Assign multiple AUVs to form a row efficiently based on a method of processing the cost matrix

2020 ◽  
Vol 101 ◽  
pp. 102177
Author(s):  
Jin Zhang ◽  
Shuai Kang ◽  
Jiancheng Yu ◽  
Shijie Liu ◽  
Wei Li ◽  
...  
Keyword(s):  
Cost Matrix ◽  
The Cost

On Some Properties of Semi-rings

2018 ◽  
pp. 35-50
Author(s):  
A. I. Belousov
Keyword(s):  
Linear Equations ◽  
Oriented Graph ◽  
Theoretical Computer Science ◽  
Alternative Methods ◽  
Main Role ◽  
Cost Matrix ◽  
Sequential Elimination ◽  
The Matrix ◽  
Systems Of Linear Equations ◽  
The Cost

The main objective of this paper is to prove a theorem according to which a method of successive elimination of unknowns in the solution of systems of linear equations in the semi-rings with iteration gives the really smallest solution of the system. The proof is based on the graph interpretation of the system and establishes a relationship between the method of sequential elimination of unknowns and the method for calculating a cost matrix of a labeled oriented graph using the method of sequential calculation of cost matrices following the paths of increasing ranks. Along with that, and in terms of preparing for the proof of the main theorem, we consider the following important properties of the closed semi-rings and semi-rings with iteration.We prove the properties of an infinite sum (a supremum of the sequence in natural ordering of an idempotent semi-ring). In particular, the proof of the continuity of the addition operation is much simpler than in the known issues, which is the basis for the well-known algorithm for solving a linear equation in a semi-ring with iteration.Next, we prove a theorem on the closeness of semi-rings with iteration with respect to solutions of the systems of linear equations. We also give a detailed proof of the theorem of the cost matrix of an oriented graph labeled above a semi-ring as an iteration of the matrix of arc labels.The concept of an automaton over a semi-ring is introduced, which, unlike the usual labeled oriented graph, has a distinguished "final" vertex with a zero out-degree.All of the foregoing provides a basis for the proof of the main theorem, in which the concept of an automaton over a semi-ring plays the main role.The article's results are scientifically and methodologically valuable. The proposed proof of the main theorem allows us to relate two alternative methods for calculating the cost matrix of a labeled oriented graph, and the proposed proofs of already known statements can be useful in presenting the elements of the theory of semi-rings that plays an important role in mathematical studies of students majoring in software technologies and theoretical computer science.

Searching Best Strategies Algorithm for the No Balance Assignment Problem

2011 ◽  
Vol 50-51 ◽  
pp. 386-390
Author(s):  
Mao Yan Fang ◽  
Min Le Wang ◽  
Yi Ming Bi
Keyword(s):  
Assignment Problem ◽  
Cost Matrix ◽  
Classical Algorithm ◽  
The Cost

The No Balance Assignment Problem (NBAP) is mainly resolved by changing it into Balance Assignment Problem (BAP) and using classical algorithm to deal with it now. This paper proposed Searching Best strategies Algorithm (SBSA) to resolve this problem, and it needn’t to change NBAP into BAP. SBSA resolves NBAP based on searching the best answer of the cost matrix. This algorithm’s theory is simple，and it is easy to operate. The result of the research indicate that the algorithm not only can deal with NBAP, but also can deal with BAP and other problems such as translation problem.

scholarly journals A Multilayer Path Planning Method for High Voltage Distribution Network Based on the Floyd-Warshall Algorithm

2021 ◽  
Vol 2121 (1) ◽  
pp. 012006
Author(s):  
Zhaolong Quan ◽  
Jie Xing ◽  
Ruilin Cao
Keyword(s):  
Path Planning ◽  
Life Cycle Cost ◽  
Cost Model ◽  
Distribution Networks ◽  
Load Flow ◽  
Planning Method ◽  
Cost Matrix ◽  
Planning Scheme ◽  
The Cost ◽  
The City

Abstract With the development of the city, a huge number of distribution networks are waiting for planning. A reasonable planning scheme can meet the power demand and reduce the investment cost. In this paper, a life cycle cost model including the investments of substation and wiring is established with the constraints about load flow calculation and maxi-mum load of wiring. Additionally, a multilayer planning method based on the Floyd-Warshall algorithm has been proposed to solve the model. The area of the city containing substations is divided based on the position of load through the hybrid clusters algorithm in the method. Then, using the divided result of power supply area, the cost matrix for the multilayer path planning method can be constructed through the principle of the method. Lastly, with the cost matrix, the planning scheme in each area will be provided by the Floyd-Warshall algorithm. The result on the actual planning area between the two algorithms shows the total cost of the investment is decreased through using the planning method in this paper.

