scholarly journals A New Generalized Partition Crossover for the Traveling Salesman Problem: Tunneling between Local Optima

2020 ◽  
Vol 28 (2) ◽  
pp. 255-288 ◽  
Author(s):  
Renato Tinós ◽  
Darrell Whitley ◽  
Gabriela Ochoa
Keyword(s):  
Traveling Salesman Problem ◽  
Execution Time ◽  
Traveling Salesman ◽  
Local Optima ◽  
The Traveling Salesman Problem ◽  
Generalized Partition

Generalized Partition Crossover (GPX) is a deterministic recombination operator developed for the Traveling Salesman Problem. Partition crossover operators return the best of [Formula: see text] reachable offspring, where [Formula: see text] is the number of recombining components. This article introduces a new GPX2 operator, which finds more recombining components than GPX or Iterative Partial Transcription (IPT). We also show that GPX2 has O([Formula: see text]) runtime complexity, while also introducing new enhancements to reduce the execution time of GPX2. Finally, we experimentally demonstrate the efficiency of GPX2 when it is used to improve solutions found by the multitrial Lin-Kernighan-Helsgaum (LKH) algorithm. Significant improvements in performance are documented on large ([Formula: see text]) and very large ([Formula: see text]) instances of the Traveling Salesman Problem.

scholarly journals A Multi Ant Colony Optimization Approach For The Traveling Salesman Problem

2021 ◽  
Vol Volume 34 - 2020 - Special... ◽  
Author(s):  
Mathurin SOH ◽  
Baudoin Nguimeya Tsofack ◽  
Clémentin Tayou Djamegni
Keyword(s):  
Traveling Salesman Problem ◽  
Execution Time ◽  
Exact Algorithm ◽  
Traveling Salesman ◽  
Optimization Approach ◽  
Solution Quality ◽  
New Approach ◽  
International Audience ◽  
The Traveling Salesman Problem

International audience In this paper, we propose a new approach to solving the Traveling Salesman Problem (TSP), for which no exact algorithm is known that allows to find a solution in polynomial time. The proposed approach is based on optimization by ants. It puts several colonies in competition for improved solutions (in execution time and solution quality) to large TSP instances, and allows to efficiently explore the range of possible solutions. The results of our experiments show that the approach leads to better results compared to other heuristics from the literature, especially in terms of the quality of solutions obtained and execution time.

scholarly journals A relax and cut approach using the multi-commodity flow formulation for the traveling salesman problem

DYNA ◽  
2015 ◽  
Vol 82 (191) ◽  
pp. 42-50 ◽  
Author(s):  
Makswell Seyiti Kawashima ◽  
Socorro Rangel ◽  
Igor Litvinchev ◽  
Luis Infante
Keyword(s):  
Traveling Salesman Problem ◽  
Execution Time ◽  
Computational Study ◽  
Traveling Salesman ◽  
Commodity Flow ◽  
Asymmetric Traveling Salesman Problem ◽  
Subtour Elimination ◽  
The Traveling Salesman Problem ◽  
Dual Bounds

<p class="ADYNAAbstrac"><span lang="EN-US">In this paper we explore the multi-commodity flow formulation for the Asymmetric Traveling Salesman Problem (ATSP) to obtain dual bounds. The procedure employed is a variant of a relax and cut procedure proposed in the literature that computes the Lagrangean multipliers associated to the subtour elimination constraints preserving the optimality of the multipliers associated to the assignment constraints. The results obtained by the computational study are encouraging and show that the proposed algorithm generated good dual bounds for the ATSP with a low execution time.</span></p>

scholarly journals Some Analytical Considerations Regarding the Traveling Salesman Problem Solved with Wolfram Mathematica Applications

2020 ◽  
pp. 68-77
Author(s):  
Bogdan-Vasile Cioruța ◽  
Alexandru Lauran ◽  
Mirela Coman
Keyword(s):  
Traveling Salesman Problem ◽  
Execution Time ◽  
Travelling Salesman Problem ◽  
Emergent Behavior ◽  
Traveling Salesman ◽  
Ant Colony Optimisation ◽  
Travelling Salesman ◽  
Wolfram Mathematica ◽  
Computational Program ◽  
The Traveling Salesman Problem

The paper presents an introduction to the Ant Colony Optimisation (ACO) algorithm and methods for solving the Travelling Salesman Problem (TSP). Documenting, understanding and knowledge of concepts regarding the emergent behavior and intelligence swarms optimization, easily led on solving the Travelling Salesman Problem using a computational program, such as Mathematics Wolfram via Creative Demostration Projects (*.cdf) module. The proposed application runs for a different number of ants, a different number of ants, a different number of leaders (elite ants), and a different pheromone evaporation index. As a result it can be stated that the execution time of the algorithm to solve the TSP is direct and strictly proportional to the number of ants, cities and elite ants considered, the increase of the execution time increasing significantly with the increase of the variables.

