A benchmark for quantum optimization: the traveling salesman

2021 ◽  
Vol 21 (7&8) ◽  
pp. 557-562
Author(s):  
Richard H. Warren
Keyword(s):  
Quantum Computing ◽  
Combinatorial Optimization ◽  
Optimization Problems ◽  
Traveling Salesman ◽  
Traveling Salesman Problems ◽  
Combinatorial Optimization Problems ◽  
Quantum Optimization

We present compelling reasons for symmetric traveling salesman problems (TSPs) to be the benchmark for quantum computing of combinatorial optimization problems for all types of quantum hardware. There are seven reasons for endorsing these TSPs to be the benchmark and no shortcomings.

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 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.

scholarly journals Influence of Probability of Variation Operator on the Performance of Quantum-Inspired Evolutionary Algorithm for 0/1 Knapsack Problem

2010 ◽  
Vol 4 (1) ◽  
pp. 37-48
Author(s):  
Mozammel H.A. Khan
Keyword(s):  
Genetic Algorithm ◽  
Quantum Computing ◽  
Combinatorial Optimization ◽  
Evolutionary Algorithm ◽  
Knapsack Problem ◽  
Optimization Problems ◽  
Exploration And Exploitation ◽  
Good Balance ◽  
Combinatorial Optimization Problems ◽  
Variation Operator

Quantum-Inspired Evolutionary Algorithm (QEA) has been shown to be better performing than classical Genetic Algorithm based evolutionary techniques for combinatorial optimization problems like 0/1 knapsack problem. QEA uses quantum computing-inspired representation of solution called Q-bit individual consisting of Q-bits. The probability amplitudes of the Q-bits are changed by application of Q-gate operator, which is classical analogous of quantum rotation operator. The Q-gate operator is the only variation operator used in QEA, which along with some problem specific heuristic provides exploitation of the properties of the best solutions. In this paper, we analyzed the characteristics of the QEA for 0/1 knapsack problem and showed that a probability in the range 0.3 to 0.4 for the application of the Q-gate variation operator has the greatest likelihood of making a good balance between exploration and exploitation. Experimental results agree with the analytical finding.

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.

scholarly journals Improving Variational Quantum Optimization using CVaR

Quantum ◽  
2020 ◽  
Vol 4 ◽  
pp. 256 ◽  
Author(s):  
Panagiotis Kl. Barkoutsos ◽  
Giacomo Nannicini ◽  
Anton Robert ◽  
Ivano Tavernelli ◽  
Stefan Woerner
Keyword(s):  
Combinatorial Optimization ◽  
Value At Risk ◽  
Optimization Problems ◽  
Conditional Value At Risk ◽  
Quantum Computers ◽  
Sample Mean ◽  
Combinatorial Optimization Problems ◽  
Classical Simulation ◽  
Variational Algorithms ◽  
Quantum Optimization

Hybrid quantum/classical variational algorithms can be implemented on noisy intermediate-scale quantum computers and can be used to find solutions for combinatorial optimization problems. Approaches discussed in the literature minimize the expectation of the problem Hamiltonian for a parameterized trial quantum state. The expectation is estimated as the sample mean of a set of measurement outcomes, while the parameters of the trial state are optimized classically. This procedure is fully justified for quantum mechanical observables such as molecular energies. In the case of classical optimization problems, which yield diagonal Hamiltonians, we argue that aggregating the samples in a different way than the expected value is more natural. In this paper we propose the Conditional Value-at-Risk as an aggregation function. We empirically show -- using classical simulation as well as quantum hardware -- that this leads to faster convergence to better solutions for all combinatorial optimization problems tested in our study. We also provide analytical results to explain the observed difference in performance between different variational algorithms.

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.

Improving Ant Colony Optimization Algorithms for Solving Traveling Salesman Problems

2007 ◽  
Vol 11 (4) ◽  
pp. 433-442 ◽  
Author(s):  
Kuo-Sheng Hung ◽  
◽  
Shun-Feng Su ◽  
Zne-Jung Lee ◽  
◽  
...  
Keyword(s):  
Ant Colony Optimization ◽  
Optimization Problems ◽  
Search Space ◽  
Traveling Salesman ◽  
Ant Colony ◽  
Computational Time ◽  
Search Performance ◽  
Problem Size ◽  
Traveling Salesman Problems ◽  
Combinatorial Optimization Problems

Ant colony optimization (ACO) has been successfully applied to solve combinatorial optimization problems, but it still has some drawbacks such as stagnation behavior, long computational time, and premature convergence. These drawbacks will be more evident when the problem size increases. In this paper, we reported the analysis of using a lower pheromone trail bound and a dynamic updating rule for the heuristic parameters based on entropy to improve the efficiency of ACO in solving Traveling Salesman Problems (TSPs). TSPs are NP-hard problem. Even though the problem itself is simple, when the number of city is large, the search space will become extremely large and it becomes very difficult to find the optimal solution in a short time. From our experiments, it can be found that the proposed algorithm indeed has superior search performance over traditional ACO algorithms do.

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