scholarly journals Graph Routing Problem Using Euler’s Theorem and Its Applications

2019 ◽  
Vol 3 (1) ◽  
pp. 1 ◽  
Author(s):  
Hashnayne Ahmed
Keyword(s):  
Routing Problem ◽  
Euler’S Theorem

scholarly journals Graph Routing Problem Using Euler’s Theorem and Its Applications

2019 ◽  
Author(s):  
Hashnayne Ahmed
Keyword(s):  
Graph Theory ◽  
Social Science ◽  
Routing Protocols ◽  
Routing Problem ◽  
Euler’S Theorem ◽  
Bridge Problem ◽  
Eulerian Circuit ◽  
History Of ◽  
Proof Techniques ◽  
Modern Era

In this modern era, time and cases related to time is very important to us. For shortening time, Eulerian Circuit canopen a new dimension. In computer science, social science and natural science, graph theory is a stimulating space for thestudy of proof techniques. Graphs are also effective in modeling a variety of optimization cases like routing protocols, networkmanagement, stochastic approaches, street mapping etc. Konigsberg Bridge Problem has seven bridges linked with four islandsdetached by a river in such a way that one can’t walk through each of the bridges exactly once and returning back to thestarting point. Leonard Euler solved it in 1735 which is the foundation of modern graph theory. Euler’s solution forKonigsberg Bridge Problem is considered as the first theorem of Graph Theory which gives the idea of Eulerian circuit. It canbe used in several cases for shortening any path. From the Konigsberg Bridge Problem to ongoing DNA fragmentationproblem, it has its applications. Aiming to build such a dimension using Euler’s theorem and Konigsberg Bridge Problem, thispaper presents about the history of remarkable Konigsberg Bridge Problem, Euler’s Explanation on it, an alternativeexplanation and some applications to Eulerian Circuit using graph routing and Fortran Coding of it.

scholarly journals Graph Routing Problem Using Euler’s Theorem and Its Applications

2019 ◽  
Author(s):  
Hashnayne Ahmed
Keyword(s):  
Graph Theory ◽  
Social Science ◽  
Routing Protocols ◽  
Routing Problem ◽  
Euler’S Theorem ◽  
Bridge Problem ◽  
Eulerian Circuit ◽  
History Of ◽  
Proof Techniques ◽  
Modern Era

In this modern era, time and cases related to time is very important to us. For shortening time, Eulerian Circuit canopen a new dimension. In computer science, social science and natural science, graph theory is a stimulating space for thestudy of proof techniques. Graphs are also effective in modeling a variety of optimization cases like routing protocols, networkmanagement, stochastic approaches, street mapping etc. Konigsberg Bridge Problem has seven bridges linked with four islandsdetached by a river in such a way that one can’t walk through each of the bridges exactly once and returning back to thestarting point. Leonard Euler solved it in 1735 which is the foundation of modern graph theory. Euler’s solution forKonigsberg Bridge Problem is considered as the first theorem of Graph Theory which gives the idea of Eulerian circuit. It canbe used in several cases for shortening any path. From the Konigsberg Bridge Problem to ongoing DNA fragmentationproblem, it has its applications. Aiming to build such a dimension using Euler’s theorem and Konigsberg Bridge Problem, thispaper presents about the history of remarkable Konigsberg Bridge Problem, Euler’s Explanation on it, an alternativeexplanation and some applications to Eulerian Circuit using graph routing and Fortran Coding of it.

Fuzzy multi-objective location and routing problem

2020 ◽  
Vol 39 (3) ◽  
pp. 3259-3273
Author(s):  
Nasser Shahsavari-Pour ◽  
Najmeh Bahram-Pour ◽  
Mojde Kazemi
Keyword(s):  
Firefly Algorithm ◽  
High Reliability ◽  
Research Area ◽  
Nsga Ii ◽  
Location Routing Problem ◽  
Routing Problem ◽  
Location Allocation ◽  
Multi Objective ◽  
Location Routing ◽  
The Cost

The location-routing problem is a research area that simultaneously solves location-allocation and vehicle routing issues. It is critical to delivering emergency goods to customers with high reliability. In this paper, reliability in location and routing problems was considered as the probability of failure in depots, vehicles, and routs. The problem has two objectives, minimizing the cost and maximizing the reliability, the latter expressed by minimizing the expected cost of failure. First, a mathematical model of the problem was presented and due to its NP-hard nature, it was solved by a meta-heuristic approach using a NSGA-II algorithm and a discrete multi-objective firefly algorithm. The efficiency of these algorithms was studied through a complete set of examples and it was found that the multi-objective discrete firefly algorithm has a better Diversification Metric (DM) index; the Mean Ideal Distance (MID) and Spacing Metric (SM) indexes are only suitable for small to medium problems, losing their effectiveness for big problems.

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