Fingerprint-based indoor localization methods are promising due to the high availability of deployed access points and compatibility with commercial-off-the-shelf user devices. However, to train regression models for localization, an extensive site survey is required to collect fingerprint data from the target areas. In this paper, we consider the problem of informative path planning (IPP) to find the optimal walk for site survey subject to a budget constraint. IPP for location fingerprint collection is related to the well-known orienteering problem (OP) but is more challenging due to edge-based non-additive rewards and revisits. Given the NP-hardness of IPP, we propose two heuristic approaches: a Greedy algorithm and a genetic algorithm. We show through experimental data collected from two indoor environments with different characteristics that the two algorithms have low computation complexity, can generally achieve higher utility and lower localization errors compared to the extension of two state-of-the-art approaches to OP.
RO was originally introduced in @cite_9 . The basic idea is to convert OP into two sub-problems: the subset selection problem and the travelling salesman problem (TSP). Specifically, vertices are randomly added and removed from the current vertex set, and path planning is done via a TSP solver among the selected vertex set. Such an approach requires that the graph is fully connected. Additionally, the utility is additively associated with the vertices and costs arise from the edges. Thus, once the set of vertices is determined, the utility is also determined. It suffices to use a TSP solver to find the least cost path to traverse those vertices.
@cite_9
1993298089 2053460888 1991149726 2142607374
We consider the travelling salesman problem (TSP) problem on (the metric completion of) 3-edge-connected cubic graphs. These graphs are interesting because of the connection between their optimal solutions and the subtour elimination LP relaxation. Our main result is an approximation algorithm better than the 3 2-approximation algorithm for TSP in general. We propose a novel non-linear extension to the Orienteering Problem (OP), called the Correlated Orienteering Problem (COP). We use COP to plan informative tours (cyclic paths) for persistent monitoring of an environment with spatial correlations, where the tours are constrained to a fixed length or time budget. The main feature of COP is a quadratic utility function that captures spatial correlations among points of interest that are close to each other. COP may be solved using mixed integer quadratic programming (MIQP) that can plan multiple disjoint tours that maximize the quadratic utility function. We perform extensive characterization of our method to verify its correctness, as well as its applicability to the estimation of a realistic, time-varying, and spatially correlated scalar field. Traveling salesman problems with profits (TSPs with profits) are a generalization of the traveling salesman problem (TSP), where it is not necessary to visit all vertices. A profit is associated with each vertex. The overall goal is the simultaneous optimization of the collected profit and the travel costs. These two optimization criteria appear either in the objective function or as a constraint. In this paper, a classification of TSPs with profits is proposed, and the existing literature is surveyed. Different classes of applications, modeling approaches, and exact or heuristic solution techniques are identified and compared. Conclusions emphasize the interest of this class of problems, with respect to applications as well as theoretical results. We consider the special case of the traveling salesman problem (TSP) in which the distance metric is the shortest-path metric of a planar unweighted graph. We present a polynomial-time approximation scheme (PTAS) for this problem.