Search results
Results from the WOW.Com Content Network
Solution of a travelling salesman problem: the black line shows the shortest possible loop that connects every red dot. In the theory of computational complexity, the travelling salesman problem (TSP) asks the following question: "Given a list of cities and the distances between each pair of cities, what is the shortest possible route that visits each city exactly once and returns to the ...
In combinatorial optimization, Lin–Kernighan is one of the best heuristics for solving the symmetric travelling salesman problem. [citation needed] It belongs to the class of local search algorithms, which take a tour (Hamiltonian cycle) as part of the input and attempt to improve it by searching in the neighbourhood of the given tour for one that is shorter, and upon finding one repeats the ...
The traveling salesman problem, in which a solution is a cycle containing all nodes of the graph and the target is to minimize the total length of the cycle The Boolean satisfiability problem , in which a candidate solution is a truth assignment, and the target is to maximize the number of clauses satisfied by the assignment; in this case, the ...
The travelling salesman problem asks to find the shortest cyclic tour of a collection of points, in the plane or in more abstract mathematical spaces. Because the problem is NP-hard, algorithms that take polynomial time are unlikely to be guaranteed to find its optimal solution; [2] on the other hand a brute-force search of all permutations would always solve the problem exactly but would take ...
The Held–Karp algorithm, also called the Bellman–Held–Karp algorithm, is a dynamic programming algorithm proposed in 1962 independently by Bellman [1] and by Held and Karp [2] to solve the traveling salesman problem (TSP), in which the input is a distance matrix between a set of cities, and the goal is to find a minimum-length tour that visits each city exactly once before returning to ...
In optimization, 2-opt is a simple local search algorithm for solving the traveling salesman problem. The 2-opt algorithm was first proposed by Croes in 1958, [1] although the basic move had already been suggested by Flood. [2] The main idea behind it is to take a route that crosses over itself and reorder it so that it does not.
The Steiner traveling salesman problem (Steiner TSP, or STSP) is an extension of the traveling salesman problem.Given a list of cities, some of which are required, and the lengths of the roads between them, the goal is to find the shortest possible walk that visits each required city and then returns to the origin city. [1]
The problem still remains NP-hard. However, many heuristics work better for it than for other distance functions. The maximum scatter traveling salesman problem is another variation of the traveling salesman problem in which the goal is to find a Hamiltonian cycle that maximizes the minimum edge length rather than minimizing the maximum length ...