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Chongqing Institute of Green and Intelligent Technology, Chinese Academy of Sceinces and University of Electronic Science and Technology of China
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1 Papers

A Near Optimal Approach for Symmetric Traveling Salesman Problem in Euclidean Space

Topics: Optimization; Mathematical Modeling; Stochastic Optimization

Authors: Wenhong Tian 1 , Chaojie Huang 2 and Xinyang Wang 2

Affiliations: 1 Chongqing Institute of Green and Intelligent Technology, Chinese Academy of Sceinces and University of Electronic Science and Technology of China, China , 2 University of Electronic Science and Technology of China, China

Digital Object Identifier: 10.5220/0006125202810287

Proceedings of ICORES 2017, ISBN: 978-989-758-218-9

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The traveling salesman problem (TSP) is one of the most challenging NP-hard problems. It has widely applications in various disciplines such as physics, biology, computer science and so forth. The best known approximation algorithm for Symmetric TSP (STSP) whose cost matrix satisfies the triangle inequality (called ?STSP) is Christofides algorithm which was proposed in 1976 and is a 3/2 approximation. Since then no proved improvement is made and improving upon this bound is a funda- mental open question in combinatorial optimization. In this paper, for the first time, we propose Trun- cated Generalized Beta distribution (TGB) for the probability distribution of optimal tour lengths in a TSP. We then introduce an iterative TGB approach to obtain quality-proved near optimal approximation, i.e., (1+1/2((a+1)/(a+2))^(K-1))-approximation where K is the number of iterations in TGB and a(>> 1) is the shape parameters of TGB. The result can approach the true optimum as K increases.
Collapse Button Related Ontology Subjects/Areas/Topics (9)
Artificial Intelligence

Mathematical Modeling

Optimization

Knowledge Discovery and Information Retrieval

Methodologies and Technologies

Stochastic Optimization

Knowledge-Based Systems

Operational Research

Symbolic Systems

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