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Local optima smoothing for global optimization
Local optima smoothing for global optimization,10.1080/10556780500140029,Optimization Methods & Software,Bernardetta Addis,Marco Locatelli,Fabio Schoe
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Local optima smoothing for global optimization
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Citations: 23
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Bernardetta Addis
,
Marco Locatelli
,
Fabio Schoen
It is widely believed that in order to solve largescale
global optimization
problems, an appropriate mixture of local approximation and global exploration is necessary. Local approximation, if firstorder information on the
objective function
is available, is efficiently performed by means of local optimization methods. Unfortunately, global exploration, in absence of some kind of global information on the problem, is a ‘blind’ procedure, aimed at placing observations as evenly as possible in the search domain. Often, this procedure reduces to uniform
random sampling
(like in Multistart algorithms or in techniques based on clustering).In this paper, we propose a new framework for global exploration which tries to guide random exploration towards the region of attraction of lowlevel local optima. The main idea originated by the use of smoothing techniques (based on Gaussian convolutions): the possibility of applying a smoothing transformation not to the
objective function
but to the result of local searches seems to have never been explored yet. Although an exact smoothing of the results of local searches is impossible to implement, in this paper we propose a computational
approximation scheme
which has proven to be very efficient and (maybe more important) extremely robust in solving largescale
global optimization
problems with huge numbers of local optima and, in particular, for problems displaying a ‘funnel’ structure.
Journal:
Optimization Methods & Software  OPTIM METHOD SOFTW
, vol. 20, no. 45, pp. 417437, 2005
DOI:
10.1080/10556780500140029
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Citation Context
(12)
...In particular, it has been observed in some papers, like, e.g., in [
2
], that MBH has serious difficulties in solving this problem, in particular when the dimension n increases...
A. Cassioli
,
et al.
Machine learning for global optimization
...
Addis et al. (2005)
proposed a smoothing transformation of the local search results as an approximation framework...
Abraham Duarte
,
et al.
Hybrid scatter tabu search for unconstrained global optimization
...Algorithm 1, called IDEA, is applied to the solution of the four cases and compared to standard DE [5] and MBH [14], [
25
]...
Massimiliano Vasile
,
et al.
An Inflationary Differential Evolution Algorithm for Space Trajectory ...
...Problems having this feature are, for instance, problems having an oscillating objective function with a funnel structure [
1
, 13]...
...Therefore, DIRMIN applied to Problem (5) will try to improve the current estimate of the global minimum point by generating a different partition of the domain [0,
1
] n . This process is reiterated if DIRMIN improves on the initial point ˜ x. Otherwise, we propose to restart DIRMIN choosing ˜ x among the set of promising stationary points produced in the previous iteration, which is updated during the iterations of the new algorithm...
G. Liuzzi
,
et al.
A DIRECTbased approach exploiting local minimizations for the solutio...
...The three tested algorithms are: Differential Evolution [2], Monotonic Basin Hopping [15], [
14
] and Algorithm 1, called IDEA...
Massimiliano Vasile
,
et al.
A dynamical system perspective on evolutionary heuristics applied to s...
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Citations
(23)
Machine learning for global optimization
(
Citations: 3
)
A. Cassioli
,
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,
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,
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(
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