An Efficient Algorithm for Improved Shape Context Feature's Cost Matrix Computation

2012 ◽  
Vol 532-533 ◽  
pp. 1631-1635
Author(s):  
Shan Shan Li ◽  
Ying Hai Zhao ◽  
Jiang An Wang
Keyword(s):  
Efficient Method ◽  
Fourier Transformation ◽  
Time Complexity ◽  
Visual Feature ◽  
Shape Context ◽  
Rotation Invariant ◽  
Matrix Computation ◽  
Cost Matrix ◽  
Feature Based ◽  
The Cost

Shape context is not rotation invariant as a local visual feature. To solve this problem, 2-D and 1-D Fourier Transformation has been performed on the feature. Based on the property of Fourier Transformation, a fast and efficient method is presented in the cost matrix computation of these improved shape context feature. The analysis shows the time complexity is much lower and the experiments show effective and efficiency of this new algorithm.

Optimizing the cost matrix for approximate string matching using genetic algorithms

1998 ◽  
Vol 31 (4) ◽  
pp. 431-440 ◽  
Author(s):  
Marc Parizeau ◽  
Nadia Ghazzali ◽  
Jean-François Hébert
Keyword(s):  
Genetic Algorithms ◽  
String Matching ◽  
Approximate String Matching ◽  
Cost Matrix ◽  
The Cost

scholarly journals Optimization of Ultrasound Information Imaging Algorithm in Cardiovascular Disease Based on Image Enhancement

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Yongfu Shao ◽  
Jue Wu ◽  
Hongping Ou ◽  
Min Pei ◽  
Li Liu ◽  
...  
Keyword(s):  
Cardiovascular Disease ◽  
Spatial Frequency ◽  
Frequency Domain ◽  
Image Enhancement ◽  
Ultrasound Imaging ◽  
Ultrasound Images ◽  
Cost Matrix ◽  
Imaging Algorithm ◽  
The Cost ◽  
Spatial Frequency Domain

To improve the interpretability or perception of information in images for human viewers is the main goal of image enhancement. Aiming at the problem that image edges are difficult to determine due to artefacts, plaques, and vascular branches in cardiovascular ultrasound, an edge ultrasound imaging detection algorithm based on spatial-frequency-domain image enhancement is proposed to improve the clarity of ultrasound images. Firstly, this paper uses the space-frequency-domain enhancement algorithm to enhance the image. This algorithm overcomes the problem of low contrast of conventional algorithms. The enhanced data matrix is used as the cost matrix, and then, the heuristic image search method is used to search the image of the cost matrix. The results show that the use of spatial-frequency-domain image ultrasound imaging algorithm can improve the contrast and sharpness of ultrasound images of cardiovascular disease, which can make the middle edge of the image clearer, the detection accuracy rate is increased to 92.76%, and the ultrasound of cardiovascular disease is improved. The edge of the image gets accuracy. The paper confirms that the ultrasound imaging algorithm based on spatial-frequency-domain image enhancement is worthy of application in clinical ultrasound image processing. The performance of the proposed technique is 32.54%, 75.30%, 21.19%, 21.26%, and 11.10% better than the existing technique in terms of edge energy, detail energy, sharpness, contrast, and information entropy, respectively.

scholarly journals Sequentially Updated Weighted Cost Opportunity Based Algorithm in Transportation Problem

2019 ◽  
Vol 38 ◽  
pp. 47-55
Author(s):  
ARM Jalal Uddin Jamali ◽  
Pushpa Akhtar
Keyword(s):  
Opportunity Cost ◽  
Feasible Solution ◽  
Supply And Demand ◽  
Optimal Solution ◽  
Basic Feasible Solution ◽  
New Approach ◽  
Cost Matrix ◽  
Transportation Problems ◽  
The Cost ◽  
First Time

