Multiscale Quantum Harmonic Oscillator Algorithm for Multimodal Optimization

Wang, Peng; Cheng, Kwang-Ting; Huang, Yan; Ye, Xinggui; Chen, Xiuhong

doi:10.1155/2018/8430175

Cited by 15 publications

(9 citation statements)

References 21 publications

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“…The double-well function, which is regarded as an ideal potential well model in quantum physics, is used to analyze the performance of quantum annealing as a heuristic optimization algorithm [3]. The multiscale quantum harmonic oscillator algorithm for multimode optimization (MQHOA-MMO) uses the MQHOA for multimodal optimization [4]. The wavefunction, which plays an important role in the MQHOA-MMO, determines the optimization ability of the algorithm, independent of the barrier parameters of the objective function.…”

Section: Eψ(x) = (−H 2mmentioning

confidence: 99%

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Analysis of Multiscale Quantum Harmonic Oscillator Algorithm Based on a New Multimode Objective Function

Cheng

Wang

2019

IEEE Access

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The wavefunction is an important element of the multiscale quantum harmonic oscillator algorithm (MQHOA). To verify the physical model and the multimode optimization performance of the MQHOA for multimode optimization in this paper, we define a multidimensional harmonic-Gaussian potential function. When the wavefunction of the MQHOA for multimode optimization and the probability amplitude of an ammonia molecule are compared, the ground-state wavefunction can reflect the probability distribution of the two-state ammonia molecule. We obtain the extrema of the proposed function using the Hessian matrix and optimize the proposed function with the multimode algorithm. The experiments show that the multimode algorithm can determine the extrema of the proposed function with appropriate parameters. Changes in the proposed function barriers have little effect on the optimization ability of the multimode algorithm. The optimization ability of the multimode algorithm is determined by its own wavefunction. INDEX TERMS Ammonia molecule, multiscale quantum harmonic oscillator algorithm for multimode optimization, multimodal optimization, multidimensional harmonic-Gaussian potential function, wavefunction.

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Section: Eψ(x) = (−H 2mmentioning

confidence: 99%

“…In the imaginary-time Schrödinger equation that is defined in the DMC, the wavefunction (x, t) of a single particle of mass m moving along the x-axis is governed by the time-dependent Schrödinger equation. (x, t) can be written as a series expansion in terms of the eigenfunctions ofĤ , as shown in (12).…”

Section: A the Qho Processmentioning

confidence: 99%

Analysis of Multiscale Quantum Harmonic Oscillator Algorithm Based on a New Multimode Objective Function

Cheng

Wang

2019

IEEE Access

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“…The gradient descent and quasi-Newton method are commonly used to solve for these functions. In addition, several evolutionary algorithms and swarm intelligence-based algorithms, such as particle swarm optimisation (PSO) [9], multiscale quantum harmonic oscillator algorithm [10], genetic algorithms (GA) [11][12][13], differential evolution (DE) approach [14,15], ACO algorithm [16], artificial bee colony (ABC) algorithm [17][18][19][20] and other evolutionary algorithms, have been successfully utilised in recent years. Amongst these algorithms, GA is the most widely used one in the literature, DE has been particularly proposed for numerical optimisation problems and PSO is well adapted to the optimisation of non-linear functions in multidimensional space [21].…”

Section: Introductionmentioning

confidence: 99%

Dynamic niche artificial bee colony algorithm for output control of MCR‐WPT system

Yang

Chen

2019

IET Microwaves, Antennas & Propagation

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The variations of parameters in magnetically coupled resonant wireless power transfer (MCR‐WPT) system leads to system detuning problem. When the operation frequency is shifted from the resonant frequency of the system, output power of load (PL) will reduce greatly. The mathematical formulation of PL is similar to a multimodal function of the operation frequency. All the maximums of PL are needed to confirm the operation frequency. This study describes a dynamic niche artificial bee colony (DNABC) algorithm for locating all the optimums of multimodal function. By judging the increment of individual fitness, DNABC algorithm divides the solution space into peaky niche and candidate niche, and updates the boundary of niches dynamically. It transforms searching multiple maximum values in the whole solution space into searching one global maximum in each niche. Taking a 3‐coil MCR‐WPT system as an example, the simulation and experiment results show that DNABC algorithm is affected little by the number of population and has high convergence speed and high optimisation accuracy.

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“…The convergence process of MQHOA in function evaluation is analogized to the transformation process of particles from a high energy level to the ground energy level. 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].…”

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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Multiscale Quantum Harmonic Oscillator Algorithm for Multimodal Optimization

Cited by 15 publications

References 21 publications

Analysis of Multiscale Quantum Harmonic Oscillator Algorithm Based on a New Multimode Objective Function

Analysis of Multiscale Quantum Harmonic Oscillator Algorithm Based on a New Multimode Objective Function

Dynamic niche artificial bee colony algorithm for output control of MCR‐WPT system

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

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