow{G}$ and its spectrum $Sp(\overleftarrow{G})$ is called the skew-spectrum of $\overleftarrow{G}$. In this paper, the coefficients of the characteristic polynomial of the skew-adjacency matrix $S(\overleftarrow{G}) $ are given in terms of $\overleftarrow{G}$ and as its applications, new combinatorial proofs of known results are obtained and new families of oriented bipartite graphs $\overleftarrow{G}$ with $Sp(\overleftarrow{G})={\bf i} Sp(G) $ are given.

scholarly journals The Square of a Directed Graph

2019 ◽  
Vol 8 (4) ◽  
pp. 8331-8335
Keyword(s):  
Directed Graph ◽  
Oriented Graph ◽  
Directed Cycle ◽  
Directed Path ◽  
The Relationship ◽  
Special Case ◽  
Cycle Graph

The square of an oriented graph is an oriented graph such that if and only if for some , both and exist. According to the square of oriented graph conjecture (SOGC), there exists a vertex such that . It is a special case of a more general Seymour’s second neighborhood conjecture (SSNC) which states for every oriented graph , there exists a vertex such that . In this study, the methods to square a directed graph and verify its correctness were introduced. Moreover, some lemmas were introduced to prove some classes of oriented graph including regular oriented graph, directed cycle graph and directed path graphs are satisfied the SOGC. Besides that, the relationship between SOGC and SSNC are also proved in this study. As a result, the verification of the SOGC in turn implies partial results for SSNC.

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