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G. A. Croes is the author of the first description of the 2-opt moves heuristic for improving non-optimal traveling salesman tours: Croes, G. A. “A Method for Solving Traveling-Salesman Problems.” Op …

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 conn …

Question: what is known about the complexity of finding the Hamilton cycle of minimum weight in graphs that resemble hypercubes with weighted edges?

Question: can the shortest Hamilton cycle in a complete symmetric graph with weighted edges be constructed from the shortest Hamilton path in the same graph by connecting its ends and then exchanging …

Weighted $K_5$ have the unique property that their edge set can be interpreted as the disjoint union of their shortest and their longest Hamilton cycle. That makes $K_5$ attractive for designing new T …

In the euclidean plane an common heuristic for the TSP is to start with the convex hull of the point set and then successively integrate as the next point and insertion position the combination that i …

You must be careful with what you are actually asking for; the criteria you give as examples are valid for every simple polygon and do not characterize simple polygons of shortest perimeter with a giv …

A simple "a posteriori" criterion is that on the optimal tour the distances to the tour-neighbors is smaller than that to any of the other vertices. Convexity alone doesn't suffice as the example of e …

By "autonomous" TSP heuristic I mean algorithms whose reported edge-set for a short Hamilton cycle is invariant under the addition of vertex weights; the terminology is borrowed from differential equa …

In the context of LP-formulations for the Traveling Salesman Problem the MTZ constraints prevent subtours via $n$ (i.e. effectively $n-1$) additional variables $$u_1=1\\2\le u_2,\,\dots ,\,u_n\le n\\ …

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-elimi …

The Dantzig-Fulkerson ILP-formulation of the symmetric TSP is $$\min\sum\limits_{i=1}^{n-1}\sum\limits_{j=i+1}^n c_{ij}x_{\lbrace i,j\rbrace}\quad\text{s.t.}\\ \sum\limits_{j\ne i,\,j=1}^n x_{\lbrace …

Given a digraph $G(E,V): (u,v)\in E\implies(v,u)\notin E$, what is known about lower bounds on the indegree and outdegree of the vertices that guarantee the existence of a vertex-disjoint directed cyc …

For a simplified formulation of necessary constraints for $\mathrm{k}$ moves it is assumed that the vertices have been relabeled so that $0,\,\dots,\,n-1$ reflects the order in which they are encounte …

In his 2009 paper General k-opt submoves for the Lin–Kernighan TSP heuristic, Helsgaun defines the local tour improvements on which the LKH heuristics are based as: with a cycle defined here: which …