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 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.

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.

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.

The Travelling Salesman Problem for finite-sized cities

2010 ◽  
Vol 20 (6) ◽  
pp. 1067-1078 ◽  
Author(s):  
HUGO FORT ◽  
MORDECHAI KORNBLUTH ◽  
FREDY ZYPMAN
Keyword(s):  
Travelling Salesman Problem ◽  
Spatial Extent ◽  
Travelling Salesman ◽  
New Approach ◽  
Standard Problem ◽  
First Approximation ◽  
Particular Solution ◽  
New Algorithms

We consider a variation of the Travelling Salesman Problem (TSP) in which the cities visited have non-zero spatial extent, in contrast with the classical TSP, which has destinations that are mathematical points. This new approach opens up both new analyses of the problem and new algorithms for solutions, while remaining an economic first approximation to the standard problem. We present one particular solution that, depending on the number and size of the cities, can improve existing algorithms solving the classical TSP.

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.

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