scholarly journals Hungarian Algorithm using Haar Tuples to Solve Fuzzy Travelling Salesman Problem

2018 ◽  
Vol 7 (4.10) ◽  
pp. 380
Author(s):  
S. Dhanasekar ◽  
Saroj Kumar Dash ◽  
S. Hariharan
Keyword(s):  
Travelling Salesman Problem ◽  
Special Kind ◽  
Travelling Salesman ◽  
Numerical Examples ◽  
Hungarian Algorithm ◽  
Assignment Model ◽  
The Given

Travelling salesman problem(TSP) deals with visiting all the given cities and return back to the starting city with the minimum travelling distance or minimum travelling cost where each city is visited exactly once. The TSP problem is a special kind of an assignment model that excludes sub tours.  In this paper we used Haar Hungarian algorithm approach [13] to solve a Fuzzy Travelling Salesman Problem (FTSP) and Numerical examples are given to validate the proposed algorithm.   

scholarly journals On Bernstein Polynomials Method to the System of Abel Integral Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
A. Jafarian ◽  
S. Measoomy Nia ◽  
Alireza K. Golmankhaneh ◽  
D. Baleanu
Keyword(s):  
Linear System ◽  
Numerical Solution ◽  
Integral Equations ◽  
Bernstein Polynomials ◽  
Singular System ◽  
Special Kind ◽  
Algebraic Equations ◽  
Numerical Examples ◽  
Abel Integral Equations ◽  
The Given

This paper deals with a new implementation of the Bernstein polynomials method to the numerical solution of a special kind of singular system. For this aim, first the truncated Bernstein series polynomials of the solution functions are substituted in the given problem. Using some properties of these polynomials, the solution of the problem is reduced to solve a linear system of algebraic equations. In order to confirm the reliability and accuracy of the proposed method, some weakly Abel integral equations systems with comparisons are solved in detail as numerical examples.

Solving Multiple Routes Travelling Salesman Problem Using Modified Genetic Algorithm

2012 ◽  
Vol 576 ◽  
pp. 718-722
Author(s):  
Muhammad Ridwan Andi Purnomo ◽  
Mohammad Iqbal ◽  
Mila Faila Sufa
Keyword(s):  
Genetic Algorithm ◽  
Travelling Salesman Problem ◽  
Initial Position ◽  
Mutation Operator ◽  
Shortest Path Algorithm ◽  
Travelling Salesman ◽  
Numerical Examples ◽  
Modified Genetic Algorithm ◽  
Multiple Routes ◽  
Crossover And Mutation

The multiple routes travelling salesman problem (mrTSP) is an extension of the well-known travelling salesman problem (TSP), where there are several points clusters to be visited by salesman. The problem to be solved is how to define the best route in every cluster and initial position of each routes as interconnection points for the salesman. In this paper, modified genetic algorithm (mGA) is proposed in order to solve the mrTSP problem. In the proposed mGA, new heuristic algorithm for crossover and mutation operator based on local shortest path algorithm is proposed in order to assist the mGA to improve 'best solution so far'. Numerical examples are also given to test the performance of proposed mGA when solving mrTSP. The result of the study shows that the mGA is superior compared to conventional GA.

scholarly journals Application of genetic algorithm in solving the travelling Salesman problem

2021 ◽  
Vol 1208 (1) ◽  
pp. 012032
Author(s):  
Fatka Kulenović ◽  
Azra Hošić
Keyword(s):  
Genetic Algorithm ◽  
Optimization Problems ◽  
Travelling Salesman Problem ◽  
Path Selection ◽  
Exact Methods ◽  
Travelling Salesman ◽  
Combinatorial Optimization Problems ◽  
Mutation Operators ◽  
Complete Problems ◽  
The Given

Abstract The Travelling Salesman Problem is categorized as NP-complete problems called combinatorial optimization problems. For the growing number of cities it is unsolvable with the use of exact methods in a reasonable time. Genetic algorithms are evolutionary techniques used for optimization purposes according to survival of the fittest idea. These methods do not ensure optimal solutions, however they give good approximation usually in time. Studies have shown that the proposed genetic algorithm can find a shorter route in real time, compared with the existing manipulator model of path selection. The genetic algorithm depends on the selection criteria, crosses, and mutation operators described in detail in this paper. Possible settings of the genetic algorithm are listed and described, as well as the influence of mutation and crossing operators on the efficiency of the genetic algorithm. The optimization results are presented graphically in the MATLAB software package for different cases, after which a comparison of the efficiency of the genetic algorithm with respect to the given parameters is performed.

