1,303 research outputs found
Combinatorial optimization over two random point sets
We analyze combinatorial optimization problems over a pair of random point
sets of equal cardinal. Typical examples include the matching of minimal
length, the traveling salesperson tour constrained to alternate between points
of each set, or the connected bipartite r-regular graph of minimal length. As
the cardinal of the sets goes to infinity, we investigate the convergence of
such bipartite functionals.Comment: 34 page
Indentations and Starting Points in Traveling Sales Tour Problems: Implications for Theory
A complete, non-trivial, traveling sales tour problem contains at least one “indentation”, where nodes in the interior of the point set are connected between two adjacent nodes on the boundary. Early research reported that human tours exhibited fewer such indentations than expected. A subsequent explanation proposed that this was because the observed human tours were close to the optimal, and the optimal tours happened to have few indentations. The present article reports two experiments. The first was designed to test the “few indentations” hypothesis under more stringent conditions than previously, by including point sets with two (near) optimal solutions that had a different number of indentations. For these critical point sets, participants produced the optimal solution with fewer indentations significantly more often than the alternative optimal solution. In addition, participants’ solutions started on boundary points significantly more often than by chance. A second experiment tested whether the preference for fewer indentations is the result of a conscious strategy, or the product of the processes that generate a solution. The results supported the latter conclusion. The implications for theories of human tour generation are discussed
An Investigation of Starting Point Preferences in Human Performance on Traveling Salesman Problems
Previous studies have shown that people start traveling sales problem tours significantly more often from boundary than from interior nodes. There are a number of possible reasons for such a tendency: first, it may arise as a direct result of the processes involved in tour construction; second, boundary points may be perceptually more salient than interior points, and selected for that reason; third, starting from the boundary may make the task easier or be more likely to result in a better tour than starting from the interior. The present research investigated each of these possibilities by analyzing start point frequencies in previously unpublished data and by conducting an experiment. The analysis of start points provided some slight but contradictory support for the hypothesis that start selections result from the process of tour construction, but no evidence for the perceptual salience explanation. The experiment required participants to start tours either from a boundary or from an interior point, to test whether there was an effect on the quality of tour construction. No evidence was found that starting point affected either the length of tours or the time required to produce them. However, there was some indication that starting from a central location may be more likely to result in crossed arcs
Genetic algorithms
Genetic algorithms are mathematical, highly parallel, adaptive search procedures (i.e., problem solving methods) based loosely on the processes of natural genetics and Darwinian survival of the fittest. Basic genetic algorithms concepts are introduced, genetic algorithm applications are introduced, and results are presented from a project to develop a software tool that will enable the widespread use of genetic algorithm technology
Planning Visual Inspection Tours for a 3D Dubins Airplane Model in an Urban Environment
This paper investigates the problem of planning a minimum-length tour for a
three-dimensional Dubins airplane model to visually inspect a series of targets
located on the ground or exterior surface of objects in an urban environment.
Objects are 2.5D extruded polygons representing buildings or other structures.
A visibility volume defines the set of admissible (occlusion-free) viewing
locations for each target that satisfy feasible airspace and imaging
constraints. The Dubins traveling salesperson problem with neighborhoods
(DTSPN) is extended to three dimensions with visibility volumes that are
approximated by triangular meshes. Four sampling algorithms are proposed for
sampling vehicle configurations within each visibility volume to define
vertices of the underlying DTSPN. Additionally, a heuristic approach is
proposed to improve computation time by approximating edge costs of the 3D
Dubins airplane with a lower bound that is used to solve for a sequence of
viewing locations. The viewing locations are then assigned pitch and heading
angles based on their relative geometry. The proposed sampling methods and
heuristics are compared through a Monte-Carlo experiment that simulates view
planning tours over a realistic urban environment.Comment: 18 pages, 10 figures, Presented at 2023 SciTech Intelligent Systems
in Guidance Navigation and Control conferenc
Path planning and optimization in the traveling salesman problem: Nearest neighbor vs. region-based strategies
According to the number of targets, route planning can be a very complex task. Human navigators, however, usually solve route planning tasks fastly and efficiently. Here two experiments are presented that studied human route planning performance, route planning strategies employed, and cognitive processes involved. For this, 25 places were arranged on a regular grid in a large room. Each place was marked by a unique symbol. Subjects were repeatedly asked to solve traveling salesman problems (TSP), i.e. to find the shortest closed loop connecting a given start place with a number of target places. For this, subjects were given a so-called \u27shopping list\u27 depicting the symbols of the start place and the target places. While the TSP is computationally hard, sufficient solutions can be found by simple strategies such as the nearest neighbor strategy. In Experiment 1, it was tested whether humans deployed the nearest neighbor strategy (NNS) when solving the TSP. Results showed that subjects outperformed the NNS in cases in which the NNS did not predict the optimal solution, suggesting that the NNS is not sufficient to explain human route planning behavior. As a second possible strategy a region-based approach was tested in Experiment 2. When optimal routes required more region transitions than other, sub-optimal routes, subjects preferred these sub-optimal routes. This result suggests that subjects first planned a coarse route on the region level and then refined the route during navigation. Such a hierarchical planning stragey would allow to reduce computational effort during route planning.
In a control condition, the target places were directly marked in the environment rather than being depicted on the shopping list. As subjects did not have to identify and remember the positions of the target places based on the shopping list during route planning, this control condition tested for the influence of spatial working memory for route planning performance. Results showed a strong performance increase in the control condition, emphasizing the prominent role of spatial working memory for route planning
Percolating paths through random points :
We prove consistency of four different approaches to formalizing the idea of
minimum average edge-length in a path linking some infinite subset of points of
a Poisson process. The approaches are (i) shortest path from origin through
some distinct points; (ii) shortest average edge-length in paths across the
diagonal of a large cube; (iii) shortest path through some specified proportion
of points in a large cube; (iv) translation-invariant measures on
paths in which contain a proportion of the Poisson points.
We develop basic properties of a normalized average length function
and pose challenging open problemComment: 28 page
- …