Potential barrier estimation criterion based on quantum dynamics framework of optimization algorithm

doi:10.11772/j.issn.1001-9081.2023040553

Journal of Computer Applications ›› 2024, Vol. 44 ›› Issue (4): 1180-1186.DOI: 10.11772/j.issn.1001-9081.2023040553

• Advanced computing • Previous Articles Next Articles

Potential barrier estimation criterion based on quantum dynamics framework of optimization algorithm

Yaqin CHEN¹, Peng WANG¹^,²()

^1.School of Computer Science and Engineering，Southwest Minzu University，Chengdu Sichuan 610225，China
^2.Chengdu Institution of Computer Application，Chinese Academy of Sciences，Chengdu Sichuan 610213，China

Received:2023-05-09 Revised:2023-07-19 Accepted:2023-07-25 Online:2023-12-04 Published:2024-04-10
Contact: Peng WANG
About author:CHEN Yaqin， born in 1998， M. S. candidate. Her research interests include quantum heuristic algorithms， high performance computing.
Supported by:
Innovative Scientific Research Project for Postgraduates of Southwest Minzu University(ZY2023987)

基于优化算法量子动力学框架的势垒估计准则

陈雅琴¹, 王鹏¹^,²()

^1.西南民族大学计算机科学与工程学院，成都 610225
^2.中国科学院成都计算机应用研究所，成都 610213

通讯作者: 王鹏
作者简介:陈雅琴（1998—），女，内蒙古乌兰察布人，硕士研究生，CCF会员，主要研究方向：量子启发式算法、高性能计算
王鹏（1975—），男，四川乐山人，教授，博士，CCF高级会员，主要研究方向：量子理论、量子启发式算法、智能计算、高性能计算。
基金资助:
西南民族大学研究生创新型科研项目(ZY2023987)

Abstract

Abstract:

Quantum Dynamics Framework （QDF） is a basic iterative process of optimization algorithm with representative and universal significance， which is obtained under the quantum dynamics model of optimization algorithm. Differential acceptance is an important mechanism to avoid the optimization algorithm falling into local optimum and to solve the premature convergence problem of the algorithm. In order to introduce the differential acceptance mechanism into the QDF， based on the quantum dynamics model， the differential solution was regarded as a potential barrier encountered in the process of particle motion， and the probability of particles penetrating the potential barrier was calculated by using the transmission coefficient in the quantum tunneling effect. Thus， the differential acceptance criterion of quantum dynamics model was obtained： Potential Barrier Estimation Criterion （PBEC）. PBEC was related to the height and width of the potential barrier and the quality of the particles. Compared with the classical Metropolis acceptance criterion， PBEC can comprehensively estimate the behavior of the optimization algorithm when it encounters the differential solution during sampling. The experimental results show that， the QDF algorithm based on PBEC has stronger ability to jump out of the local optimum and higher search efficiency than the QDF algorithm based on Metropolis acceptance criterion， and PBEC is a feasible and effective differential acceptance mechanism in quantum optimization algorithms.

Key words: optimization algorithm, differential acceptance mechanism, transmission coefficient, potential barrier estimation criterion, Metropolis acceptance criterion

摘要：

量子动力学框架（QDF）是在优化算法量子动力学模型下得到的具有代表性和普遍意义的优化算法的基本迭代过程，差解接受是避免优化算法陷入局部最优、解决算法早熟问题的一种重要机制。为了在QDF中引入差解接受机制，以量子动力学模型为基础将差解视为粒子运动过程中遇到的势垒，利用量子隧道效应中的透射系数计算粒子穿透该势垒的概率，从而得到量子动力学模型下的差解接受准则：势垒估计准则（PBEC）。PBEC与势垒高度和宽度、粒子的质量均有关系，比经典的Metropolis接受准则更能全面地估计优化算法采样时遇到差解时的行为。实验结果表明，基于PBEC的QDF算法相较于基于Metropolis接受准则的QDF算法，在求解函数过程中算法跳出局部最优的能力更强、搜索效率更高，表明PBEC在量子优化算法中是一种可行且有效的差解接受机制。

关键词: 优化算法, 差解接受机制, 透射系数, 势垒估计准则, Metropolis接受准则

CLC Number:

TP301.6

Yaqin CHEN, Peng WANG. Potential barrier estimation criterion based on quantum dynamics framework of optimization algorithm[J]. Journal of Computer Applications, 2024, 44(4): 1180-1186.

陈雅琴, 王鹏. 基于优化算法量子动力学框架的势垒估计准则[J]. 《计算机应用》唯一官方网站, 2024, 44(4): 1180-1186.

Figures/Tables 10

Fig. 1 Schematic diagram of barrier tunneling process of particles

Tab. 1 Names， expressions， and definition domains of four test functions

函数名	类型	表达式	定义域
Ackley	多峰	$f 1 = - 20 e x p - 0.2 1 d ∑ i = 1 d x i 2 - e x p 1 d ∑ i = 1 d c o s (2 π x i) + 20 + e$	$- 32.77,32.77$
Griewank	多峰	$f 2 = 1 4 000 ∑ i = 1 d x i 2 - ∏ i = 1 d c o s x i / i + 1$	$- 100,100$
Lévy	多峰	$f 3 = s i n 2 (π ω 1) + ∑ i = 1 d - 1 (ω i - 1) 2 [1 + 10 s i n 2 (π ω i + 1)] + (ω d - 1) 2 [1 + s i n 2 (2 π ω d)]$	$- 10,10$
Sphere	单峰	$f 4 = ∑ i = 1 d x i 2$	$- 5.12,5.12$

Tab. 1 Names， expressions， and definition domains of four test functions

函数名	类型	表达式	定义域
Ackley	多峰	$f 1 = - 20 e x p - 0.2 1 d ∑ i = 1 d x i 2 - e x p 1 d ∑ i = 1 d c o s (2 π x i) + 20 + e$	$- 32.77,32.77$
Griewank	多峰	$f 2 = 1 4 000 ∑ i = 1 d x i 2 - ∏ i = 1 d c o s x i / i + 1$	$- 100,100$
Lévy	多峰	$f 3 = s i n 2 (π ω 1) + ∑ i = 1 d - 1 (ω i - 1) 2 [1 + 10 s i n 2 (π ω i + 1)] + (ω d - 1) 2 [1 + s i n 2 (2 π ω d)]$	$- 10,10$
Sphere	单峰	$f 4 = ∑ i = 1 d x i 2$	$- 5.12,5.12$

Fig. 2 Convergence curves of function value based on two acceptance criteria and differential acceptance probability curve of PBEC for f1

Fig. 3 Convergence curves of function value based on two acceptance criteria and differential acceptance probability curve of PBEC for f2

Fig. 4 Convergence curves of function value based on two acceptance criteria and differential acceptance probability curve of PBEC for f3

Fig. 5 Convergence curves of function value based on two acceptance criteria and differential acceptance probability curve of PBEC for f4

Fig. 6 Function optimal solution and search time of f1 varying with dimension

Fig. 7 Function optimal solution and search time of f2 varying with dimension

Fig. 8 Function optimal solution and search time of f3 varying with dimension

Fig. 9 Function optimal solution and search time of f4 varying with dimension

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Potential barrier estimation criterion based on quantum dynamics framework of optimization algorithm

基于优化算法量子动力学框架的势垒估计准则

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