A metaheuristic framework for stochastic combinatorial optimization problems based on GPGPU with a case study on the probabilistic traveling salesman problem with deadlines

2013 ◽  
Vol 73 (1) ◽  
pp. 74-85 ◽  
Author(s):  
Dennis Weyland ◽  
Roberto Montemanni ◽  
Luca Maria Gambardella
Keyword(s):  
Combinatorial Optimization ◽  
Traveling Salesman Problem ◽  
Optimization Problems ◽  
Traveling Salesman ◽  
Combinatorial Optimization Problems ◽  
Stochastic Combinatorial Optimization

The Traveling Salesman Problem, the Vehicle Routing Problem, and Their Impact on Combinatorial Optimization

2010 ◽  
Vol 1 (2) ◽  
pp. 82-92 ◽  
Author(s):  
Gilbert Laporte
Keyword(s):  
Combinatorial Optimization ◽  
Vehicle Routing ◽  
Traveling Salesman Problem ◽  
Vehicle Routing Problem ◽  
Heuristic Algorithms ◽  
Optimization Problems ◽  
Traveling Salesman ◽  
Routing Problem ◽  
Combinatorial Optimization Problems ◽  
The Traveling Salesman Problem

The Traveling Salesman Problem (TSP) and the Vehicle Routing Problem (VRP) are two of the most popular problems in the field of combinatorial optimization. Due to the study of these two problems, there has been a significant growth in families of exact and heuristic algorithms being used today. The purpose of this paper is to show how their study has fostered developments of the most popular algorithms now applied to the solution of combinatorial optimization problems. These include exact algorithms, classical heuristics and metaheuristics.

scholarly journals Branch and Bound Algorithm for the Traveling Salesman Problem is not a Direct Type Algorithm

2020 ◽  
Vol 27 (1) ◽  
pp. 72-85
Author(s):  
Aleksandr N. Maksimenko
Keyword(s):  
Combinatorial Optimization ◽  
Traveling Salesman Problem ◽  
Branch And Bound ◽  
Optimization Problems ◽  
Clique Number ◽  
Traveling Salesman ◽  
Branch And Bound Algorithm ◽  
Combinatorial Optimization Problems ◽  
Type Algorithm ◽  
The Traveling Salesman Problem

In this paper, we consider the notion of a direct type algorithm introduced by V. A. Bondarenko in 1983. A direct type algorithm is a linear decision tree with some special properties. the concept of a direct type algorithm is determined using the graph of solutions of a combinatorial optimization problem. ‘e vertices of this graph are all feasible solutions of a problem. Two solutions are called adjacent if there are input data for which these and only these solutions are optimal. A key feature of direct type algorithms is that their complexity is bounded from below by the clique number of the solutions graph. In 2015-2018, there were five papers published, the main results of which are estimates of the clique numbers of polyhedron graphs associated with various combinatorial optimization problems. the main motivation in these works is the thesis that the class of direct type algorithms is wide and includes many classical combinatorial algorithms, including the branch and bound algorithm for the traveling salesman problem, proposed by J. D. C. Little, K. G. Murty, D. W. Sweeney, C. Karel in 1963. We show that this algorithm is not a direct type algorithm. Earlier, in 2014, the author of this paper showed that the Hungarian algorithm for the assignment problem is not a direct type algorithm. ‘us, the class of direct type algorithms is not so wide as previously assumed.

scholarly journals PARALLEL TEMPERING FOR THE TRAVELING SALESMAN PROBLEM

2009 ◽  
Vol 20 (04) ◽  
pp. 539-556 ◽  
Author(s):  
CHIAMING WANG ◽  
JEFFREY D. HYMAN ◽  
ALLON PERCUS ◽  
RUSSEL CAFLISCH
Keyword(s):  
Simulated Annealing ◽  
Combinatorial Optimization ◽  
Traveling Salesman Problem ◽  
Minimum Distance ◽  
Optimization Problems ◽  
Optimization Method ◽  
Traveling Salesman ◽  
Parallel Tempering ◽  
Combinatorial Optimization Problems ◽  
The Traveling Salesman Problem

We explore the potential of parallel tempering as a combinatorial optimization method, applying it to the traveling salesman problem. We compare simulation results of parallel tempering with a benchmark implementation of simulated annealing, and study how different choices of parameters affect the relative performance of the two methods. We find that a straightforward implementation of parallel tempering can outperform simulated annealing in several crucial respects. When parameters are chosen appropriately, both methods yield close approximation to the actual minimum distance for an instance with 200 nodes. However, parallel tempering yields more consistently accurate results when a series of independent simulations are performed. Our results suggest that parallel tempering might offer a simple but powerful alternative to simulated annealing for combinatorial optimization problems.

scholarly journals Focusing on the Golden Ball Metaheuristic: An Extended Study on a Wider Set of Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-17 ◽  
Author(s):  
E. Osaba ◽  
F. Diaz ◽  
R. Carballedo ◽  
E. Onieva ◽  
A. Perallos
Keyword(s):  
Genetic Algorithms ◽  
Combinatorial Optimization ◽  
Vehicle Routing ◽  
Vehicle Routing Problem ◽  
Optimization Problems ◽  
Traveling Salesman ◽  
Routing Problem ◽  
Combinatorial Optimization Problems ◽  
Golden Ball ◽  
The One

Nowadays, the development of new metaheuristics for solving optimization problems is a topic of interest in the scientific community. In the literature, a large number of techniques of this kind can be found. Anyway, there are many recently proposed techniques, such as the artificial bee colony and imperialist competitive algorithm. This paper is focused on one recently published technique, the one called Golden Ball (GB). The GB is a multiple-population metaheuristic based on soccer concepts. Although it was designed to solve combinatorial optimization problems, until now, it has only been tested with two simple routing problems: the traveling salesman problem and the capacitated vehicle routing problem. In this paper, the GB is applied to four different combinatorial optimization problems. Two of them are routing problems, which are more complex than the previously used ones: the asymmetric traveling salesman problem and the vehicle routing problem with backhauls. Additionally, one constraint satisfaction problem (the n-queen problem) and one combinatorial design problem (the one-dimensional bin packing problem) have also been used. The outcomes obtained by GB are compared with the ones got by two different genetic algorithms and two distributed genetic algorithms. Additionally, two statistical tests are conducted to compare these results.

Microcanonical Optimization Applied to the Traveling Salesman Problem

1998 ◽  
Vol 09 (01) ◽  
pp. 133-146 ◽  
Author(s):  
Alexandre Linhares ◽  
José R. A. Torreão
Keyword(s):  
Simulated Annealing ◽  
Traveling Salesman Problem ◽  
Optimization Problems ◽  
Search Algorithm ◽  
New Physics ◽  
Traveling Salesman ◽  
Tabu Search Algorithm ◽  
Combinatorial Optimization Problems ◽  
Microcanonical Annealing ◽  
The Traveling Salesman Problem

Optimization strategies based on simulated annealing and its variants have been extensively applied to the traveling salesman problem (TSP). Recently, there has appeared a new physics-based metaheuristic, called the microcanonical optimization algorithm (μO), which does not resort to annealing, and which has proven a superior alternative to the annealing procedures in various applications. Here we present the first performance evaluation of μO as applied to the TSP. When compared to three annealing strategies (simulated annealing, microcanonical annealing and Tsallis annealing), and to a tabu search algorithm, the microcanonical optimization has yielded the best overall results for several instances of the euclidean TSP. This confirms μO as a competitive approach for the solution of general combinatorial optimization problems.

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