DIMMA

2010 ◽  
Vol 1 (4) ◽  
pp. 57-74 ◽  
Author(s):  
Masoud Yaghini ◽  
Rahim Akhavan
Keyword(s):  
Tabu Search ◽  
Optimization Problems ◽  
Travelling Salesman Problem ◽  
Metaheuristic Algorithms ◽  
Standard Process ◽  
Travelling Salesman ◽  
Design And Implementation ◽  
The Future ◽  
Implementation Methodology

Metaheuristic algorithms will gain more and more popularity in the future as optimization problems are increasing in size and complexity. In order to record experiences and allow project to be replicated, a standard process as a methodology for designing and implementing metaheuristic algorithms is necessary. To the best of the authors’ knowledge, no methodology has been proposed in literature for this purpose. This paper presents a Design and Implementation Methodology for Metaheuristic Algorithms, named DIMMA. The proposed methodology consists of three main phases and each phase has several steps in which activities that must be carried out are clearly defined in this paper. In addition, design and implementation of tabu search metaheuristic for travelling salesman problem is done as a case study to illustrate applicability of DIMMA.

DIMMA

2012 ◽  
pp. 583-601
Author(s):  
Masoud Yaghini ◽  
Mohammad Rahim Akhavan Kazemzadeh
Keyword(s):  
Tabu Search ◽  
Optimization Problems ◽  
Travelling Salesman Problem ◽  
Metaheuristic Algorithms ◽  
Standard Process ◽  
Travelling Salesman ◽  
Design And Implementation ◽  
The Future ◽  
Implementation Methodology

Metaheuristic algorithms will gain more and more popularity in the future as optimization problems are increasing in size and complexity. In order to record experiences and allow project to be replicated, a standard process as a methodology for designing and implementing metaheuristic algorithms is necessary. To the best of the authors’ knowledge, no methodology has been proposed in literature for this purpose. This paper presents a Design and Implementation Methodology for Metaheuristic Algorithms, named DIMMA. The proposed methodology consists of three main phases and each phase has several steps in which activities that must be carried out are clearly defined in this paper. In addition, design and implementation of tabu search metaheuristic for travelling salesman problem is done as a case study to illustrate applicability of DIMMA.

DIMMA

2012 ◽  
pp. 90-108
Author(s):  
Masoud Yaghini ◽  
Mohammad Rahim Akhavan Kazemzadeh
Keyword(s):  
Tabu Search ◽  
Optimization Problems ◽  
Travelling Salesman Problem ◽  
Metaheuristic Algorithms ◽  
Standard Process ◽  
Travelling Salesman ◽  
Design And Implementation ◽  
The Future ◽  
Implementation Methodology

Metaheuristic algorithms will gain more and more popularity in the future as optimization problems are increasing in size and complexity. In order to record experiences and allow project to be replicated, a standard process as a methodology for designing and implementing metaheuristic algorithms is necessary. To the best of the authors’ knowledge, no methodology has been proposed in literature for this purpose. This paper presents a Design and Implementation Methodology for Metaheuristic Algorithms, named DIMMA. The proposed methodology consists of three main phases and each phase has several steps in which activities that must be carried out are clearly defined in this paper. In addition, design and implementation of tabu search metaheuristic for travelling salesman problem is done as a case study to illustrate applicability of DIMMA.

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 Travelling Santa Problem: Optimization of a Million-Households Tour Within One Hour

2021 ◽  
Vol 8 ◽  
Author(s):  
Tilo Strutz
Keyword(s):  
Computational Complexity ◽  
Optimization Problems ◽  
State Of The Art ◽  
Travelling Salesman Problem ◽  
Limited Time ◽  
Two Dimensional ◽  
Optimal Solutions ◽  
Major Difficulty ◽  
Travelling Salesman ◽  
New Approach

Finding the shortest tour visiting all given points at least ones belongs to the most famous optimization problems until today [travelling salesman problem (TSP)]. Optimal solutions exist for many problems up to several ten thousand points. The major difficulty in solving larger problems is the required computational complexity. This shifts the research from finding the optimum with no time limitation to approaches that find good but sub-optimal solutions in pre-defined limited time. This paper proposes a new approach for two-dimensional symmetric problems with more than a million coordinates that is able to create good initial tours within few minutes. It is based on a hierarchical clustering strategy and supports parallel processing. In addition, a method is proposed that can correct unfavorable paths with moderate computational complexity. The new approach is superior to state-of-the-art methods when applied to TSP instances with non-uniformly distributed coordinates.

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

2. Four types of problem

2016 ◽  
pp. 7-27
Author(s):  
Robin Wilson
Keyword(s):  
Optimization Problem ◽  
Optimization Problems ◽  
Travelling Salesman Problem ◽  
Travelling Salesman ◽  
Counting Problems ◽  
Problem Construction ◽  
Colour Problem ◽  
Efficiency Of Algorithms ◽  
Enumeration Problems ◽  
Knight’S Tour

‘Four types of problem’ explains that combinatorics is concerned with four types of problem: existence problems (does x exist?); construction problems (if x exists, how can we construct it?); enumeration problems (how many x are there?); and optimization problems (which x is best?). Existence problems discussed include tilings, placing dominoes on a chess board, the knight’s tour problem, the Königsberg bridges problem, the Gas–Water–Electricity problem, and the map-colour problem. Construction problems include solving mazes, and the two types of enumeration problems considered are counting problems and listing problems. Examples of an optimization problem include the minimum connector problem and the travelling salesman problem. The efficiency of algorithms is also explained.

Solution of Travelling Salesman Problem Using Ant Colony Algorithm

2014 ◽  
Vol 548-549 ◽  
pp. 1206-1212
Author(s):  
Sevda Dayıoğlu Gülcü ◽  
Şaban Gülcü ◽  
Humar Kahramanli
Keyword(s):  
Discrete Optimization ◽  
Ant Colony Algorithm ◽  
Optimization Problems ◽  
Travelling Salesman Problem ◽  
Heuristic Method ◽  
Ant Colony ◽  
Ant Colony System ◽  
Travelling Salesman ◽  
Ant Colonies ◽  
Discrete Optimization Problems

Recently some studies have been revealed by inspiring from animals which live as colonies in the nature. Ant Colony System is one of these studies. This system is a meta-heuristic method which has been developed based upon food searching characteristics of the ant colonies. Ant Colony System is applied in a lot of discrete optimization problems such as travelling salesman problem. In this study solving the travelling salesman problem using ant colony system is aimed.

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.   

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