scholarly journals Finding the Best 3-OPT Move in Subcubic Time

Algorithms ◽  
2020 ◽  
Vol 13 (11) ◽  
pp. 306
Author(s):  
Giuseppe Lancia ◽  
Marcello Dalpasso
Keyword(s):  
Empirical Evidence ◽  
Traveling Salesman Problem ◽  
Random Graphs ◽  
Wide Class ◽  
Traveling Salesman ◽  
Problem Solution ◽  
Worst Case ◽  
Average Case ◽  
Problem Library ◽  
Better Than

Given a Traveling Salesman Problem solution, the best 3-OPT move requires us to remove three edges and replace them with three new ones so as to shorten the tour as much as possible. No worst-case algorithm better than the Θ(n3) enumeration of all triples is likely to exist for this problem, but algorithms with average case O(n3−ϵ) are not ruled out. In this paper we describe a strategy for 3-OPT optimization which can find the best move by looking only at a fraction of all possible moves. We extend our approach also to some other types of cubic moves, such as some special 6-OPT and 5-OPT moves. Empirical evidence shows that our algorithm runs in average subcubic time (upper bounded by O(n2.5)) on a wide class of random graphs as well as Traveling Salesman Problem Library (TSPLIB) instances.

scholarly journals Improvement of Traveling Salesman Problem Solution Using Hybrid Algorithm Based on Best-Worst Ant System and Particle Swarm Optimization

2021 ◽  
Vol 11 (11) ◽  
pp. 4780
Author(s):  
Muhammad Salman Qamar ◽  
Shanshan Tu ◽  
Farman Ali ◽  
Ammar Armghan ◽  
Muhammad Fahad Munir ◽  
...  
Keyword(s):  
Particle Swarm Optimization ◽  
Traveling Salesman Problem ◽  
Particle Swarm ◽  
Standard Test ◽  
Traveling Salesman ◽  
Problem Solution ◽  
Ant System ◽  
Swarm Optimization ◽  
Hybrid Particle Swarm Optimization ◽  
Novel Approach

This work presents a novel Best-Worst Ant System (BWAS) based algorithm to settle the Traveling Salesman Problem (TSP). The researchers has been involved in ordinary Ant Colony Optimization (ACO) technique for TSP due to its versatile and easily adaptable nature. However, additional potential improvement in the arrangement way decrease is yet possible in this approach. In this paper BWAS based incorporated arrangement as a high level type of ACO to upgrade the exhibition of the TSP arrangement is proposed. In addition, a novel approach, based on hybrid Particle Swarm Optimization (PSO) and ACO (BWAS) has also been introduced in this work. The presentation measurements of arrangement quality and assembly time have been utilized in this work and proposed algorithm is tried against various standard test sets to examine the upgrade in search capacity. The outcomes for TSP arrangement show that initial trail setup for the best particle can result in shortening the accumulated process of the optimization by a considerable amount. The exhibition of the mathematical test shows the viability of the proposed calculation over regular ACO and PSO-ACO based strategies.

LEARNING TO COOPERATE IN SOLVING THE TRAVELING SALESMAN PROBLEM

2005 ◽  
Vol 15 (01n02) ◽  
pp. 151-162 ◽  
Author(s):  
DEHU QI ◽  
RON SUN
Keyword(s):  
Reinforcement Learning ◽  
Traveling Salesman Problem ◽  
Single Agent ◽  
Traveling Salesman ◽  
Cooperative Team ◽  
The Traveling Salesman Problem ◽  
Better Than

A cooperative team of agents may perform many tasks better than single agents. The question is how cooperation among self-interested agents should be achieved. It is important that, while we encourage cooperation among agents in a team, we maintain autonomy of individual agents as much as possible, so as to maintain flexibility and generality. This paper presents an approach based on bidding utilizing reinforcement values acquired through reinforcement learning. We tested and analyzed this approach and demonstrated that a team indeed performed better than the best single agent as well as the average of single agents.

