# A Novel Binary QUasi-Affine TRansformation Evolutionary (QUATRE) Algorithm
## 1 Introduction
A binary version of the CS was proposed by [PERSON] by [PERSON] [52]. In Reference [53] a hyper learning binary Dragonfly Algorithm (DA) was designed for coronavirus disease 2019 (COVID-19). In Reference [54], an improved binary GWO was discussed and used for feature selection by [PERSON] A optimized binary BA was presented and applied for classification of white blood cells by [PERSON] [55]. The GSA was converted into binary form based on mutual information by [PERSON] [56] for intrusion detection systems. Almost all excellent meta-heuristic algorithms have variants of the binary version. However, QUATRE was designed for solving continuous optimization problems and no one has yet turned it into a binary version. Therefore, we discussed how to change the QUATRE algorithm into binary form in this manuscript for the first time. Remote sensing is an important technology, which is widely used in the military and by civilians [57; 58]. On the military side, sensing technology is widely used in military reconnaissance, missile early warning, military surveying and mapping, marine surveillance, and meteorological observation. On the civil side, remote sensing technology is widely used in earth resources survey, vegetation classification, crop pests, crop diseases and crop yield surveys, environmental pollution monitoring, marine development, and earthquake monitoring. At present, high resolution remote sensing has become the mainstream of remote sensing [59]. Hyperspectral remote sensing is an important aspect of high resolution remote sensing. It is a technique to obtain approximately continuous spectral data by imaging spectrometer within the range of visible, near-infrared, mid-infrared and thermal infrared bands of electromagnetic spectrum. Hyperspectral remote sensing can obtain hundreds of spectral bands at the same time, and the wavelength range of each spectral band is only about 10 nm. This many bands can provide extremely rich spectral information for ground object information extraction, so hyperspectral images are often used for fine object classification. Nevertheless, the phenomenon of \"Hughes\" is also introduced into many dimensions [60; 61], that is, with a certain number of samples, the classification accuracy increases first and then decreases with the increase in data dimension. Hughes phenomenon has seriously affected the application and popularization of hyperspectral remote sensing technology. Therefore, dimensionality reduction is often needed before a fine classification. The main contributions of this paper are concluded as follows:  
1. Two approaches are presented to convert QUATRE to binary version and four families of transfer functions are used by the two approaches, respectively. 2. The search space of the proposed binary QUATRE is analyzed, then new transfer functions are introduced. 3. A new scaling factor is proposed in order to balance exploration and exploitation. 4. The proposed algorithm is performed on 23 benchmark functions and HSI. 5. A new fitness function for dimensionality reduction of HSI is proposed. The rest of the paper is organized as follows. Section 2 describes related works include QUATRE and transfer functions. Section 3 describes the proposed two binary QUATRE approaches. Section 4 is experimental results and analysis on benchmark test functions and HSI. Section 5 depicts the main work of the paper and gives some suggestions for further work.