Advanced

Physically Inspired Optimization

D Costa, Emmanuel-Roosevelt LU (2020) FYSK02 20201
Mathematical Physics
Department of Physics
Abstract
Optimization is the study of finding the best solution for a problem. The applications of this field ranges from finding the best routes for travelling to finding the ground state of physical systems. This thesis looks at gradient based and gradient-less optimization algorithms which are applied to two problems: the linear least square and the position of a system of springs. The algorithms used are Sparse Levenberg-Marquardt, Particle Swarm Optimization and Nelder-Mead algorithm. The goal of this paper is to benchmark these algorithms on the two problems. The results show that for small problems the gradient-less algorithms converge faster than the gradient based algorithm. However for big problems the gradient-less algorithms face... (More)
Optimization is the study of finding the best solution for a problem. The applications of this field ranges from finding the best routes for travelling to finding the ground state of physical systems. This thesis looks at gradient based and gradient-less optimization algorithms which are applied to two problems: the linear least square and the position of a system of springs. The algorithms used are Sparse Levenberg-Marquardt, Particle Swarm Optimization and Nelder-Mead algorithm. The goal of this paper is to benchmark these algorithms on the two problems. The results show that for small problems the gradient-less algorithms converge faster than the gradient based algorithm. However for big problems the gradient-less algorithms face converging issues. Finally, more research into implementation of gradient-less algorithms is suggested. (Less)
Popular Abstract
Optimization is the study of finding the best solutions for a given problem. The applications of this field ranges from finding the best routes for travelling between different locations to maximizing output of products in a factory. In this thesis two families of algorithms are benchmarked: ones that use mathematical tools and ones that mimic behaviour of biological systems (physically inspired). The results show that physically inspired algorithms have the potential to be more efficient than the algorithms that use mathematical tools however more research needs to be done.
Please use this url to cite or link to this publication:
author
D Costa, Emmanuel-Roosevelt LU
supervisor
organization
course
FYSK02 20201
year
type
M2 - Bachelor Degree
subject
keywords
Optimization, Particle Swarm Optimization, PSO, Levenberg-Marquardt algorithm, Gradient descent algorithm, Gauss-Newton algorithm, Linear Least Squares, System of Springs
language
English
id
9022116
date added to LUP
2020-07-13 15:24:48
date last changed
2020-07-13 15:24:48
@misc{9022116,
  abstract     = {Optimization is the study of finding the best solution for a problem. The applications of this field ranges from finding the best routes for travelling to finding the ground state of physical systems. This thesis looks at gradient based and gradient-less optimization algorithms which are applied to two problems: the linear least square and the position of a system of springs. The algorithms used are Sparse Levenberg-Marquardt, Particle Swarm Optimization and Nelder-Mead algorithm. The goal of this paper is to benchmark these algorithms on the two problems. The results show that for small problems the gradient-less algorithms converge faster than the gradient based algorithm. However for big problems the gradient-less algorithms face converging issues. Finally, more research into implementation of gradient-less algorithms is suggested.},
  author       = {D Costa, Emmanuel-Roosevelt},
  keyword      = {Optimization,Particle Swarm Optimization,PSO,Levenberg-Marquardt algorithm,Gradient descent algorithm,Gauss-Newton algorithm,Linear Least Squares,System of Springs},
  language     = {eng},
  note         = {Student Paper},
  title        = {Physically Inspired Optimization},
  year         = {2020},
}