Research on MPI-Based Parallel Max-Min Ant System

2012 ◽  
Vol 198-199 ◽  
pp. 1321-1326 ◽  
Author(s):  
Yu Liu ◽  
Guo Dong Wu
Keyword(s):  
Combinatorial Optimization ◽  
Numerical Experiments ◽  
Large Scale ◽  
Optimization Problems ◽  
Computation Time ◽  
Traveling Salesman ◽  
Ant System ◽  
Combinatorial Optimization Problems ◽  
The Traveling Salesman Problem

When solving large scale combinatorial optimization problems, Max-Min Ant System requires long computation time. MPI-based Parallel Max-Min Ant System described in this paper can ensure the quality of the solution, as well as reduce the computation time. Numerical experiments on the multi-node cluster system show that when solving the traveling salesman problem, MPI-based Parallel Max-Min Ant System can get better computational efficiency.

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 Multilevel Combinatorial Optimization across Quantum Architectures

2021 ◽  
Vol 2 (1) ◽  
pp. 1-29
Author(s):  
Hayato Ushijima-Mwesigwa ◽  
Ruslan Shaydulin ◽  
Christian F. A. Negre ◽  
Susan M. Mniszewski ◽  
Yuri Alexeev ◽  
...  
Keyword(s):  
Combinatorial Optimization ◽  
Large Scale ◽  
Optimization Problems ◽  
Combinatorial Optimization Problems ◽  
Large Scale Problems ◽  
Quantum Processor ◽  
Partitioning Problem ◽  
Real World Datasets ◽  
Near Future

Emerging quantum processors provide an opportunity to explore new approaches for solving traditional problems in the post Moore’s law supercomputing era. However, the limited number of qubits makes it infeasible to tackle massive real-world datasets directly in the near future, leading to new challenges in utilizing these quantum processors for practical purposes. Hybrid quantum-classical algorithms that leverage both quantum and classical types of devices are considered as one of the main strategies to apply quantum computing to large-scale problems. In this article, we advocate the use of multilevel frameworks for combinatorial optimization as a promising general paradigm for designing hybrid quantum-classical algorithms. To demonstrate this approach, we apply this method to two well-known combinatorial optimization problems, namely, the Graph Partitioning Problem, and the Community Detection Problem. We develop hybrid multilevel solvers with quantum local search on D-Wave’s quantum annealer and IBM’s gate-model based quantum processor. We carry out experiments on graphs that are orders of magnitude larger than the current quantum hardware size, and we observe results comparable to state-of-the-art solvers in terms of quality of the solution. Reproducibility : Our code and data are available at Reference [1].

scholarly journals A MULTI-COLONY ANT SYSTEM FOR COMBINATORIAL OPTIMIZATION PROBLEM

2012 ◽  
Vol 11 (02) ◽  
pp. 1250012
Author(s):  
RONG-LONG WANG ◽  
XIAO-FAN ZHOU ◽  
LI-QING ZHAO ◽  
ZE-WEI XIA
Keyword(s):  
Combinatorial Optimization ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Natural World ◽  
Search Procedure ◽  
Ant System ◽  
Combinatorial Optimization Problems ◽  
Time Period ◽  
The Traveling Salesman Problem ◽  
Better Than

A multi-colony ant system (MAS) is proposed for the combinatorial optimization problems. The proposed MAS is inspired by the knowledge that there are many colonies of ants in the natural world and organized with multiple colonies of ants. At first, ants perform solution search procedure by cooperating with each other in the same colony until no better solution is found after a certain time period. Then, communication between different colonies is performed to build new pheromone distributions for each colony, and ants start their search procedure again in each separate colony, based on the new pheromone distribution. The proposed algorithm is tested by simulating the traveling salesman problem (TSP). Simulation results show that the proposed method performs better than the traditional ACO.