Transportation models are of multidisciplinary fields of interest. In classical transportation approaches, the flow of allocation is controlled by the cost entries and/or manipulation of cost entries – so called Distribution Indicator (DI) or Total Opportunity Cost (TOC). But these DI or TOC tables are formulated by the manipulation of cost entries only. None of them considers demand and/or supply entry to formulate the DI/ TOC table. Recently authors have developed weighted opportunity cost (WOC) matrix where this weighted opportunity cost matrix is formulated by the manipulation of supply and demand entries along with cost entries as well. In this WOC matrix, the supply and demand entries act as weight factors. Moreover by incorporating this WOC matrix in Least Cost Matrix, authors have developed a new approach to find out Initial Basic Feasible Solution of Transportation Problems. But in that approach, WOC matrix was invariant in every step of allocation procedures. That is, after the first time formulation of the weighted opportunity cost matrix, the WOC matrix was invariant throughout all allocation procedures. On the other hand in VAM method, the flow of allocation is controlled by the DI table and this table is updated after each allocation step. Motivated by this idea, we have reformed the WOC matrix as Sequentially Updated Weighted Opportunity Cost (SUWOC) matrix. The significance difference of these two matrices is that, WOC matrix is invariant through all over the allocation procedures whereas SUWOC   matrix is updated in each step of allocation procedures. Note that here update (/invariant) means changed (/unchanged) the weighted opportunity cost of the cells. Finally by incorporating this SUWOC matrix in Least Cost Matrix, we have developed a new approach to find out Initial Basic Feasible Solution of Transportation Problems.  Some experiments have been carried out to justify the validity and the effectiveness of the proposed SUWOC-LCM approach. Experimental results reveal that the SUWOC-LCM approach outperforms to find out IBFS. Moreover sometime this approach is able to find out optimal solution too. GANIT J. Bangladesh Math. Soc.Vol. 38 (2018) 47-55

scholarly journals An Algorithm for Mapping the Asymmetric Multiple Traveling Salesman Problem onto Colored Petri Nets

Algorithms ◽  
2018 ◽  
Vol 11 (10) ◽  
pp. 143 ◽  
Author(s):  
Furqan Essani ◽  
Sajjad Haider
Keyword(s):  
Petri Nets ◽  
Traveling Salesman Problem ◽  
Feasible Solution ◽  
Optimal Solution ◽  
Traveling Salesman ◽  
Colored Petri Nets ◽  
Cost Matrix ◽  
Multiple Traveling Salesman Problem ◽  
Hard Problems ◽  
The Cost

The Multiple Traveling Salesman Problem is an extension of the famous Traveling Salesman Problem. Finding an optimal solution to the Multiple Traveling Salesman Problem (mTSP) is a difficult task as it belongs to the class of NP-hard problems. The problem becomes more complicated when the cost matrix is not symmetric. In such cases, finding even a feasible solution to the problem becomes a challenging task. In this paper, an algorithm is presented that uses Colored Petri Nets (CPN)—a mathematical modeling language—to represent the Multiple Traveling Salesman Problem. The proposed algorithm maps any given mTSP onto a CPN. The transformed model in CPN guarantees a feasible solution to the mTSP with asymmetric cost matrix. The model is simulated in CPNTools to measure two optimization objectives: the maximum time a salesman takes in a feasible solution and the collective time taken by all salesmen. The transformed model is also formally verified through reachability analysis to ensure that it is correct and is terminating.

scholarly journals A Data-Guided Lexisearch Algorithm for the Asymmetric Traveling Salesman Problem

2011 ◽  
Vol 2011 ◽  
pp. 1-18 ◽  
Author(s):  
Zakir Hussain Ahmed
Keyword(s):  
Traveling Salesman Problem ◽  
Optimal Solution ◽  
Traveling Salesman ◽  
Computational Time ◽  
Cost Matrix ◽  
Asymmetric Traveling Salesman Problem ◽  
Path Representation ◽  
Random Instances ◽  
Representation Method ◽  
The Cost

A simple lexisearch algorithm that uses path representation method for the asymmetric traveling salesman problem (ATSP) is proposed, along with an illustrative example, to obtain exact optimal solution to the problem. Then a data-guided lexisearch algorithm is presented. First, the cost matrix of the problem is transposed depending on the variance of rows and columns, and then the simple lexisearch algorithm is applied. It is shown that this minor preprocessing of the data before the simple lexisearch algorithm is applied improves the computational time substantially. The efficiency of our algorithms to the problem against two existing algorithms has been examined for some TSPLIB and random instances of various sizes. The results show remarkably better performance of our algorithms, especially our data-guided algorithm.

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