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.

scholarly journals Representasi Matriks untuk Proses Crossover Pada Algoritma Genetika untuk Optimasi Travelling Salesman Problem

Matematika ◽  
2017 ◽  
Vol 16 (1) ◽  
Author(s):  
Ismi Fadhillah ◽  
Yurika Permanasari ◽  
Erwin Harahap
Keyword(s):  
Genetic Algorithm ◽  
Genetic Algorithms ◽  
Optimization Problems ◽  
Matrix Representation ◽  
Travelling Salesman Problem ◽  
Optimal Number ◽  
Travelling Salesman ◽  
Combinatorial Optimization Problems ◽  
Fitness Value ◽  
The City

Abstrak. Travelling Salesman Problem (TSP) merupakan salah satu permasalahan optimasi kombinatorial yang biasa terjadi dalam kehidupan sehari-hari. Permasalahan TSP yaitu mengenai seseorang yang harus mengunjungi semua kota tepat satu kali dan kembali ke kota awal dengan jarak tempuh minimal. TSP dapat diselesaikan dengan menggunakan metode Algoritma Genetika. Dalam Algoritma Genetika, representasi matriks merupakan representasi kromosom yang menunjukan sebuah perjalanan. Jika dalam perjalanan tersebut melewati n kota maka akan dibentuk matriks n x n. Matriks elemen Mij dengan baris i dan kolom j dimana entry M(i,j) akan bernilai 1 jika dan hanya jika kota i dikunjungi sebelum kota j dalam satu perjalanan tersebut, selain itu M(i,j)=0. Crossover adalah mekanisme yang dimiliki algoritma genetika dengan menggabungkan dua kromosom sehingga menghasilkan anak kromosom yang mewarisi ciri-ciri dasar dari parent. Algoritma Genetika selain melibatkan populasi awal dalam proses optimasi juga membangkitkan populasi baru melalui proses crossover, sehingga dapat memberikan daftar variabel yang optimal bukan hanya solusi tunggal. Dari hasil proses crossover dalam contoh kasus TSP melewati 6 kota, terdapat 2 kromosom anak terbaik dengan nilai finess yang sama yaitu 0.014. Algoritma Genetika dapat berhenti pada generasi II karena berturut-turut mendapat nilai fitness tertinggi yang tidak berubahKata kunci : Travelling Salesman Program (TSP), Algoritma Genetika, Representasi Matriks, Proses Crossover Abstract. Travelling Salesman Problem (TSP) is one of combinatorial optimization problems in everyday life. TSP is about someone who had to visit all the cities exactly once and return to the initial city with minimal distances. TSP can be solved using Genetic Algorithms. In a Genetic Algorithm, a matrix representation represents chromosomes which indicates a journey. If in the course of the past n number of city will set up a matrix n x n. The matrix element Mij with row i and column j where entry M (i, j) will be equal to 1 if and only if the city i before the city j visited in one trip. In addition to the M (i, j) = 0. Crossover is a mechanism that is owned by the Genetic Algorithm to combine the two chromosomes to produce offspring inherited basic characteristics of the parent. Genetic Algorithms in addition to involve the population early in the optimization process will also generate new populations through the crossover process, so as to provide optimal number of variables is not just a single solution. From the results of the crossover process in the case of TSP passing through six cities, there are two the best offspring with the same finess value which is 0.014. Genetic Algorithms can be stopped on the second generation due to successive received the highest fitness value unchanged.Keywords: Travelling Salesman Program (TSP), Genetic Algorithm, Matrix Representation, Crossover Process

scholarly journals An efficient genetic algorithm for solving open multiple travelling salesman problem with load balancing constraint

2021 ◽  
Vol 10 (4) ◽  
pp. 525-534 ◽  
Author(s):  
Purusotham Singamsetty ◽  
Jayanth Kumar Thenepalle
Keyword(s):  
Genetic Algorithm ◽  
Load Balancing ◽  
Optimization Problems ◽  
Travelling Salesman Problem ◽  
Limited Attention ◽  
Travelling Salesman ◽  
Practical Applications ◽  
Combinatorial Optimization Problems ◽  
Comparative Results ◽  
Multiple Travelling Salesman Problem

The multiple travelling salesman problem (MTSP) is one of the widely studied combinatorial optimization problems with various theoretical and practical applications. However, most of the studies intended to deal with classical MTSP, very limited attention has been given to an open multiple travelling salesman problem and its variants. In this paper, an open multiple travelling salesman problem with load balancing constraint (OMTSPLB) is addressed. The OMTSPLB differs from the conventional MTSP, in which all the salesmen start from the central depot and need not come back to it after visiting the given number of cities by accomplishing the load balance constraint, which helps in fairly distributing the task among all salesmen. The problem aims to minimize the overall traversal distance/cost for operating open tours subject to the load balancing constraint. A zero-one integer linear programming (0-1 ILP) model and an efficient metaheuristic genetic algorithm (GA), is established for the OMTSPLB. Since no existing study on OMTSPLB, the proposed GA is tested on the relaxed version of the present model, comparative results are reported. The comparative results show that the proposed GA is competent over the existing algorithms. Furthermore, extensive experiments are carried out on OMTSPLB and the results show that proposed GA can find the global solution effectively.

