scholarly journals On sequential traversal of sets

2021 ◽  
Vol 31 (3) ◽  
pp. 487-504
Author(s):  
A.G. Chentsov ◽  
P.A. Chentsov
Keyword(s):  
Dynamic Programming ◽  
Mechanical Engineering ◽  
Metal Cutting ◽  
Solution Procedure ◽  
Starting Point ◽  
Precedence Conditions ◽  
Natural Solution ◽  
Optimizing Algorithm ◽  
Terminal Component

The problem of sequential traversal of megapolises with precedence conditions is investigated; this problem is oriented to mechanical engineering — CNC metal cutting machines. There is the following setting singularity: the terminal component of additive criterion contains the dependence on the starting point. This singularity leads to the fact that the natural solution procedure based on dynamic programming must be applied individually for every starting point. The investigation goal consists in the construction of an optimizing algorithm for determining a complex including a route (a variant of megapolis numbering), a trajectory, and a starting point. The proposed algorithm realizes an idea of directed enumeration of starting points. This algorithm is realized as a program for PC; computations for model examples are made.

scholarly journals To the question of optimization of the starting point in the routing problem with restrictions

2020 ◽  
Vol 55 ◽  
pp. 135-154
Author(s):  
A.G. Chentsov ◽  
P.A. Chentsov
Keyword(s):  
Dynamic Programming ◽  
Optimal Algorithm ◽  
Finite Sets ◽  
Global Extremum ◽  
Routing Problem ◽  
Starting Point ◽  
Final System ◽  
Terminal Component

We consider the extreme routing problem with an additive criterion, the terminal component of which depends on the starting point. This dependence may be associated, in particular, with the requirement to return to the starting point region after completing the final system of tasks that need to be ordered. The work assumes that the tasks to be performed are related with visiting non-empty finite sets called megacities. In turn, the mentioned visits are associated with the performance of works, the costs of which are involved in the formation of the criterion. Finally, the costs of external movements (between megacities) supplement the formation of an additive criterion to be minimized. It is required to find a global extremum and a solution that includes a starting point, the order of visits to megacities and a specific trajectory of the process. The solution uses widely understood dynamic programming (DP). It is significant that procedures based on DP use starting point. Therefore, enumeration of mentioned points is required. The article proposes an approach to solving the problem of reducing this enumeration through the use of auxiliary DP that are universal with respect to the choice of a starting point. The optimal algorithm was built and implemented on a PC using the aforementioned approach.

scholarly journals ON ROUTING PROBLEM WITH STARTING POINT OPTIMIZATION

2020 ◽  
Vol 6 (2) ◽  
pp. 44
Author(s):  
Alexander G. Chentsov ◽  
Pavel A. Chentsov
Keyword(s):  
Dynamic Programming ◽  
Engineering Applications ◽  
Routing Problem ◽  
Starting Point ◽  
Complex Dependence ◽  
Terminal Component

One problem focused on engineering applications is considered. It is assumed that sequential visits to megacities have been implemented. After all visits have been made, it is required to return to the starting point (a more complex dependence on the starting point is also considered). But the last requirement is not strict: some weakening of the return condition is acceptable. Under these assumptions, it is required to optimize the choice of starting point, route, and specific trajectory. The well-known dynamic programming (DP) is used for the solution. But when using DP, significant difficulties arise associated with the dependence of the terminal component of the criterion on the starting point. Starting point enumeration is required. We consider the possibility of reducing the enumeration associated with applied variants of universal (relative to the starting point) dynamic programming. Of course, this approach requires some transformation of the problem.

scholarly journals One task of routing jobs in high radiation conditions

2021 ◽  
Vol 58 ◽  
pp. 94-126
Author(s):  
A.G. Chentsov ◽  
A.A. Chentsov ◽  
A.N. Sesekin
Keyword(s):  
Dynamic Programming ◽  
Numerical Solution ◽  
Model Problem ◽  
Optimal Solution ◽  
High Radiation ◽  
Dose Load ◽  
Route Problem ◽  
Precedence Conditions ◽  
Sequential Bypass ◽  
Radiation Conditions

The problem of sequential bypass of megalopolises is investigated, focused on the problem of dismantling a system of radiation hazardous objects under constraints in the form of precedence conditions. The radiation impact on the performers is assessed by the doses received during movements and during the performance of dismantling works. The route problem of minimizing the dose load of workers carrying out dismantling in one or another sequence of operations is considered. The procedure for constructing an optimal solution using a variant of dynamic programming is investigated. On this basis, an algorithm is built, implemented on a PC. Examples of the numerical solution of a model problem for the minimum dose load are given.

scholarly journals Cold thread Forming – the chipless alternative for high resistant internal threads

2018 ◽  
Vol 251 ◽  
pp. 02046
Author(s):  
Roland Heiler
Keyword(s):  
Mechanical Engineering ◽  
Metal Cutting ◽  
Typical Application ◽  
Cold Forming ◽  
Process Characteristics ◽  
Pull Out ◽  
Wide Range ◽  
Thread Milling

In the area of construction and mechanical engineering the designers and production engineers very often do have the task to produce high resistant connections with the possibility of assembling and de assembling parts in a wide range of different materials. Most often connection bolts and internal threads are used to fulfill this task. To produce the internal threads typically the three following internal threading technologies are used: tapping, cold thread forming and thread milling. Tapping and thread milling are metal cutting technologies but cold thread forming is a chipless alternative. Due to the cold forming of the thread this process does have several benefits in comparison to the traditional cutting technologies, but also some special features and process characteristics have to be considered, that it is possible to produce reliable internal threads. In the article the technology is presented with information about the process characteristics, the modern tools design and typical application areas. Results of pull out tests are showing the possibility for producing high resistant threads.

