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In this paper, we study the use of multiple mobile charging vehicles to charge sensors in a large-scale wireless sensor network for a given monitoring period, where sensors can be charged by the vehicles with wireless power transfer. Since each sensor may experience multiple charges to avoid its energy expiration for the period, we first consider a charging problem of scheduling the multiple mobile...
Travelling salesman problem (TSP) is one of the famous discrete optimization problems. Due to its NP-completeness, the exact methods are not found till now. Here we use a nearest neighbor method to search the approximations with a frequency graph. The frequency graph is computed with a set of local optimal paths derived from a weighted graph. The frequencies on the edges represent the number of edges...
We consider a single Unmanned Aerial Vehicle (UAV) routing problem where there are multiple depots and the vehicle is allowed to refuel at any depot. The objective of the problem is to find a path for the UAV such that each target is visited at least once by the vehicle, the fuel constraint is never violated along the path for the UAV, and the total fuel required by the UAV is a minimum. We develop...
Traveling salesman problem (TSP) has been proven to be NP-complete and it is regarded for more than half a century. It is often represented as a weighted graph whereas the weighted graph cannot provide enough heuristic information for TSP. We do not know which edges belong to the best solution according to the edges' weights. Here the frequency graph is introduced as a novel representation model for...
Small UAVs are currently used in several monitoring applications to monitor a set of targets and collect relevant data. One of the main constraints that characterize a small UAV is the maximum amount of fuel the vehicle carry. In this article, we consider a single UAV routing problem where there are multiple depots and the vehicle is allowed to refuel at any depot. The objective of the problem is...
For some positive constant \eps_0, we give a (3/2-\eps_0)-approximation algorithm for the following problem: given a graph G_0=(V,E_0), find the shortest tour that visits every vertex at least once. This is a special case of the metric traveling salesman problem when the underlying metric is defined by shortest path distances in G_0. The result improves on the 3/2-approximation algorithm due to Christofides...
There has been growing interest in studying combinatorial optimization problems by clustering strategy, with a special emphasis on the traveling salesman problem (TSP). Since TSP naturally arises as a sub problem in many transportation, manufacturing and various logistics application, this problem has caught much attention of mathematicians and computer scientists. A clustering strategy will decompose...
We study the prize-collecting versions of the Steiner tree, traveling salesman, and stroll (a.k.a. Path-TSP) problems (PCST, PCTSP, and PCS, respectively): given a graph (V, E) with costs on each edge and a penalty (a.k.a. prize) on each node, the goal is to find a tree (for PCST), cycle (for PCTSP), or stroll (for PCS) that minimizes the sum of the edge costs in the tree/cycle/stroll and the penalties...
Traveling salesman problem (TSP) is one of the unsolved problems nowadays that carry significant value to the transportation work in the complete graph. There are some good approximation algorithms that can provide an approximate solution. Here, we propose a method of extending the conventional Traveling salesman problem to construct plans for multi-objects which we may encounter frequently in real...
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