Heuristic combinatorial optimization by simulated Darwinian evolution: a polynomial time algorithm for the Traveling Salesman Problem

1991 ◽  
Vol 65 (1) ◽  
pp. 31-35 ◽  
Author(s):  
B. K. Ambati ◽  
J. Ambati ◽  
M. M. Mokhtar
Keyword(s):  
Combinatorial Optimization ◽  
Traveling Salesman Problem ◽  
Polynomial Time ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Traveling Salesman ◽  
Darwinian Evolution ◽  
The Traveling Salesman Problem

scholarly journals Solving the Traveling Salesman Problem on the D-Wave Quantum Computer

2021 ◽  
Vol 9 ◽  
Author(s):  
Siddharth Jain
Keyword(s):  
Combinatorial Optimization ◽  
Traveling Salesman Problem ◽  
Quantum Computer ◽  
Traveling Salesman ◽  
Hard Problem ◽  
Problem Size ◽  
Quadratic Unconstrained Binary Optimization ◽  
Np Hard Problem ◽  
The Traveling Salesman Problem ◽  
D Wave

The traveling salesman problem is a well-known NP-hard problem in combinatorial optimization. This paper shows how to solve it on an Ising Hamiltonian based quantum annealer by casting it as a quadratic unconstrained binary optimization (QUBO) problem. Results of practical experiments are also presented using D-Wave’s 5,000 qubit Advantage 1.1 quantum annealer and the performance is compared to a classical solver. It is found the quantum annealer can only handle a problem size of 8 or less nodes and its performance is subpar compared to the classical solver both in terms of time and accuracy.

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.

Evolving Ant Colony Optimization

1998 ◽  
Vol 01 (02n03) ◽  
pp. 149-159 ◽  
Author(s):  
Hozefa M. Botee ◽  
Eric Bonabeau
Keyword(s):  
Genetic Algorithm ◽  
Combinatorial Optimization ◽  
Ant Colony Optimization ◽  
Traveling Salesman Problem ◽  
Traveling Salesman ◽  
Ant Colony ◽  
New Approach ◽  
The Traveling Salesman Problem

Ant Colony Optimization (ACO) is a promising new approach to combinatorial optimization. Here ACO is applied to the traveling salesman problem (TSP). Using a genetic algorithm (GA) to find the best set of parameters, we demonstrate the good performance of ACO in finding good solutions to the TSP.

scholarly journals ОГЛЯД ЗАВДАНЬ МАРШРУТИЗАЦІЇ, ЩО ЗВОДЯТЬСЯ ДО ЗАДАЧІ КОМІВОЯЖЕРА

2020 ◽  
pp. 152-159
Author(s):  
Ольга Борисовна Маций
Keyword(s):  
Combinatorial Optimization ◽  
Traveling Salesman Problem ◽  
Information Technologies ◽  
Traveling Salesman ◽  
Routing Problems ◽  
Routing Problem ◽  
Combinatorial Optimization Problems ◽  
Np Complete ◽  
Modern Information ◽  
The Traveling Salesman Problem

The solution to the problem of improving the management of the transport process depends not only on the level of modernization of vehicles and the degree of use of modern information technologies, but also on the choice of routes that reduce the cost of transporting goods and passengers. Actual working conditions of vehicles in road networks put forward a number of tasks for optimizing closed routes, which are based on the classic routing problem (VRP - Vehicle Routing Problem).VRP is one of the generalizations of the hard-to-solve traveling salesman problem. The traveling salesman task is NP-complete. It refers to the main tasks of combinatorial optimization and, forming a continuously replenished set of applications and generalizations, remains an urgent research topic. An exact solution to the traveling salesman problem can be found only by reducing the enumeration of the type of branches and boundaries, which are not always applicable in operational planning by vehicle traffic. Therefore, the development of new and improvement of currently known methods for solving routing problems, reducible to the traveling salesman problem, and their software implementation is both a theoretical and practically important problem.The article considers the class of routing problems reducible to the traveling salesman problem. It is shown that optimization tasks for closed routes (routing problems), which are an important part of transport logistics, occupy key positions in the management of the processes of moving goods and passengers with the support of modern information technologies. An obvious feature that combines the considered list of routing problems (the symmetric traveling salesman problem, the problem of packing in containers, the school bus problem) is that they are formulated as generalizations or variants of the NP-complete traveling salesman problem with restrictions that narrow the scope of feasible solutions. The strongest restrictions become insufficient solvability conditions, stimulating interest in the study of combinatorial optimization problems associated with the traveling salesman problem.

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