Quality analysis of the solution produced by dissection algorithms applied to the traveling salesman problem
The aim of this paper is to analyze experimentally the quality of the solution obtained with dissection algorithms applied to the geometric Traveling Salesman Problem. Starting from Karp`s results. We apply a divide and conquer strategy, first dividing the plane into subregions where we calculate optimal subtours and then merging these subtours to obtain the final tour. The analysis is restricted to problem instances where points are uniformly distributed in the unit square. For relatively small sets of cities we analyze the quality of the solution by calculating the length of the optimal tour and by comparing it with our approximate solution. When the problem instance is too large we perform an asymptotical analysis estimating the length of the optimal tour. We apply the same dissection strategy also to classical heuristics by calculating approximate subtours and by comparing the results with the average quality of the heuristic. Our main result is the estimate of the rate of convergence of the approximate solution to the optimal solution as a function of the number of dissection steps, of the criterion used for the plane division and of the quality of the subtours. We have implemented our programs on MUSIC (MUlti Signal processor system with Intelligent Communication), a Single-Program-Multiple-Data parallel computer with distributed memory developed at the ETH Zurich.
- OSTI ID:
- 35883
- Report Number(s):
- CONF-9408161--
- Country of Publication:
- United States
- Language:
- English
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