The Interest of Mechanical Engineering Students in the Grand Challenges for Engineering in the 21st Century

2011 ◽  
Author(s):  
Christine Hailey ◽  
Michael Drysdale ◽  
Daniel Householder
Keyword(s):  
21St Century ◽  
Mechanical Engineering ◽  
Engineering Students ◽  
Strong Relationship ◽  
Structured Interview ◽  
Grand Challenges ◽  
Complex Problems ◽  
Starting Point ◽  
Undergraduate Engineering Education ◽  
Survey Results

In 2008, the National Academy of Engineering (NAE) announced 14 Grand Challenges for Engineering in the 21st Century, a set of exceptionally complex problems associated with national security, quality of life, and a sustainable future. Understanding the extent to which engineering students are interested in these complex problems and the extent to which they feel confident that they can contribute to the solution of these problems could serve as a starting point to foster engagement with the Grand Challenges. This paper presents results from a survey of mechanical engineering (ME) students’ interest in the NAE Grand Challenges and their confidence in their ability to contribute to resolutions of the Challenges. Seventy-six sophomore mechanical engineering majors completed the survey composed of 36 examples of problems described within the NAE Challenge report. Survey results show a strong relationship between students’ interest and their confidence in meeting a challenge. Six students participated in a semi-structured interview regarding their experience with and knowledge of the Challenges. Interview results indicated the students had few course-related experiences that exposed them to the Challenges. Results of this study can contribute to a broader conversation among ME educators about ways to integrate the NAE Grand Challenges in undergraduate engineering education.

Sequential Global Approximation in Non-Hierarchic System Decomposition and Optimization

1991 ◽  
Author(s):  
J. E. Renaud ◽  
G. A. Gabriele
Keyword(s):  
Iterative Solution ◽  
Approximation Problem ◽  
Solution Procedure ◽  
Global Approximation ◽  
Design Data ◽  
System Decomposition ◽  
Local Functions ◽  
Starting Point ◽  
Non Local ◽  
Hierarchic System

Abstract A procedure for the optimization of non-hierarchic systems by decomposition into reduced subspaces is presented. Sequential global approximation is proposed as a coordination procedure for subspace optimizations. The same objective function and cumulative constraints are imposed at each subspace. Non-local functions are approximated at the subspaces using global sensitivities. The method optimizes the subspace problems concurrently allowing for parallel processing. Following each sequence of concurrent subspace optimizations an approximation to the global problem is formed using design data accumulated during the subspace optimizations. The solution of the global approximation problem is used as the starting point for subsequent subspace optimizations in an iterative solution procedure. Preliminary studies on two engineering design examples illustrate the methods potential.

Shortest Route Application via Dynamic Programming in the Transportation Networks

2021 ◽  
pp. 362-371
Author(s):  
Arzu Eren Şenaras ◽  
Şahin İnanç ◽  
Hayrettin Kemal Sezen ◽  
Onur Mesut Şenaras
Keyword(s):  
Dynamic Programming ◽  
Shortest Path ◽  
Dynamic Programming Method ◽  
Programming Approach ◽  
Dynamic Programming Approach ◽  
Transportation Sector ◽  
Shortest Route ◽  
Starting Point ◽  
Visual Basic Application ◽  
Destination Point

The purpose of this study is to develop an application for finding the shortest path in the transportation sector. The application was developed using the dynamic programming method in MS Excel Visual Basic application. These types of problems are also called stagecoach problems. The purpose of the problem is finding the shortest path between the starting point (node) and the destination point. Values are related to the roads in the network to specify the distance between two nodes. In case of a small number of nodes (activities), a solution can be reached by evaluating all options. But the number of possible options to be scanned for real problems is quite large. In such cases, a suitable method is needed for the solution. It can produce effective solutions with the dynamic programming approach.

An Approach to Dynamic Regional Planning with Multiple Objectives

1976 ◽  
Vol 8 (3) ◽  
pp. 341-350
Author(s):  
G G Roy
Keyword(s):  
Dynamic Programming ◽  
Programming Problem ◽  
Optimality Condition ◽  
Regional Planning ◽  
Solution Procedure ◽  
Time Dependent ◽  
Small Scale ◽  
Worked Example ◽  
Dynamic Programming Problem ◽  
Planning Problems

A proposal is made for the solution of multiobjective, time-dependent planning problems which are essentially discrete valued. The solution procedure, based on a particular multiobjective optimality condition (developed elsewhere), is structured as a stepwise dynamic programming problem. The detailed theory of the proposed procedure is followed by a small-scale worked example which shows the application of the method.

Network-Based Approach to Korean Handwriting Analysis

1998 ◽  
Vol 12 (02) ◽  
pp. 233-249 ◽  
Author(s):  
Bong-Kee Sin ◽  
Jin H. Kim
Keyword(s):  
Time Series ◽  
Dynamic Programming ◽  
Character Recognition ◽  
Stochastic Approach ◽  
Handwriting Analysis ◽  
State Observation ◽  
Starting Point ◽  
Observation Sequence ◽  
On Line ◽  
Analysis Of Time Series

It is well known that the stochastic approach using the HMM and dynamic programming-based search is particularly suited to the analysis of time series signals including on-line handwriting. The starting point of this research is a network of HMMs which models the whole set of characters. Then it is followed by the assertion that the HMM for the on-line script can be applied to not only on-line character recognition but also to the handwriting synthesis and even pen-trajectory recovery in off-line character images. The solutions to these problems are based on the single network of HMMs and the single principle of DP-based state-observation alignment. Given an observation sequence, the search for the best path in the network corresponds to the recognition. Given a character model, the search for the best observation sequence corresponds to the handwriting generation. The proposed framework has been shown to work nicely through a set of tests on Korean characters.

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