Difference Schemes for Nonlinear BVPS on the Semiaxis

2007 ◽  
Vol 7 (1) ◽  
pp. 25-47 ◽  
Author(s):  
I.P. Gavrilyuk ◽  
M. Hermann ◽  
M.V. Kutniv ◽  
V.L. Makarov
Keyword(s):  
Differential Equation ◽  
Exact Solution ◽  
Boundary Value Problem ◽  
Difference Scheme ◽  
Adaptive Algorithm ◽  
Order Differential Equation ◽  
Constructive Method ◽  
Numerical Examples ◽  
Exact Difference ◽  
The Given

Abstract The scalar boundary value problem (BVP) for a nonlinear second order differential equation on the semiaxis is considered. Under some natural assumptions it is shown that on an arbitrary finite grid there exists a unique three-point exact difference scheme (EDS), i.e., a difference scheme whose solution coincides with the projection of the exact solution of the given differential equation onto the underlying grid. A constructive method is proposed to derive from the EDS a so-called truncated difference scheme (n-TDS) of rank n, where n is a freely selectable natural number. The n-TDS is the basis for a new adaptive algorithm which has all the advantages known from the modern IVP-solvers. Numerical examples are given which illustrate the theorems presented in the paper and demonstrate the reliability of the new algorithm.

scholarly journals Tourist Route Optimization in the Context of Covid-19 Pandemic

2021 ◽  
Vol 13 (10) ◽  
pp. 5492
Author(s):  
Cristina Maria Păcurar ◽  
Ruxandra-Gabriela Albu ◽  
Victor Dan Păcurar
Keyword(s):  
Travelling Salesman Problem ◽  
Route Planning ◽  
Route Optimization ◽  
Travelling Salesman ◽  
Social Distancing ◽  
Tourist Destinations ◽  
Innovative Method ◽  
The Social ◽  
Immediate Response

The paper presents an innovative method for tourist route planning inside a destination. The necessity of reorganizing the tourist routes within a destination comes as an immediate response to the Covid-19 crisis. The implementation of the method inside tourist destinations can bring an important advantage in transforming a destination into a safer one in times of Covid-19 and post-Covid-19. The existing trend of shortening the tourist stay length has been accelerated while the epidemic became a pandemic. Moreover, the wariness for future pandemics has brought into spotlight the issue of overcrowded attractions inside a destination at certain moments. The method presented in this paper proposes a backtracking algorithm, more precisely an adaptation of the travelling salesman problem. The method presented is aimed to facilitate the navigation inside a destination and to revive certain less-visited sightseeing spots inside a destination while facilitating conformation with the social distancing measures imposed for Covid-19 control.

A column-and-row generation approach for the flying sidekick travelling salesman problem

2021 ◽  
Vol 124 ◽  
pp. 102913
Author(s):  
Maurizio Boccia ◽  
Adriano Masone ◽  
Antonio Sforza ◽  
Claudio Sterle
Keyword(s):  
Travelling Salesman Problem ◽  
Travelling Salesman

scholarly journals Two matrix methods for solution of nonlinear and linear Lane-Emden type equations with mixed condition by operational matrix

2015 ◽  
Vol 4 (3) ◽  
pp. 420 ◽  
Author(s):  
Behrooz Basirat ◽  
Mohammad Amin Shahdadi
Keyword(s):  
Bernstein Polynomials ◽  
Operational Matrix ◽  
Numerical Procedure ◽  
Operational Matrices ◽  
Algebraic Equations ◽  
Mixed Condition ◽  
Matrix Methods ◽  
Numerical Examples ◽  
Linear Algebraic Equations ◽  
The Given

<p>The aim of this article is to present an efficient numerical procedure for solving Lane-Emden type equations. We present two practical matrix method for solving Lane-Emden type equations with mixed conditions by Bernstein polynomials operational matrices (BPOMs) on interval [<em>a; b</em>]. This methods transforms Lane-Emden type equations and the given conditions into matrix equation which corresponds to a system of linear algebraic equations. We also give some numerical examples to demonstrate the efficiency and validity of the operational matrices for solving Lane-Emden type equations (LEEs).</p>

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