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 Solving the Traveling Salesman Problem: A Modified Metaheuristic Algorithm

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Majid Yousefikhoshbakht
Keyword(s):  
Traveling Salesman Problem ◽  
Optimization Problems ◽  
Minimum Cost ◽  
Pso Algorithm ◽  
Traveling Salesman ◽  
Local Search Algorithms ◽  
Combinatorial Optimization Problems ◽  
Engineering Sciences ◽  
The Traveling Salesman Problem

The traveling salesman problem (TSP) is one of the most important issues in combinatorial optimization problems that are used in many engineering sciences and has attracted the attention of many scientists and researchers. In this issue, a salesman starts to move from a desired node called warehouse and returns to the starting place after meeting n customers provided that each customer is only met once. The aim of this issue is to determine a cycle with a minimum cost for this salesman. One of the major weaknesses of the PSO algorithm in the classical version is that it gets stuck in local optimizations. Therefore, in the proposed algorithm, called MPSO, the best solution in the current iteration is also used in the movement step. In addition, a variety of local search algorithms are provided that are used when better answers are generated than before. Also, a new method for moving the particle towards the best particle is presented, which, in addition to probably increasing the quality of the new answer, prevents the premature convergence of the algorithm due to consideration of the concept of random. The results evaluated with the results of several metaheuristic algorithms in the literature show the efficiency of the MPSO algorithm because it has been able to achieve excellent solutions in most of these instances.

scholarly journals Combinatorial optimization by simulating adiabatic bifurcations in nonlinear Hamiltonian systems

2019 ◽  
Vol 5 (4) ◽  
pp. eaav2372 ◽  
Author(s):  
Hayato Goto ◽  
Kosuke Tatsumura ◽  
Alexander R. Dixon
Keyword(s):  
Combinatorial Optimization ◽  
Hamiltonian Systems ◽  
Large Scale ◽  
Optimization Problems ◽  
Approximate Solutions ◽  
Combinatorial Optimization Problems ◽  
Bifurcation Phenomena ◽  
Field Programmable ◽  
Max Cut Problem ◽  
Adiabatic Optimization

Combinatorial optimization problems are ubiquitous but difficult to solve. Hardware devices for these problems have recently been developed by various approaches, including quantum computers. Inspired by recently proposed quantum adiabatic optimization using a nonlinear oscillator network, we propose a new optimization algorithm simulating adiabatic evolutions of classical nonlinear Hamiltonian systems exhibiting bifurcation phenomena, which we call simulated bifurcation (SB). SB is based on adiabatic and chaotic (ergodic) evolutions of nonlinear Hamiltonian systems. SB is also suitable for parallel computing because of its simultaneous updating. Implementing SB with a field-programmable gate array, we demonstrate that the SB machine can obtain good approximate solutions of an all-to-all connected 2000-node MAX-CUT problem in 0.5 ms, which is about 10 times faster than a state-of-the-art laser-based machine called a coherent Ising machine. SB will accelerate large-scale combinatorial optimization harnessing digital computer technologies and also offer a new application of computational and mathematical physics.

Study on Free Search for Combinatorial Optimization Problem

2013 ◽  
Vol 411-414 ◽  
pp. 1904-1910
Author(s):  
Kai Zhong Jiang ◽  
Tian Bo Wang ◽  
Zhong Tuan Zheng ◽  
Yu Zhou
Keyword(s):  
Combinatorial Optimization ◽  
Optimization Problem ◽  
Feasible Solution ◽  
Optimization Problems ◽  
Search Algorithm ◽  
Search Process ◽  
Standard Data ◽  
Combinatorial Optimization Problems ◽  
Free Search

An algorithm based on free search is proposed for the combinatorial optimization problems. In this algorithm, a feasible solution is converted into a full permutation of all the elements and a transformation of one solution into another solution can be interpreted the transformation of one permutation into another permutation. Then, the algorithm is combined with intersection elimination. The discrete free search algorithm greatly improves the convergence rate of the search process and enhances the quality of the results. The experiment results on TSP standard data show that the performance of the proposed algorithm is increased by about 2.7% than that of the genetic algorithm.

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