All Questions
Tagged with traveling-salesman-problem combinatorial-optimization
7 questions with no upvoted or accepted answers
6
votes
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104
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Knotted Traveling Salesperson route
Let us consider fixed points in space, if we apply the well-known Traveling Salesperson Problem algorithm, we get the shortest route. It can give a nontrivial knot in the three-space. The question is ...
- 121
3
votes
0
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87
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Additional symmetries of the Traveling Salesman Polytope
Given the complete graph $K_n=(V,E)$, the Traveling Salesman Polytope is a convex polytope in $\Bbb R^E$ obtained as the convex hull of the indicator vectors of (edge-sets of) Hamiltonian cycles in $...
- 13.6k
3
votes
0
answers
145
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Hamiltonian cycle polytope for the hypercube graph
Let $Q_n$ denote the $n$ dimensional hypercube graph (i.e., graph formed from the vertices and edges of an n-dimensional hypercube). Denote the set of edges and vertices of $Q_n$ by $E_n$ and $V_n$ ...
- 393
2
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119
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Corporate salesman problem
A salesman is employed by a large corporation. He has a $n$ cities to visit, connected by roads, forming a graph. But as travel takes a lot of time, he has to pick hotels between visits. He cannot ...
- 1,626
1
vote
1
answer
115
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$\mathrm{LP}$ formulation for $\mathrm{k}$-$\operatorname{opt}$ moves
$\mathrm{k}$-$\operatorname{opt}$ moves are an idea to improve non-optimal Hamilton cycles in weighted symmetric graphs by exchanging $\mathrm{k}$ tour-edges with $\mathrm{k}$ edges that do not belong ...
- 13.2k
0
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26
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Monotony of enforced subtour merging
Is it true that for a symmetric TSP instance in the sequence of edges generated by successively:
calculating the optimal 2-factor
adding cardinality constraints on the edgesets of the 2-factor's ...
- 13.2k
0
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0
answers
40
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Subtour-gluing constraints for ILP formulation of TSPs
If one doesn't want to introduce additional variables to the ILP of a TSP instance, one has to add exponentially many so-called subtour-elimination constraints; in practical calculations subtour-...
- 13.2k