Research on the Utilization of Mean Value Information in Optimization Algorithm

doi:10.12068/j.issn.1005-3026.2024.01.007

Abstract

Abstract:

The strategy of population migration towards the mean point in heuristic optimization algorithms is investigated， and the strategy is found that it has significant impact on the algorithm’s performance and has both physical and mathematical implications. By using the maximum likelihood estimation method， the parameters of the ground state wave function are estimated， and the connection between the probability density function of the optimal solution when the quantum system reaches the ground state and the population mean point is established. The physical significance of the population mean point is explained from a dynamic perspective. The operations that utilize the information of the mean point’s position is added to several classical optimization algorithms and a comparative experiment is carried out on the CEC2013 test set and the engineering application of camera layout optimization. Experimental results show that reasonable use of the mean point position information can effectively improve the performance of the algorithm.

Key words: quantum dynamics, optimization problems, mean-value information, kinetic equation, maximum likelihood estimation

CLC Number:

TP 183

Fang WANG, Peng WANG, Yu-wei JIAO. Research on the Utilization of Mean Value Information in Optimization Algorithm[J]. Journal of Northeastern University(Natural Science), 2024, 45(1): 49-57.

Figures/Tables 6

Fig. 1 Convergence process of the approximate

Fig. 2 Average error and the minimum error

Fig. 3 Average error and the minimum error

Fig. 4 Results of the Wilcoxon signed‐rank test for 51 replicate experiments

Fig. 5 Evolution of the wave function

Table 1 Maximum coverage of different algorithms in 51 repeated experiments

摄像机数量	8	9	10	11	12	13	14	15
PSO	65.99	73.98	80.44	84.61	88.52	92.18	93.71	95.15
PSO-mean	65.99	74.23	81.21	86.05	89.71	91.84	94.13	95.92

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