Circle generation algorithm for solving generalized traveling salesman problem
A technology of traveling salesman problem and generation algorithm, applied in the field of comprehensive planning of traveling salesman, can solve problems such as low calculation efficiency and achieve the effect of small time
Pending Publication Date: 2022-04-22
UNIV OF SHANGHAI FOR SCI & TECH
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[0004] Aiming at the deficiencies in the prior art, the purpose of the present invention is to provide a circle generation algorithm for solving the generalized traveling salesman problem, which can obtain an approximate optimal solution of an NP-hard problem in polynomial time, avoiding the existing The problem of computational inefficiency of the method
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[0032] The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only some, not all, embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by persons of ordinary skill in the art without making creative efforts belong to the protection scope of the present invention.
[0033] refer to Figure 1-3 , a cycle generation algorithm for solving the generalized traveling salesman problem, including: S1, searching for the shortest path between all service nodes, converting GTSP into TSP;
[0034] S2. Construct an initial cost matrix;
[0035] S3. Construct the assignment problem and solve it;
[0036] S4. Obtain a sequence set connecting all elements in the network from the solution of the assignment problem;
[0037] S5, generat...
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The invention discloses a circle generation algorithm for solving a generalized traveling salesman problem, and the algorithm comprises the following steps: S1, searching a shortest path among all service nodes, and converting GTSP into TSP; s2, constructing an initial cost matrix; s3, constructing and solving an assignment problem; s4, obtaining a sequence set connected with all elements in the network through the solution of the assignment problem; s5, generating a circle according to the sequence, and synthesizing the circle; s6, whether a final loop is generated or not is judged, and if yes, a result is output; otherwise, calculating the cost between the circles and constructing a cost matrix, returning to S3 to construct the assignment problem to generate the circles, and ending the algorithm until one circle is generated. According to the method, the approximate optimal solution of the NP difficult problem can be obtained within the polynomial time, and the problem that an existing method is low in calculation efficiency is solved.
Description
technical field [0001] The invention relates to the technical field of comprehensive planning of traveling salesman, in particular to a circle generation algorithm for solving generalized traveling salesman problem. Background technique [0002] The circle generation algorithm uses the classic shortest path algorithm and assignment problem algorithm in operations research to generate and synthesize circles multiple times by searching for the shortest path between elements, constructing a cost matrix and corresponding assignment problems, so as to obtain all links in the network. A closed loop of nodes that must be traversed. Among them: the assignment problem has the following characteristics: 1) Both the agent and the task are elements that must be served. 2) An assignment relationship cannot be established between the same agent and task. [0003] The classic Traveling Salesman Problem (TSP) requires finding the shortest route back to the starting point after traversing ...
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IPC IPC(8): G06Q10/04
CPCG06Q10/047
Inventor 何胜学崔允汀梁士栋袁鹏程何建佳
Owner UNIV OF SHANGHAI FOR SCI & TECH