旅行商问题外文文献翻译
(含：英文原文及中文译文)
文献出处：Mask Dorigo. Traveling salesman problem [C]// IEEE International Conference on Evolutionary Computation. IEEE, 2013,3(1), PP:30-41.
英文原文
Traveling salesman problem
Mask Dorigo
1 Introduction
In operational research and theoretical computer science, the Traveling Salesman Problem (TSP) is a NP-difficult combinatorial optimization problem. By giving pairs of city-to-city distances, find each city exactly one shortest trip. It is a special case of buyer travel problems.
The problem was first elaborated in 1930 as one of the most in-depth research questions in mathemati
cs problems and optimization. It becomes a benchmark for many optimization methods. Although the problem is difficult to calculate, a large number of heuristic detections and exact methods are known to solve certain situations that contain tens of thousands of cities.
TSP has many applications, even based on its most essential concept itself, such as planning, logistics, and manufacturing microchips. With minor changes, it has emerged as a sub-problem in many areas, such as
DNA sequencing. In these applications, the cities in the TSP represent the customers, welding points, or DNA fragments. The distance in the TSP represents the travel time or cost, or similarity measure between DNA fragments. In many applications, additional constraints, such as limited resources or time windows, make the problem quite difficult. In computational complexity theory, the decision version of the TSP (given a length L, the goal is to judge whether there is any travel shorter than L) belongs to the class of np complete problems. Therefore, it is likely that in the worst case scenario, the operating time required to solve any of the TSP's algorithms increases exponentially with the number of cities.
2 History
The origin of the traveling salesman problem is still unclear. A manual of 1832 referred to the problem of travel salesmen, including examples from Germany and Switzerland. However, there is no mathematical treatment in the book. The traveling salesman problem was elaborated in the 19th century by the Irish mathematician W.R. and the English mathematician Thomas Kirkman. Hamilton's Icosian game is a casual game based on finding the Hamilton Circle. The general form of TSP, first studied by mathematicians and especially Karl Menger at the Vienna and Harvard universities in 1930, Karl Menger defined the problem, considered the obvious brute force algorithm, and examined the heuristics of non-nearest neighbors:
We express the messenger problem (because in practice, every postman must solve this problem, and many tourists do the same), and its task is to know the limited number of points and their paired distances and find the shortest connection route. Of course, this problem is solvable for a limited number of trials. The rule allows the number of trials to be less than the number of species at a given point, but it is not known. First from the starting point to the nearest point, then from that point to the next point from its nearest point, this rule does not generally constitute the shortest possible line.
After Hassler Whitney introduced the TSP at Princeton University, this issue quickly became popular in the European and American scientific communities in the 1950s and 1960s. In Dan Monica, the R
AND Corporation's George Dantzig, Delbert Ray Fulkerson, and Selmer M. Johnson contributed to this and they solved TSP as an integer linear programming and an improved cutting plane problem. With these new solution methods, they built an optimal tour that solved an instance with 49 cities, and at the same time proved that no other tour can be shorter. In the following decades, the problem was studied by many researchers in mathematics, computer science, chemistry, physics, and other sciences.
Richard M. Karp's research in 1972 showed that the Hamiltonian problem is NP-complete, which means that the TSP is NP-hard. This
provides a mathematical explanation as to why it is difficult to find the best travel.
In the late 1970s and 1980s, there was a major breakthrough in the problem. Together with others, Gröötschel, Padberg, and Rinaldi used cut-plane methods and branch-and-bound methods to successfully solve instances of up to 2,392 cities.
In the 1990s, Applegate, Bixby, Chvátal, and Cook developed the "Concordance" program that was used in many recent solutions. In 1991, Gerhard Reinelt published TSPLIB, which collected examples of different difficulties and was used by many research groups to compare results. In 2005,
Cook and others found the best travel through 33,810 cities from a chip layout problem. This is the largest example of solving problems in TSPLIB. For many other examples with millions of cities, problem solving can be found and 1% is guaranteed to be the best one.
3 Description
3.1 As a Graphic Problem
TSP can be transformed into an undirected weighted graph. For example, the city is the vertex of the graph, the path is the edge of the graph, and the path distance is the length of the edge. This is a minimization problem that starts and ends at a specified vertex, and other vertices have exactly one access. A Hamiltonian circle is one of the best travels of the TSP and is proportional to the distance on each side.
Normally, the model is a complete graph (ie each pair of vertices is connected by edges). If there is no path between the two cities, adding an edge of any length that does not affect the best travel becomes a complete picture.
3.2 Asymmetry and symmetry
postman的中文翻译
In a symmetrical TSP, the distance between two cities in each opposite direction is the same, forming an undirected graph. This symmetry splits the possible solutions in half. In an asymmetric TSP, there may be no two-way paths or two-way paths different to form a directed graph. Traffic accidents, one-way flights, and tickets of different times and prices are examples of disruptions to this symmetry.
3.3 Related issues
An equivalent proposition in graph theory is to give a complete weighted graph (where the vertices represent cities, the paths represented by the edges, and the weights represent costs or distances) and find the Hamiltonian ring with the smallest weight. Returning to the requirements of the departure city does not change the computational complexity of the problem. Look at the Hamilton route problem.
Another related problem is the Bottleneck Traveling Salesman Problem (bottlenecks TSP): Find a Hamiltonian ring with the lowest critical edge weight in the weighted graph. The problem is of considerable practical significance, except that in the obvious areas of

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