Abstract
Travelling salesman problem (TSP) has been widely studied for the classical closed loop variant but less attention has been paid to the open loop variant. Open loop solution has property of being also a spanning tree, although not necessarily the minimum spanning tree (MST). In this paper, we present a simple branch elimination algorithm that removes the branches from MST by cutting one link and then reconnecting the resulting subtrees via selected leaf nodes. The number of iterations equals to the number of branches (b) in the MST. Typically, b << n where n is the number of nodes. With O-Mopsi and Dots datasets, the algorithm reaches gap of 1.69% and 0.61 %, respectively. The algorithm is suitable especially for educational purposes by showing the connection between MST and TSP, but it can also serve as a quick approximation for more complex metaheuristics whose efficiency relies on quality of the initial solution.
Highlights
If considered all possible start points, it would reach the same result as Prim-travelling salesman problem (TSP), Kruskal-TSP and the greedy variant of minimum spanning tree (MST)-to-TSP
The all-pairs variant of MST-to-TSP is the only heuristic that finds the optimal solution, which includes the detour in the middle of the longer route
It is clearly superior to the existing MST-based heuristics and very close to the more sophisticated local search (0.00% and 0.01%)
Summary
Euler tour by removing nodes that are visited repeatedly This algorithm is often used as classroom example because it provides upper limit how far the solution can be from the. Prim’s and Kruskal’s algorithms canthat modified to obtain sub-optimal solutions tour by removing nodes arebeen visited repeatedly. This algorithm is often used as classfor TSP. Experiments show that the all-pairs First, a simple greedy variant removes the longest all links connecting to any of thebetter branching variant provide average gaps of 1.69% The resulting sub-trees are reconnected by selecting the shortest link between than those of the existing MST-based variants including Christofides (12.77% and 9.10%), leaf nodes.
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