scholarly journals Optimal recombination in genetic algorithms for combinatorial optimization problems: Part II

2014 ◽  
Vol 24 (2) ◽  
pp. 165-186 ◽  
Author(s):  
Anton Eremeev ◽  
Julia Kovalenko
Keyword(s):  
Genetic Algorithm ◽  
Genetic Algorithms ◽  
Computational Complexity ◽  
Optimization Problems ◽  
Travelling Salesman Problem ◽  
Makespan Minimization ◽  
Travelling Salesman ◽  
Hamilton Path ◽  
Combinatorial Optimization Problems ◽  
Optimal Recombination

This paper surveys results on complexity of the optimal recombination problem (ORP), which consists in finding the best possible offspring as a result of a recombination operator in a genetic algorithm, given two parent solutions. In Part II, we consider the computational complexity of ORPs arising in genetic algorithms for problems on permutations: the Travelling Salesman Problem, the Shortest Hamilton Path Problem and the Makespan Minimization on Single Machine and some other related problems. The analysis indicates that the corresponding ORPs are NP-hard, but solvable by faster algorithms, compared to the problems they are derived from.

A Hybrid Approach of Heuristic and Neural Network for Packing Problems

1994 ◽  
Author(s):  
Zuo Dai ◽  
Jianzhong Cha
Keyword(s):  
Neural Network ◽  
Large Scale ◽  
Optimization Problems ◽  
Travelling Salesman Problem ◽  
Hybrid Approach ◽  
Two Dimensions ◽  
Packing Problems ◽  
Combinatorial Optimization Problems ◽  
Complete Problems ◽  
Np Complete

Abstract Artificial Neural Networks, particularly the Hopfield-Tank network, have been effectively applied to the solution of a variety of tasks formulated as large scale combinatorial optimization problems, such as Travelling Salesman Problem and N Queens Problem [1]. The problem of optimally packing a set of geometries into a space with finite dimensions arises frequently in many applications and is far difficult than general NP-complete problems listed in [2]. Until now within accepted time limit, it can only be solved with heuristic methods for very simple cases (e.g. 2D layout). In this paper we propose a heuristic-based Hopfield neural network designed to solve the rectangular packing problems in two dimensions, which is still NP-complete [3]. By comparing the adequacy and efficiency of the results with that obtained by several other exact and heuristic approaches, it has been concluded that the proposed method has great potential in solving 2D packing problems.

scholarly journals Experimental Study of a Hybrid Genetic Algorithm for the Multiple Travelling Salesman Problem

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Maha Ata Al-Furhud ◽  
Zakir Hussain Ahmed
Keyword(s):  
Genetic Algorithm ◽  
Heuristic Algorithms ◽  
Optimization Problems ◽  
Travelling Salesman Problem ◽  
Hybrid Genetic Algorithm ◽  
Travelling Salesman ◽  
Complex Optimization ◽  
Problem Instances ◽  
Search Approach ◽  
Multiple Travelling Salesman Problem

The multiple travelling salesman problem (MTSP), an extension of the well-known travelling salesman problem (TSP), is studied here. In MTSP, starting from a depot, multiple salesmen require to visit all cities so that each city is required to be visited only once by one salesman only. It is NP-hard and is more complex than the usual TSP. So, exact optimal solutions can be obtained for smaller sized problem instances only. For large-sized problem instances, it is essential to apply heuristic algorithms, and amongst them, genetic algorithm is identified to be successfully deal with such complex optimization problems. So, we propose a hybrid genetic algorithm (HGA) that uses sequential constructive crossover, a local search approach along with an immigration technique to find high-quality solution to the MTSP. Then our proposed HGA is compared against some state-of-the-art algorithms by solving some TSPLIB symmetric instances of several sizes with various number of salesmen. Our experimental investigation demonstrates that the HGA is one of the best algorithms.

scholarly journals Improving Genetic Algorithm with Fine-Tuned Crossover and Scaled Architecture

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Ajay Shrestha ◽  
Ausif Mahmood
Keyword(s):  
Genetic Algorithm ◽  
Evolutionary Biology ◽  
Optimization Problems ◽  
Search Space ◽  
Island Model ◽  
Fine Tuning ◽  
Small Subset ◽  
Combinatorial Optimization Problems ◽  
Mutation Operators ◽  
New Concepts

