Weiqi Li
ABSTRACT
The intrinsic difficulty of the Traveling Salesman Problem (TSP) is associated with the combinatorial explosion of potential solutions in the solution space. The significant difficulty with search algorithms for the TSP is how to quickly find the optimal tour and make sure it is optimal. Scamming of all possible solutions requires exponential computing time. Do we need exploring all the possibilities to find the optimal solution? How can we narrow down the search space effectively and efficiently for an exhausted search? This paper describes a new search strategy for solving the TSP. The search strategy combines local search and exhausted search. Local search is used to reduce the search space quickly for exhausted search. In this paper, local search is treated as a discrete dynamical system. A set of local search trajectories converges to small area of the solution space. Then exhausted search is used to search the small area to find the optimal solution. The global optimization features and computing complexity of this new search system are also discussed.
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Index Terms
- A new approach to the traveling salesman problem
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