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Complex System Modeling and Simulation 2022, 2(1): 59-77 https://doi.org/10.23919/CSMS.2022.0001
Open Access | Issue | Published: 30 March 2022

Adaptive Dimensional Learning with a Tolerance Framework for the Differential Evolution Algorithm

Show Author's Information Wei Li1,  Xinqiang Ye1,  Ying Huang2( ),  Soroosh Mahmoodi3
School of Information Engineering, Jiangxi University of Science and Technology, Ganzhou 341000, China
School of Mathematical and Computer Science, Gannan Normal University, Ganzhou 341000, China
Soroosh Khorshid Iranian Co., Qazvin 999067, Iran
Keywords:
Differential Evolution (DE), tolerance mechanism, dimensional learning, parameter adaptation, continuous optimization
Cite this article:
Li W, Ye X, Huang Y, et al. Adaptive Dimensional Learning with a Tolerance Framework for the Differential Evolution Algorithm. Complex System Modeling and Simulation, 2022, 2(1): 59-77. https://doi.org/10.23919/CSMS.2022.0001
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Abstract Full text About this article

The Differential Evolution (DE) algorithm, which is an efficient optimization algorithm, has been used to solve various optimization problems. In this paper, adaptive dimensional learning with a tolerance framework for DE is proposed. The population is divided into an elite subpopulation, an ordinary subpopulation, and an inferior subpopulation according to the fitness values. The ordinary and elite subpopulations are used to maintain the current evolution state and to guide the evolution direction of the population, respectively. The inferior subpopulation learns from the elite subpopulation through the dimensional learning strategy. If the global optimum is not improved in a specified number of iterations, a tolerance mechanism is applied. Under the tolerance mechanism, the inferior and elite subpopulations implement the restart strategy and the reverse dimensional learning strategy, respectively. In addition, the individual status and algorithm status are used to adaptively adjust the control parameters. To evaluate the performance of the proposed algorithm, six state-of-the-art DE algorithm variants are compared on the benchmark functions. The results of the simulation show that the proposed algorithm outperforms other variant algorithms regarding function convergence rate and solution accuracy.


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About this article

Adaptive Dimensional Learning with a Tolerance Framework for the Differential Evolution Algorithm

Show Author's information Wei Li1, Xinqiang Ye1, Ying Huang2( ), Soroosh Mahmoodi3
School of Information Engineering, Jiangxi University of Science and Technology, Ganzhou 341000, China
School of Mathematical and Computer Science, Gannan Normal University, Ganzhou 341000, China
Soroosh Khorshid Iranian Co., Qazvin 999067, Iran

Abstract

The Differential Evolution (DE) algorithm, which is an efficient optimization algorithm, has been used to solve various optimization problems. In this paper, adaptive dimensional learning with a tolerance framework for DE is proposed. The population is divided into an elite subpopulation, an ordinary subpopulation, and an inferior subpopulation according to the fitness values. The ordinary and elite subpopulations are used to maintain the current evolution state and to guide the evolution direction of the population, respectively. The inferior subpopulation learns from the elite subpopulation through the dimensional learning strategy. If the global optimum is not improved in a specified number of iterations, a tolerance mechanism is applied. Under the tolerance mechanism, the inferior and elite subpopulations implement the restart strategy and the reverse dimensional learning strategy, respectively. In addition, the individual status and algorithm status are used to adaptively adjust the control parameters. To evaluate the performance of the proposed algorithm, six state-of-the-art DE algorithm variants are compared on the benchmark functions. The results of the simulation show that the proposed algorithm outperforms other variant algorithms regarding function convergence rate and solution accuracy.

Keywords: Differential Evolution (DE), tolerance mechanism, dimensional learning, parameter adaptation, continuous optimization

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Published: 30 March 2022
Issue date: March 2022

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Acknowledgment

This work was supported by the National Natural Science Foundation of China (Nos. 61903089 and 62066019), the Natural Science Foundation of Jiangxi Province (Nos. 20202BABL202020 and 20202BAB202014), and the National Key Research and Development Program of China (No. 2020YFB1713700).

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