scholarly journals Influence of parameters of the ant colony algorithm on the traveling salesman problem solution

2014 ◽  
Vol 4 (4(70)) ◽  
pp. 18
Author(s):  
Ігор Андрійович Могила ◽  
Ірина Іванівна Лобач ◽  
Оксана Андріївна Якимець
Keyword(s):  
Traveling Salesman Problem ◽  
Ant Colony Algorithm ◽  
Traveling Salesman ◽  
Ant Colony ◽  
Problem Solution ◽  
The Traveling Salesman Problem

scholarly journals Solving Mean-Payoff Games via Quasi Dominions

2020 ◽  
pp. 289-306
Author(s):  
Massimo Benerecetti ◽  
Daniele Dell’Erba ◽  
Fabio Mogavero
Keyword(s):  
Solution Algorithm ◽  
Problem Solution ◽  
Worst Case ◽  
Case Complexity ◽  
Worst Case Complexity ◽  
Mean Payoff Games ◽  
Parity Games ◽  
Mean Payoff ◽  
Novel Algorithm ◽  
Better Than

Abstract We propose a novel algorithm for the solution of mean-payoff games that merges together two seemingly unrelated concepts introduced in the context of parity games, small progress measures and quasi dominions. We show that the integration of the two notions can be highly beneficial and significantly speeds up convergence to the problem solution. Experiments show that the resulting algorithm performs orders of magnitude better than the asymptotically-best solution algorithm currently known, without sacrificing on the worst-case complexity.

scholarly journals A Self-Organizing Neural Network for the Traveling Salesman Problem That Is Competitive with Simulated Annealing

1996 ◽  
Vol 8 (2) ◽  
pp. 416-424 ◽  
Author(s):  
Marco Budinich
Keyword(s):  
Neural Network ◽  
Simulated Annealing ◽  
Unsupervised Learning ◽  
Traveling Salesman Problem ◽  
Approximate Solutions ◽  
Elastic Net ◽  
Traveling Salesman ◽  
The Traveling Salesman Problem ◽  
Better Than ◽  
Self Organizing

Unsupervised learning applied to an unstructured neural network can give approximate solutions to the traveling salesman problem. For 50 cities in the plane this algorithm performs like the elastic net of Durbin and Willshaw (1987) and it improves when increasing the number of cities to get better than simulated annealing for problems with more than 500 cities. In all the tests this algorithm requires a fraction of the time taken by simulated annealing.

scholarly journals GENETIC ALGORITHM FOR OPTIMIZING DISTRIBUTION WITH ROUTE RESTRICTION CONSTRAINT DUE TO TRAFFIC JAMS

2020 ◽  
Vol XLIV-4/W3-2020 ◽  
pp. 295-301
Author(s):  
N. Mouttaki ◽  
J. Benhra ◽  
G. Rguiga
Keyword(s):  
Genetic Algorithm ◽  
Combinatorial Optimization ◽  
Traveling Salesman Problem ◽  
Travelling Salesman Problem ◽  
Classical Problem ◽  
Traveling Salesman ◽  
Travelling Salesman ◽  
Simple Method ◽  
Traffic Jams ◽  
Better Than

Abstract. The Travelling Salesman Problem (TSP) is a classical problem in combinatorial optimization that consists of finding the shortest tour through all cities such that the salesman visits each city only one time and returns to the starting city. Genetic algorithm is one of the powerful ways to solve problems of traveling salesman problem TSP. The current genetic algorithm aims to take in consideration the constraints happening during the execution of genetic algorithm, such as traffic jams when solving TSP. This program has two important contributions. First one is proposing simple method into taking in consideration an inconvenient route linked to traffic jams. The second one is the use of closeness strategy during the initialization step, which can accelerate the execution time of the algorithm.The results of the experiments show that the improved algorithm works better than some other algorithms. The conclusion ends the analysis with recommendations and future works.

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