Optimization Techniques in the Localization Problem: A Survey on Recent Advances

Optimization is a mathematical discipline or tool suitable for minimizing or maximizing a function. It has been largely used in every scientific field to solve problems where it is necessary to find a local or global optimum. In the engineering field of localization, optimization has been adopted to...

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Published in:Machines (Basel) Vol. 12; no. 8; p. 569
Main Authors: Stefanoni, Massimo, Sarcevic, Peter, Sárosi, József, Odry, Akos
Format: Journal Article
Language:English
Published: Basel MDPI AG 01.08.2024
Subjects:
Algorithms
Convex analysis
Evolutionary computation
Functions (mathematics)
Genetic algorithms
Global optimization
Heuristic methods
Linear programming
local optimization
Localization
Mathematical optimization
Mathematical programming
metaheuristic algorithms
Methods
multi-objective problem
Multiple objective analysis
Newton methods
Optimization algorithms
Optimization techniques
Particle swarm optimization
single objective problem
Variables
United Kingdom
ISSN:2075-1702, 2075-1702
Online Access:Get full text
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Abstract Optimization is a mathematical discipline or tool suitable for minimizing or maximizing a function. It has been largely used in every scientific field to solve problems where it is necessary to find a local or global optimum. In the engineering field of localization, optimization has been adopted too, and in the literature, there are several proposals and applications that have been presented. In the first part of this article, the optimization problem is presented by considering the subject from a purely theoretical point of view and both single objective (SO) optimization and multi-objective (MO) optimization problems are defined. Additionally, it is reported how local and global optimization problems can be tackled differently, and the main characteristics of the related algorithms are outlined. In the second part of the article, extensive research about local and global localization algorithms is reported and some optimization methods for local and global optimum algorithms, such as the Gauss–Newton method, Genetic Algorithm (GA), Particle Swarm Optimization (PSO), Differential Evolution (DE), and so on, are presented; for each of them, the main concept on which the algorithm is based, the mathematical model, and an example of the application proposed in the literature for localization purposes are reported. Among all investigated methods, the metaheuristic algorithms, which do not exploit gradient information, are the most suitable to solve localization problems due to their flexibility and capability in solving non-convex and non-linear optimization functions.
AbstractList Optimization is a mathematical discipline or tool suitable for minimizing or maximizing a function. It has been largely used in every scientific field to solve problems where it is necessary to find a local or global optimum. In the engineering field of localization, optimization has been adopted too, and in the literature, there are several proposals and applications that have been presented. In the first part of this article, the optimization problem is presented by considering the subject from a purely theoretical point of view and both single objective (SO) optimization and multi-objective (MO) optimization problems are defined. Additionally, it is reported how local and global optimization problems can be tackled differently, and the main characteristics of the related algorithms are outlined. In the second part of the article, extensive research about local and global localization algorithms is reported and some optimization methods for local and global optimum algorithms, such as the Gauss–Newton method, Genetic Algorithm (GA), Particle Swarm Optimization (PSO), Differential Evolution (DE), and so on, are presented; for each of them, the main concept on which the algorithm is based, the mathematical model, and an example of the application proposed in the literature for localization purposes are reported. Among all investigated methods, the metaheuristic algorithms, which do not exploit gradient information, are the most suitable to solve localization problems due to their flexibility and capability in solving non-convex and non-linear optimization functions.
Audience Academic
Author Sárosi, József
Sarcevic, Peter
Odry, Akos
Stefanoni, Massimo
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  fullname: Odry, Akos
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Snippet Optimization is a mathematical discipline or tool suitable for minimizing or maximizing a function. It has been largely used in every scientific field to solve...
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SubjectTerms Algorithms
Convex analysis
Evolutionary computation
Functions (mathematics)
Genetic algorithms
Global optimization
Heuristic methods
Linear programming
local optimization
Localization
Mathematical optimization
Mathematical programming
metaheuristic algorithms
Methods
multi-objective problem
Multiple objective analysis
Newton methods
Optimization algorithms
Optimization techniques
Particle swarm optimization
single objective problem
Variables
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