scholarly journals Complexity indices for the traveling salesman problem continued

2021 ◽  
pp. 14-14
Author(s):  
Dragos Cvetkovic ◽  
Zorica Drazic ◽  
Vera Kovacevic-Vujcic
Keyword(s):  
Uniform Distribution ◽  
Traveling Salesman Problem ◽  
Execution Time ◽  
Traveling Salesman ◽  
Computational Experiments ◽  
Connected Components ◽  
Complete Graphs ◽  
Short Edge ◽  
Symmetric Traveling Salesman Problem ◽  
The Traveling Salesman Problem

We consider the symmetric traveling salesman problem (TSP) with instances represented by complete graphs G with distances between cities as edge weights. A complexity index is an invariant of an instance I by which we predict the execution time of an exact TSP algorithm for I. In the paper [5] we have considered some short edge subgraphs of G and defined several new invariants related to their connected components. Extensive computational experiments with instances on 50 vertices with the uniform distribution of integer edge weights in the interval [1,100] show that there exists correlation between the sequences of selected invariants and the sequence of execution times of the well-known TSP Solver Concorde. In this paper we extend these considerations for instances up to 100 vertices.

scholarly journals Use of Ant Colony Optimization Algorithm for Determining Traveling Salesman Problem Routes

2019 ◽  
Vol 5 (2) ◽  
pp. 100-111
Author(s):  
Bib Paruhum Silalahi ◽  
Nurul Fathiah ◽  
Prapto Tri Supriyo
Keyword(s):  
Ant Colony Optimization ◽  
Traveling Salesman Problem ◽  
Optimization Algorithm ◽  
Execution Time ◽  
Traveling Salesman ◽  
Ant Colony ◽  
Food Sources ◽  
Ant Colony Optimization Algorithm ◽  
Initial Node ◽  
The Traveling Salesman Problem

Ant Colony Optimization is one of the meta-heuristic methods used to solve combinatorial optimization problems that are quite difficult. Ant Colony Optimization algorithm is inspired by ant behavior in the real world to build the shortest path between food sources and their nests. Traveling Salesman Problem is a problem in optimization. Traveling Salesman Problem is a problem to find the minimum distance from the initial node to the whole node with each node must be visited exactly once and must return to the initial node. Traveling Salesman Problem is a non-deterministic polynomial-time complete problem. This research discusses the solution of the Traveling Salesman Problem using the Ant Colony Optimization algorithm and also using the exact algorithm. The results showed that the greater the size of the Traveling Salesman Problem case, the longer the execution time required. The results also showed that the execution times of the Ant Colony Optimization are much faster than the execution time of the exact method.

A New Heuristic Procedure To Solve The Traveling Salesman Problem

2007 ◽  
Vol 5 (1) ◽  
pp. 1-9
Author(s):  
Paulo Henrique Siqueira ◽  
Sérgio Scheer ◽  
Maria Teresinha Arns Steiner
Keyword(s):  
Traveling Salesman Problem ◽  
Traveling Salesman ◽  
Heuristic Procedure ◽  
The Traveling Salesman Problem

scholarly journals An Improved Whale Optimization Algorithm for the Traveling Salesman Problem

Symmetry ◽  
2020 ◽  
Vol 13 (1) ◽  
pp. 48
Author(s):  
Jin Zhang ◽  
Li Hong ◽  
Qing Liu
Keyword(s):  
Traveling Salesman Problem ◽  
Optimization Algorithm ◽  
Optimization Problems ◽  
Relevant Literature ◽  
Population Diversity ◽  
Traveling Salesman ◽  
Whale Optimization Algorithm ◽  
Neighborhood Search ◽  
Whale Optimization ◽  
The Traveling Salesman Problem

The whale optimization algorithm is a new type of swarm intelligence bionic optimization algorithm, which has achieved good optimization results in solving continuous optimization problems. However, it has less application in discrete optimization problems. A variable neighborhood discrete whale optimization algorithm for the traveling salesman problem (TSP) is studied in this paper. The discrete code is designed first, and then the adaptive weight, Gaussian disturbance, and variable neighborhood search strategy are introduced, so that the population diversity and the global search ability of the algorithm are improved. The proposed algorithm is tested by 12 classic problems of the Traveling Salesman Problem Library (TSPLIB). Experiment results show that the proposed algorithm has better optimization performance and higher efficiency compared with other popular algorithms and relevant literature.

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