Genetic Algorithm (GA) is a metaheuristic used in solving combinatorial optimization problems. Inspired by evolutionary biology, GA uses selection, crossover, and mutation operators to efficiently traverse the solution search space. This paper proposes nature inspired fine-tuning to the crossover operator using the untapped idea of Mitochondrial DNA (mtDNA). mtDNA is a small subset of the overall DNA. It differentiates itself by inheriting entirely from the female, while the rest of the DNA is inherited equally from both parents. This unique characteristic of mtDNA can be an effective mechanism to identify members with similar genes and restrict crossover between them. It can reduce the rate of dilution of diversity and result in delayed convergence. In addition, we scale the well-known Island Model, where instances of GA are run independently and population members exchanged periodically, to a Continental Model. In this model, multiple web services are executed with each web service running an island model. We applied the concept of mtDNA in solving Traveling Salesman Problem and to train Neural Network for function approximation. Our implementation tests show that leveraging these new concepts of mtDNA and Continental Model results in relative improvement of the optimization quality of GA.

scholarly journals Travelling Salesman Problem Solution Based-on Grey Wolf Algorithm over Hypercube Interconnection Network

2018 ◽  
Vol 12 (8) ◽  
pp. 142 ◽  
Author(s):  
Ameen Shaheen ◽  
Azzam Sleit ◽  
Saleh Al-Sharaeh
Keyword(s):  
Optimization Problems ◽  
Interconnection Network ◽  
Travelling Salesman Problem ◽  
Benchmark Problems ◽  
Grey Wolf Optimizer ◽  
Gray Wolf ◽  
Problem Solution ◽  
Grey Wolf ◽  
Travelling Salesman ◽  
Complete Problems

Travelling Salesman Problem (TSP) is one of the most popular NP-complete problems for the researches in the field of computer science which focused on optimization. TSP goal is to find the minimum path between cities with a condition of each city must to visit exactly once by the salesman. Grey Wolf Optimizer (GWO) is a new swarm intelligent optimization mechanism where it success in solving many optimization problems. In this paper, a parallel version of GWO for solving the TSP problem on a Hypercube Interconnection Network is presented. The algorithm has been compared to the alternative algorithms. Algorithms have been evaluated analytically and by simulations in terms of execution time, optimal cost, parallel runtime, speedup and efficiency. The algorithms are tested on a number of benchmark problems and found parallel Gray wolf algorithm is promising in terms of speed-up, efficiency and quality of solution in comparison with the alternative algorithms.   

A Lamarckian Genetic Algorithm Applied to the Travelling Salesman Problem

1999 ◽  
Vol 02 (04) ◽  
pp. 431-457 ◽  
Author(s):  
Bereket T. Tesfaldet ◽  
Augusto Y. Hermosilla
Keyword(s):  
Genetic Algorithm ◽  
Traveling Salesman Problem ◽  
Large Scale ◽  
Optimization Problems ◽  
Travelling Salesman Problem ◽  
Traveling Salesman ◽  
Local Optimum ◽  
Performance Improvements ◽  
Mutation Operators ◽  
Lamarckian Genetic Algorithm

Genetic Algorithms (GAs) comprise a class of adaptive heuristic search methods analogous to genetic inheritance and Darwinian strife for survivial of individuals within a population. Today, GAs are widely used to solve complex optimization problems, including ill-conditioned and NP-complete types arising in business, commerce, engineering, large-scale industries, and many other areas. To address these wide areas of applications and to improve upon their drawbacks, many variations and modifications of GAs have been proposed. The GA variation proposed in this paper has four basic operators: reproduction, recombination and two mutation operators, particularly applied to the famous and extensively studied Traveling Salesman Problem (TSP) in large-scale combinatorial optimization. Three of the operators use diversity information (standard deviation of costs) from the current population to adjust the diversity of the next population. The fourth one is an introduced new mutation operator called p-displacement that simulates the Lamarckian evolutionary learning and training concepts of gene improvement to bring chromosomes to their local optimum. We call the proposed GA: Lamarckian Genetic Algorithm-Traveling Salesman Problem (LGA-TSP). Emprical results show performance improvements compared to the classic and other modified GAs, as well as simulated annealing.

scholarly journals A Comprehensive Survey on the Multiple Travelling Salesman Problem: Applications, Approaches and Taxonomy

2021 ◽  
Author(s):  
omar cheikhrouhou
Keyword(s):  
Unmanned Aerial Vehicles ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Travelling Salesman Problem ◽  
Real Life ◽  
Travelling Salesman ◽  
Combinatorial Optimization Problems ◽  
Comprehensive Survey ◽  
Multiple Travelling Salesman Problem

The Multiple Travelling Salesman Problem (MTSP) is among the most interesting combinatorial optimization problems because it is widely adopted in real-life applications, including robotics, transportation, networking, etc.Although the importance of this optimization problem, there is no survey dedicated to reviewing recent MTSP contributions. In this paper, we aim to fill this gap by providing a comprehensive review of existing studies on MTSP. In this survey, we focus on MTSP’s recent contributions to both classical vehicles/robots and unmanned aerial vehicles. We highlight the approaches applied to solve the MTSP as well as its application domains. We analyze the MTSP variants and propose a taxonomy and a classification of recent studies.

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