An Approach for Solving Minimum Spanning Tree Problem Using a Modified Ant Colony Optimization Algorithm
Kankanam Pathiranage Oshan Niluminda,
Ekanayake Mudiyanselage Uthpala Senarath Bandara Ekanayake
Issue:
Volume 10, Issue 6, December 2022
Pages:
223-235
Received:
22 October 2022
Accepted:
4 November 2022
Published:
8 December 2022
DOI:
10.11648/j.ajam.20221006.11
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Abstract: In real life, people often want to do tasks at the lowest possible cost while also taking into consideration travel time and distance. The term "minimum spanning tree" refers to the spanning tree that has a weight that is less than or equal to the weight of all other feasible spanning trees. A spanning tree is created when every vertex in a network is linked and has no cycles in it; there must be no other spanning tree with a lesser weight. The minimum spanning tree problem has been solved using a variety of methods that have been published in the literature. They provide the best answer to the minimum spanning tree problems given an undirected graph using Prim's and Kruskal's algorithms. A probabilistic method for resolving computational issues that may be simplified to finding the best route via graphs is the Ant Colony Optimization Algorithm (ACOA). This algorithm has been developed based on how ants search for a route between their nest and a food source while foraging. This paper proposes a novel technique and effective method for studying the large scale of the problem and determining the minimum cost-spanning tree of a connected weight undirected graph with fewer iterations using the Modified Ant Colony Optimization Algorithm (ACOA). When the graph has a large number of nodes, this novel approach is simpler and easier to implement than other existing algorithms, and by comparing our methods to Prim's and Kruskal's, we can get the same results.
Abstract: In real life, people often want to do tasks at the lowest possible cost while also taking into consideration travel time and distance. The term "minimum spanning tree" refers to the spanning tree that has a weight that is less than or equal to the weight of all other feasible spanning trees. A spanning tree is created when every vertex in a network...
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Application of Log and Exponential Functions for Velocity Calculation in Axis Symmetrical Conductor’s Cross-Section
Issue:
Volume 10, Issue 6, December 2022
Pages:
236-239
Received:
16 November 2022
Accepted:
6 December 2022
Published:
15 December 2022
DOI:
10.11648/j.ajam.20221006.12
Downloads:
Views:
Abstract: The paper is occupied with laminar and turbulence flow in round conductors having as main theme velocity division in pipes cross – section. For this problem there are existing formulas that are analyzed, and also some new formulas are presented. Rectilinear flow is researched with constant cross – section therefor flow through all cross – sections is parallel and normal on cross – section. Flow is uniform through flow direction, average velocity is constant value. Laminar flow where analytic solution is existed and turbulence flow where experimental formulas are applied, were analyzed. Log and exponential formulas for velocity division in turbulence flow are analyzed through short calculation and the graphic for identical flow conditions with same Re number. Reynolds equation applied for steady turbulence flow, for flow plane do not allowed determination of velocity division in cross – section. Therefor relations between average values and fluctuations were assumed as log or exponential functions and they were experimentally validated. Some existing formulas are shown below. Laminar uniform axis symmetrical flow having analytic solution as square parable is shown. Formula for turbulence axis symmetrical flow with log velocity division called ”velocity deficit” is analyzed. Also formula for turbulence axis symmetrical flow with exponential velocity division for smooth wall has been analyzed. At the end new and original formulas for turbulence flow with log and exponential velocity division are presented having significant advantages. These mathematical formula have to be validated experimentally and justified for use in some areas of fluid mechanics. Analyze is valid also for plane flow between two plane boards.
Abstract: The paper is occupied with laminar and turbulence flow in round conductors having as main theme velocity division in pipes cross – section. For this problem there are existing formulas that are analyzed, and also some new formulas are presented. Rectilinear flow is researched with constant cross – section therefor flow through all cross – sections ...
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, by Frobenious method yields a pair {y1(z),y2(z)} of linearly independent solutions in the form of k...
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