Sufficient Conditions for Global Convergence of Differential Evolution Algorithm

Hu, Zhongbo; Xiong, Shengwu; Su, Qinghua; Zhang, Xiaowei

doi:10.1155/2013/193196

Cited by 37 publications

(21 citation statements)

References 39 publications

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“…The frequency range was informed by previous studies in cartilage and was chosen to capture the behavior of the samples while limiting the influence of measurement noise [22]. A differential evolution algorithm was used to cover a wide expanse of the parameter space and decrease the chance of local minima convergence [23] during minimization of the chosen objective function [24],…”

Section: Discussionmentioning

confidence: 99%

A Biphasic Approach for Characterizing Tensile, Compressive, and Hydraulic Properties of the Sclera

Brown

Pardue

Ethier

2020

Preprint

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Measuring the biomechanical properties of the mouse sclera is of great interest, since altered scleral properties are features of many common ocular pathologies, and the mouse is a powerful species for studying genetic factors in disease. Here, a poroelastic material model is used to analyze data from unconfined compression testing of both pig and mouse sclera, and the tensile modulus, compressive modulus, and permeability of the sclera are obtained at three levels of compressive strain. Values for all three properties measured simultaneously by unconfined compression of pig sclera were comparable to previously reported values measured by tests specific for each property, i.e., compression tests, biaxial tensile tests, and falling-head permeability assays. The repeatability of the approach was evaluated using test-retest experimental paradigm on pig sclera. Repeatability was low for measured compressive stiffness, indicating permanent changes to the samples occurring after the first test. However, reasonable repeatability for tensile stiffness and permeability was observed. The intrinsic material properties of the mouse sclera were measured for the first time. Tensile stiffness and permeability of the sclera in both species were seen to be dependent on the state of compressive strain. We conclude that unconfined compression testing of sclera, when analyzed with poroelastic theory, can be used as a powerful tool to phenotype mouse scleral changes in future genotype-phenotype association studies. Statement of SignificanceOcular biomechanics is strongly influenced by the sclera, the outermost white coat of the eye. Many ocular diseases are believed to be influenced by pathological changes to scleral microstructure and biomechanics, making intrinsic biomechanical properties an important outcome measure in many studies. However, the small mouse eye precludes the use of most traditional biomechanical characterization techniques. Here, we show that unconfined compression testing analyzed with poroelastic theory can produce measurements of biomechanical properties in the pig sclera comparable to those measured by other traditional techniques. Importantly, this technique can be successfully applied to the mouse sclera, enabling more widespread use of the species as a model for ocular disease.

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Section: Discussionmentioning

confidence: 99%

A Biphasic Approach for Characterizing Tensile, Compressive, and Hydraulic Properties of the Sclera

Brown

Pardue

Ethier

2020

Preprint

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“…Convergence property and efficiency of DE is well studied [73], [74]. A probabilistic viewpoint of DE convergence followed by a description of global convergence condition for DE is described in [75]. They show that indeed DE converges to an optimal solution.…”

Section: B Approximation Ability Of Hierarchical Fuzzy Inference Treementioning

confidence: 99%

Multiobjective Programming for Type-2 Hierarchical Fuzzy Inference Trees

Ojha

Snášel

Abraham

2018

IEEE Trans. Fuzzy Syst.

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Originally published in:IEEE Transactions on Fuzzy Systems (99), http://doi.org/10.1109/tfuzz.2017.2698399 Rights / License:In Copyright -Non-Commercial Use Permitted This page was generated automatically upon download from the ETH Zurich Research Collection. For more information please consult the Terms of use. ETH Library1063-6706 (c) 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Abstract-This paper proposes a design of hierarchical fuzzy inference tree (HFIT). An HFIT produces an optimum tree-like structure, i.e., a natural hierarchical structure that accommodates simplicity by combining several low-dimensional fuzzy inference systems (FISs). Such a natural hierarchical structure provides a high degree of approximation accuracy. The construction of HFIT takes place in two phases. Firstly, a nondominated sorting based multiobjective genetic programming (MOGP) is applied to obtain a simple tree structure (a low complexity model) with a high accuracy. Secondly, the differential evolution algorithm is applied to optimize the obtained tree's parameters. In the derived tree, each node acquires a different input's combination, where the evolutionary process governs the input's combination. Hence, HFIT nodes are heterogeneous in nature, which leads to a high diversity among the rules generated by the HFIT. Additionally, the HFIT provides an automatic feature selection because it uses MOGP for the tree's structural optimization that accepts inputs only relevant to the knowledge contained in data. The HFIT was studied in the context of both type-1 and type-2 FISs, and its performance was evaluated through six application problems. Moreover, the proposed multiobjective HFIT was compared both theoretically and empirically with recently proposed FISs methods from the literature, such as McIT2FIS, TSCIT2FNN, SIT2FNN, RIT2FNS-WB, eT2FIS, MRIT2NFS, IT2FNN-SVR, etc. From the obtained results, it was found that the HFIT provided less complex and highly accurate models compared to the models produced by the most of other methods. Hence, the proposed HFIT is an efficient and competitive alternative to the other FISs for function approximation and feature selection.

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“…The classical DE (Hu et al. 2008, 2013, 2014, 2016; Su and Hu 2013) works through a simple cycle of operators including mutation, crossover and selection operator after initialization. The classical DE procedures are described in detail as follows.…”

Section: Classical Differential Evolutionmentioning

confidence: 99%

Modified differential evolution algorithm with onlooker bee operator for mixed discrete-continuous optimization

Miao

et al. 2016

SpringerPlus

Self Cite

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For solving non-linear programming problems containing discrete and continuous variables, this article suggests two modified algorithms based on differential evolution (DE). The two proposed algorithms incorporate a novel random search strategy into DE/best/1 and DE/cur-to-best/1 respectively. Inspired by the artificial bee colony algorithm, the random search strategy overcomes the searching unbalance of DE/best/1 and DE/cur-to-best/1 by enhancing the global exploration capability of promising individuals. Two numerical experiments are given to test the two modified algorithms. Experiment 1 is conducted on the benchmark function set of CEC2005 in order to verify the effectiveness of the improved strategy. Experiment 2 is designed to optimize two mixed discrete-continuous problems to illustrate the competitiveness and the practicality of the proposed algorithms. In particular, the modified DE/cur-to-best/1 finds the new optima of two engineering optimization problems.

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Sufficient Conditions for Global Convergence of Differential Evolution Algorithm

Cited by 37 publications

References 39 publications

A Biphasic Approach for Characterizing Tensile, Compressive, and Hydraulic Properties of the Sclera

A Biphasic Approach for Characterizing Tensile, Compressive, and Hydraulic Properties of the Sclera

Multiobjective Programming for Type-2 Hierarchical Fuzzy Inference Trees

Modified differential evolution algorithm with onlooker bee operator for mixed discrete-continuous optimization

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