Multi-Scale Quantum Harmonic Oscillator Algorithm With Truncated Mean Stabilization Strategy for Global Numerical Optimization Problems

A multi-scale quantum harmonic oscillator algorithm (MQHOA) is a quantum population-based algorithm proposed recently. It utilizes the quantum wave function to locate the global optimum of a global numerical optimization problem. As the MQHOA employs the elitism to replace the worst particle in each...

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Published in:	IEEE access Vol. 7; pp. 18926 - 18939
Main Authors:	Ye, Xinggui, Wang, Peng, Xin, Gang, Jin, Jin, Huang, Yan
Format:	Journal Article
Language:	English
Published:	Piscataway IEEE 2019 The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:	Algorithms Convergence Energy states Harmonic analysis Harmonic oscillators Iterative methods Multi-scale quantum harmonic oscillator algorithm Optimization Oscillators Particle swarm optimization population-based algorithm Sociology Stabilization Statistics stochastic algorithm Swarm intelligence truncated mean stabilization strategy Wave functions
ISSN:	2169-3536, 2169-3536
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Abstract	A multi-scale quantum harmonic oscillator algorithm (MQHOA) is a quantum population-based algorithm proposed recently. It utilizes the quantum wave function to locate the global optimum of a global numerical optimization problem. As the MQHOA employs the elitism to replace the worst particle in each iteration cycle, it reduces one of the particles in each run, which will cripple the diversity of the population and slow down the convergence speed. Therefore, the particles will be easily trapped into local optima. In this paper, we suggest a new MQHOA with truncated mean stabilization (TS-MQHOA) policy to alleviate the above-mentioned problems. The theoretical and experimental analyses indicate that the truncated mean stabilization strategy helps to diversify the populations and improve the convergence efficiency. The proposed TS-MQHOA is evaluated on a number of dimensionwise unimodal and multimodal CEC benchmark functions, and the computational results are compared with several popular population-based algorithms. The experimental results on complex test problems demonstrate that the proposed TS-MQHOA, in most function evaluations, is able to obtain better convergence toward the global optimum compared with several renowned heuristic algorithms based on swarm intelligence. Meanwhile, the comparative results reveal the competitiveness and superiority of the proposed algorithm, especially on high-dimensional function evaluations.
AbstractList	A multi-scale quantum harmonic oscillator algorithm (MQHOA) is a quantum population-based algorithm proposed recently. It utilizes the quantum wave function to locate the global optimum of a global numerical optimization problem. As the MQHOA employs the elitism to replace the worst particle in each iteration cycle, it reduces one of the particles in each run, which will cripple the diversity of the population and slow down the convergence speed. Therefore, the particles will be easily trapped into local optima. In this paper, we suggest a new MQHOA with truncated mean stabilization (TS-MQHOA) policy to alleviate the above-mentioned problems. The theoretical and experimental analyses indicate that the truncated mean stabilization strategy helps to diversify the populations and improve the convergence efficiency. The proposed TS-MQHOA is evaluated on a number of dimensionwise unimodal and multimodal CEC benchmark functions, and the computational results are compared with several popular population-based algorithms. The experimental results on complex test problems demonstrate that the proposed TS-MQHOA, in most function evaluations, is able to obtain better convergence toward the global optimum compared with several renowned heuristic algorithms based on swarm intelligence. Meanwhile, the comparative results reveal the competitiveness and superiority of the proposed algorithm, especially on high-dimensional function evaluations. A multi-scale quantum harmonic oscillator algorithm (MQHOA) is a quantum population-based algorithm proposed recently. It utilizes the quantum wave function to locate the global optimum of a global numerical optimization problem. As the MQHOA employs the elitism to replace the worst particle in each iteration cycle, it reduces one of the particles in each run, which will cripple the diversity of the population and slow down the convergence speed. Therefore, the particles will be easily trapped into local optima. In this paper, we suggest a new MQHOA with truncated mean stabilization (TS-MQHOA) policy to alleviate the above-mentioned problems. The theoretical and experimental analyses indicate that the truncated mean stabilization strategy helps to diversify the populations and improve the convergence efficiency. The proposed TS-MQHOA is evaluated on a number of dimension-wise unimodal and multimodal CEC benchmark functions, and the computational results are compared with several popular population-based algorithms. The experimental results on complex test problems demonstrate that the proposed TS-MQHOA, in most function evaluations, is able to obtain better convergence toward the global optimum compared with several renowned heuristic algorithms based on swarm intelligence. Meanwhile, the comparative results reveal the competitiveness and superiority of the proposed algorithm, especially on high-dimensional function evaluations.
Author	Huang, Yan Wang, Peng Jin, Jin Xin, Gang Ye, Xinggui
Author_xml	– sequence: 1 givenname: Xinggui orcidid: 0000-0002-1636-1260 surname: Ye fullname: Ye, Xinggui organization: University of Chinese Academy of Sciences, Beijing, China – sequence: 2 givenname: Peng surname: Wang fullname: Wang, Peng email: qhoalab@163.com organization: School of Computer Science and Technology, Southwest Minzu University, Chengdu, China – sequence: 3 givenname: Gang surname: Xin fullname: Xin, Gang organization: University of Chinese Academy of Sciences, Beijing, China – sequence: 4 givenname: Jin orcidid: 0000-0003-3745-3233 surname: Jin fullname: Jin, Jin organization: University of Chinese Academy of Sciences, Beijing, China – sequence: 5 givenname: Yan surname: Huang fullname: Huang, Yan organization: School of Computer Science and Technology, Huaiyin Normal University, Huai'an, China
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SubjectTerms	Algorithms Convergence Energy states Harmonic analysis Harmonic oscillators Iterative methods Multi-scale quantum harmonic oscillator algorithm Optimization Oscillators Particle swarm optimization population-based algorithm Sociology Stabilization Statistics stochastic algorithm Swarm intelligence truncated mean stabilization strategy Wave functions
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Title	Multi-Scale Quantum Harmonic Oscillator Algorithm With Truncated Mean Stabilization Strategy for Global Numerical Optimization Problems
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