Fruit fly optimization algorithm based on a novel fluctuation model and its application in band selection for hyperspectral image

Abstract

Spectral band selection is an important operation in the field of hyperspectral remote sensing. However, most of the techniques cannot satisfy the needs of efficiency and accuracy at the same time. In this paper, we present a novel spectral band selection method, fruit fly optimization algorithm (FOA). As yet, FOA has not been used to solve the problem of band selection in hyperspectral image. Through the study of the algorithm, we know that the advantages of FOA are its simple structure and fewer parameters to be adjusted, but the algorithm itself also has some drawbacks. Thus, we first analyze the shortcomings of the traditional FOA, and the corresponding proofs are given by mathematical method. Then, we separate the whole optimization process into two sub-processes, each of which plays a different role. According to the change of the current iteration information and historical optimum value, a fluctuation model is designed in sub-pro1, and its validity is analyzed and validated theoretically and experimentally. In sub-pro2, a control factor is defined to guide the change rate of the step size. These two sub-processes have their own emphasis, and they cooperate with each other, taking into account the global and local optimization capabilities of the algorithm. The test results on 26 benchmark functions also prove that the proposed algorithm is superior to various state-of-art comparison algorithms. Finally, we introduce the proposed algorithm into the band selection of hyperspectral remote sensing, the gratifying results indicate that the proposed algorithm has great potential in hyperspectral remote sensing field.

Appendix: Sensitivity of the parameter for FMFOA

As described in Sect. 3.2, $\chi$ is used to limit the fluctuation amplitude of the step size in sub-pro1 and to adjust the global exploration capability of the algorithm. $\kappa$ mainly controls the convergence rate in sub-pro2 stage. The two parameters interact with each other and work together to guide the evolution direction of the algorithm. Therefore, we attempt to analyze their effects on the performance of the proposed algorithm. A single-peak function F1 and a multi-peak function F22 are selected to test the difference of the experimental results caused by their different values in the case of $\chi = 2,3,4,5,6,7,8,9,10,11$ and $\kappa = 0.05,0.15,0.25,0.35,0.45,0.55,0.65$, respectively. All experimental settings are the same as those in Sect. 3.2. Tables

Table 8 The results of FMFOA algorithm under different $\chi$ and $\kappa$ for F1

8 and

Table 9 The results of FMFOA algorithm under different $\chi$ and $\kappa$ for F22

9 are the average and the root mean square error values obtained by FMFOA with different values for $\chi$ and $\kappa$.

From the data in the tables, it can be seen that when the value of $\chi$ is too large or too small, it is difficult for the algorithm to achieve the optimal state. This is because the probability of the algorithm falling into local extremum increases as the value of $\chi$ is small, while when the value is large, the algorithm is easy to cross the boundary, which weakens its global control ability. Similar to the case of $\chi$, too large or too small the value of $\kappa$ will lead to a decline in the accuracy of the algorithm, but the reasons for the decline are different. When the value of $\kappa$ is small, the step size of sub-pro2 is too small. If there is another local extremum near the global optimal solution, the algorithm may not converge to the global optimal solution. As the value of $\kappa$ is larger, it will be better understood, since too large step size will inevitably lead to the convergence accuracy of the algorithm at a very low level.

All in all, through the above analysis and experimental results, it can be concluded that when the value of $\chi$ is near 5 and $\kappa$ is near 0.25, the performance of the algorithm reaches the best state. This shows that the global optimization ability and local optimization ability of the algorithm have been effectively balanced.