Journal ArticleDOI
The Prize collecting traveling salesman problem
TLDR
This paper identifies several families of facet defining inequalities for this polytope, the convex hull of solutions to the PCTSP, and uses these inequalities either as cutting planes or as ingredients of a Lagrangean optimand.Abstract:
The following is a valid model for an important class of scheduling and routing problems A salesman who travels between pairs of cities at a cost depending only on the pair, gets a prize in every city that he vitis and pays a penalty to every city that he fails to visit, wishes to minimize his travel costs and net penalties, while visiting enough cities to collect a prescribed amount of prize money We call this problem the Prize Collecting Traveling Salesman Problem (PCTSP) This paper discusses structural properties of the PCTS polytope, the convex hull of solutions to the PCTSP In particular, it identifies several families of facet defining inequalities for this polytope Some of these inequalities are related to facets of the ordinary TS polytope, others to facets of the knapsack polytope They can be used in algorithms for the PCTSP either as cutting planes or as ingredients of a Lagrangean optimandread more
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References
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The traveling salesman problem
TL;DR: This study tested human performance on a real and virtual floor, as well as in a threedimensional (3D) virtual space, and modeled these results by a graph pyramid algorithm, which suggests that deterioration of performance in the 3D space can be attributed to geometrical relations between hierarchical clustering in a3D space and coarse-to-fine production of a tour.
Book
The Traveling Salesman Problem: A Guided Tour of Combinatorial Optimization
TL;DR: In this paper, Johnson and Papadimitriou proposed a performance guarantee for heuristics, based on the notion of well-solved special cases (P. Gilmore, et al.).
Journal ArticleDOI
On the facial structure of set packing polyhedra
TL;DR: This paper shows that the cliques of the intersection graph provide a first set of facets for the polyhedron in question, and it is shown that the cycles without chords of odd length of the intersections graph give rise to a further set of facet.
Journal ArticleDOI
Facets of the knapsack polytope
TL;DR: A necessary and sufficient condition is given for an inequality with coefficients 0 or 1 to define a facet of the knapsack polytope, i.e., of the convex hull of 0–1 points satisfying a given linear inequality.
Journal ArticleDOI
Properties of vertex packing and independence system polyhedra
TL;DR: A general class of facets of = convex hull{x∈Rn:Ax≤1m,x binary} is described which subsumes a class examined by Padberg [13].