INFINITE CONFORMAL ITERATED FUNCTIONS SYSTEMS AND MEASURABILITY OF MEASURE AND DIMENSION FUNCTIONS

A new algorithm for the solution of the inverse problem concerning interpolatory iterated functions systems (IFS) is presented. It combines the advantages of the greedy least squares approach of Mazel and Hayes, and the self-affinity in the wavelet scalogram. Thus, the algorithm is computationally cheap and yields results with high accuracy.

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Dade groups for finite groups and dimension functions

Journal of Algebra ◽

10.1016/j.jalgebra.2021.01.035 ◽

2021 ◽

Vol 576 ◽

pp. 146-196

Author(s):

Matthew Gelvin ◽

Ergün Yalçın

Keyword(s):

Finite Groups ◽

Dimension Functions

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GBUO: “The Good, the Bad, and the Ugly” Optimizer

Applied Sciences ◽

10.3390/app11052042 ◽

2021 ◽

Vol 11 (5) ◽

pp. 2042

Author(s):

Hadi Givi ◽

Mohammad Dehghani ◽

Zeinab Montazeri ◽

Ruben Morales-Menendez ◽

Ricardo A. Ramirez-Mendoza ◽

...

Keyword(s):

High Dimension ◽

Essential Role ◽

Optimization Problems ◽

Optimization Algorithms ◽

Stochastic Search ◽

Objective Functions ◽

Science And Engineering ◽

Fixed Dimension ◽

Dimension Functions ◽

Simulation Results

Optimization problems in various fields of science and engineering should be solved using appropriate methods. Stochastic search-based optimization algorithms are a widely used approach for solving optimization problems. In this paper, a new optimization algorithm called “the good, the bad, and the ugly” optimizer (GBUO) is introduced, based on the effect of three members of the population on the population updates. In the proposed GBUO, the algorithm population moves towards the good member and avoids the bad member. In the proposed algorithm, a new member called ugly member is also introduced, which plays an essential role in updating the population. In a challenging move, the ugly member leads the population to situations contrary to society’s movement. GBUO is mathematically modeled, and its equations are presented. GBUO is implemented on a set of twenty-three standard objective functions to evaluate the proposed optimizer’s performance for solving optimization problems. The mentioned standard objective functions can be classified into three groups: unimodal, multimodal with high-dimension, and multimodal with fixed dimension functions. There was a further analysis carried-out for eight well-known optimization algorithms. The simulation results show that the proposed algorithm has a good performance in solving different optimization problems models and is superior to the mentioned optimization algorithms.

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