Reoptimization of Minimum Latency Problem

Dai, Wenkai

doi:10.1007/978-3-319-62389-4_14

Cited by 4 publications

(4 citation statements)

References 20 publications

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“…Algorithm 2 was used to perform this step and was based on the ideas of other methods, such as Reference [ 48 , 49 ]. The main idea behind this algorithm is to allow new points to be added to the already established path solution with minimal disruption.…”

Section: Proposed Methodologymentioning

confidence: 99%

Dynamic Optimization and Heuristics Based Online Coverage Path Planning in 3D Environment for UAVs

Melo

Pinto

Marcato

et al. 2021

Sensors

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Path planning is one of the most important issues in the robotics field, being applied in many domains ranging from aerospace technology and military tasks to manufacturing and agriculture. Path planning is a branch of autonomous navigation. In autonomous navigation, dynamic decisions about the path have to be taken while the robot moves towards its goal. Among the navigation area, an important class of problems is Coverage Path Planning (CPP). The CPP technique is associated with determining a collision-free path that passes through all viewpoints in a specific area. This paper presents a method to perform CPP in 3D environment for Unmanned Aerial Vehicles (UAVs) applications, namely 3D dynamic for CPP applications (3DD-CPP). The proposed method can be deployed in an unknown environment through a combination of linear optimization and heuristics. A model to estimate cost matrices accounting for UAV power usage is proposed and evaluated for a few different flight speeds. As linear optimization methods can be computationally demanding to be used on-board a UAV, this work also proposes a distributed execution of the algorithm through fog-edge computing. Results showed that 3DD-CPP had a good performance in both local execution and fog-edge for different simulated scenarios. The proposed heuristic is capable of re-optimization, enabling execution in environments with local knowledge of the environments.

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Section: Proposed Methodologymentioning

confidence: 99%

Dynamic Optimization and Heuristics Based Online Coverage Path Planning in 3D Environment for UAVs

Melo

Pinto

Marcato

et al. 2021

Sensors

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“…The concept of reoptimization was first mentioned by Schäffter [31] in the context of postoptimality analysis for a scheduling problem. Since then, the concept of reoptimization has been investigated for several different problems, including the traveling salesman problem [1,5,7,15,16,30], the minimum latency problem [4,26], the rural postman problem [3], fast reoptimization of the spanning tree problem [23], the knapsack problem [2], covering problems [12], the shortest common superstring problem [10], maximum-weight induced hereditary problems [22], and scheduling [6,21,31]. There are several overviews on reoptimization [4,19,24,33].…”

Section: Related Workmentioning

confidence: 99%

Robust Reoptimization of Steiner Trees

Goyal¹,

Mömke

2020

Algorithmica

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In reoptimization, one is given an optimal solution to a problem instance and a (locally) modified instance. The goal is to obtain a solution for the modified instance. We aim to use information obtained from the given solution in order to obtain a better solution for the new instance than we are able to compute from scratch. In this paper, we consider Steiner tree reoptimization and address the optimality requirement of the provided solution. Instead of assuming that we are provided an optimal solution, we relax the assumption to the more realistic scenario where we are given an approximate solution with an upper bound on its performance guarantee. We show that for Steiner tree reoptimization there is a clear separation between local modifications where optimality is crucial for obtaining improved approximations and those instances where approximate solutions are acceptable starting points. For some of the local modifications that have been considered in previous research, we show that for every fixed > 0 , approximating the reoptimization problem with respect to a given (1 + )-approximation is as hard as approximating the Steiner tree problem itself. In contrast, with a given optimal solution to the original problem it is known that one can obtain considerably improved results. Furthermore, we provide a new algorithmic technique that, with some further insights, allows us to obtain improved performance guarantees for Steiner tree reoptimization with respect to all remaining local modifications that have been considered in the literature: a required node of degree more than one becomes a Steiner node; a Steiner node becomes a required node; the cost of one edge is increased.

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“…The term reoptimization was mentioned for the first time in the paper of Schäffter [35], where the author addressed an NP-hard scheduling problem with forbidden sets in the scenario of adding/removing a forbidden set. Since then, reoptimization has been successfully applied to other NP-hard problems including 1 : the Steiner tree problem [8, 11, 13-15, 31, 32, 37], the traveling salesman problem and some of its variants [1,5,7,12,[15][16][17][18][19]34], scheduling problems [6,21], the minimum latency problem [28,29], the minimum spanning tree problem [24], the rural postman problem [3], many covering problems [10], the shortest superstring problem [9], the knapsack problem [2], the maximum-weight induced hereditary subgraph problems [22], and the maximum P k subgraph problem [23]. Some overviews on other NP-hard reoptimization problems can be found in [4,25,36].…”

Section: Introductionmentioning

confidence: 99%

New Algorithms for Steiner Tree Reoptimization

Bilò

2024

Algorithmica

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Reoptimization is a setting in which we are given a good approximate solution of an optimization problem instance and a local modification that slightly changes the instance. The main goal is that of finding a good approximate solution of the modified instance. We investigate one of the most studied scenarios in reoptimization known as Steiner tree reoptimization. Steiner tree reoptimization is a collection of strongly $$\textsf {NP}$$ NP -hard optimization problems that are defined on top of the classical Steiner tree problem and for which several constant-factor approximation algorithms have been designed in the last decades. In this paper we improve upon all these results by developing a novel technique that allows us to design polynomial-time approximation schemes. Remarkably, prior to this paper, no approximation algorithm better than recomputing a solution from scratch was known for the elusive scenario in which the cost of a single edge decreases. Our results are best possible since none of the problems addressed in this paper admits a fully polynomial-time approximation scheme, unless $$\textsf {P}=\textsf {NP}$$ P = NP

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Reoptimization of Minimum Latency Problem

Cited by 4 publications

References 20 publications

Dynamic Optimization and Heuristics Based Online Coverage Path Planning in 3D Environment for UAVs

Dynamic Optimization and Heuristics Based Online Coverage Path Planning in 3D Environment for UAVs

Robust Reoptimization of Steiner Trees

New Algorithms for Steiner Tree Reoptimization

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