Multi-scale Quantum Harmonic Oscillator Algorithm with Individual Stabilization Strategy

Wang, Peng; Li, Bo; Jin, Jin; Mu, Lei; Xin, Gang; Huang, Yan; Ye, Xinggui

doi:10.1007/978-3-319-93815-8_59

Cited by 9 publications

(4 citation statements)

References 7 publications

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“…The smaller the value of D is, the greater the quantum effect of the system, and the higher the accuracy of the solution, which corresponds to the local description of the optimization problem. In the work of [21], based on the Schrödinger equation of the optimization problem, the operator method is used to prove the necessity of the multi-scale process when solving the optimization problem, i.e., the uncertainty principle of the optimization problem.…”

Section: B Schrödinger Equation For Optimization Problemsmentioning

confidence: 99%

“…According to the Copenhagen interpretation of quantum mechanics, the solution in the quantum dynamics equation of the optimization algorithm is the wave function Ψ(x), which represents the probability distribution of the solution of the optimization problem. In work [21], it has been proved that the position operator of the optimization algorithm is L = x, and the scale operator of the optimization algorithm is Ŝ = d dx . If the current wave function of the algorithm is Ψ(x), the commutation of the position operator and scale operator is applied to the wave function as follows:…”

Section: Multiscale Process and Uncertainty Relation Of Optimization ...mentioning

confidence: 99%

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Quantum Dynamics of Optimization Problems

Wang,

Xin,

Jiao

2020

Preprint

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In this letter, by establishing the Schrödinger equation of the optimization problem, the optimization problem is transformed into a constrained state quantum problem with the objective function as the potential energy. The mathematical relationship between the objective function and the wave function is established, and the quantum interpretation of the optimization problem is realized. Under the black box model, the Schrödinger equation of the optimization problem is used to establish the kinetic equation, i.e., the Fokker-Planck equation of the time evolution of the optimization algorithm, and the basic iterative structure of the optimization algorithm is given according to the interpretation of the Fokker-Planck equation. The establishment of the Fokker-Planck equation allows optimization algorithms to be studied using dynamic methods and is expected to become an important theoretical basis for algorithm dynamics.

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Section: B Schrödinger Equation For Optimization Problemsmentioning

confidence: 99%

Section: Multiscale Process and Uncertainty Relation Of Optimization ...mentioning

confidence: 99%

Quantum Dynamics of Optimization Problems

Wang,

Xin,

Jiao

2020

Preprint

Self Cite

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“…Although the structure of MQHOA is concise, it is found effective and efficient to solve unimodal and multimodal problems [15], [16]. Meanwhile, it has been proved to be more effective and efficient when an individual stabilization strategy is introduced to the original MQHOA (IS-MQHOA) in the course of the function evaluation [17]. However, sometimes the arithmetic mean position applied to IS-MQHOA is too closed to the local optimum that the algorithm still can not avoid premature stagnation and time consuming.…”

Section: Introductionmentioning

confidence: 99%

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

Wang

Xin

et al. 2019

IEEE Access

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A multi-scale quantum harmonic oscillator algorithm (MQHOA) is a quantum populationbased 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.

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“…MQHOA has been applied in many fields such as multimodal problems [24], project scheduling [25], [26]. An individual steady mechanism is introduced into MQHOA(IS-MQHOA) [27] by setting the steady state for each particle in the iteration cycle. The competition mechanism is the main evolutionary mechanism adopted during the convergence process in the MQHOA and IS-MQHOA.…”

Section: Introductionmentioning

confidence: 99%

Multiscale Quantum Harmonic Oscillator Algorithm With Multi-Harmonic Oscillators for Numerical Optimization

Wang

2019

IEEE Access

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The multiscale quantum harmonic oscillator algorithm (MQHOA) is inspired by the physical meaning of quantum wavefunction. Particles have no efficient interaction and share a wavefunction during the evolution process. In this paper, a multi-harmonic oscillator strategy is introduced, which employs multiple wavefunctions to generate new particles. The external population information can be utilized in the process of evolution. The proposed method enhances the cooperation and interaction for particles by a local collaborative operation. Moreover, an adaptive weight operator is employed in the proposed algorithm, which makes a fine-tune of solutions to keep the diversity of particles. The proposed algorithm is verified on standard benchmark functions. Wilcoxon rank sum test is adopted to ascertain the superiority of the proposed algorithm. The experiments have been conducted with several renowned heuristic algorithms. The numerical results reveal that the proposed algorithm outperforms the comparison algorithms for numerical optimization. INDEX TERMS Multiscale quantum harmonic oscillator algorithm, multi-harmonic oscillators, wavefunction, quantum-inspired algorithm, cooperation and interaction.

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Multi-scale Quantum Harmonic Oscillator Algorithm with Individual Stabilization Strategy

Cited by 9 publications

References 7 publications

Quantum Dynamics of Optimization Problems

Quantum Dynamics of Optimization Problems

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

Multiscale Quantum Harmonic Oscillator Algorithm With Multi-Harmonic Oscillators for Numerical Optimization

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