# A Novel Binary QUasi-Affine TRansformation Evolutionary (QUATRE) Algorithm
## 1 Introduction
It requires very few adjustment parameters and is easy to implement; Symbiotic Organism Search (SOS) [24; 25] imitated the interactive population relationship between different organisms in nature to enhance their adaptability to the environment, so as to improve the survival ability of the population; Grey Wolf Optimizer (GWO) [26; 27] simulated the hierarchy and predation behavior of wolves. However, it is easy to fall into local extremum and hard to converge; Cuckoo Search (CS) [28; 29; 30; 31] mimicked brood parasitism of cuckoo and it has a strong exploration ability; Monkey King Evolutionary (MKE) [32; 33] Algorithm was inspired by the action of the [PERSON], a character of a famous Chinese mythological novel, named Journey to the West. In evolutionary algorithms, Genetic Algorithm (GA) [34; 35; 36; 37] was proposed based on the theory of natural selection and the principle of genetics, and the optimal solution was obtained by mutation, crossover and selection; DE [38; 39; 40; 41] was proposed to improve GA. The difference was that DE generated the mutation vector by the difference vector of the parent generation, and performed crossover with the individual vector of the parent generation to generate the new individual vector. In particular, QUATRE was proposed by [PERSON], [PERSON] [42] to improve the drawback of DE that did not achieve equilibrium search in search space without prior knowledge. QUATRE generalized the crossover operation of DE from vector to matrix. Therefore, DE can be regarded as a special case of QUATRE. Subsequently, a series of algorithms based on QUATRE was proposed due to the good performance of QUATRE. The relations between QUATRE and other meta-heuristic algorithms are discussed by [PERSON] [PERSON] [43], including PSO variants and DE variants and a framework of gesture recognition was proposed based on QUATRE also by [PERSON] [PERSON] [44]. A compact QUATRE algorithm that used a pairwise competition mechanism to enhance the performance of QUATRE was proposed [45] and an enhanced mutation strategy with time stamp mechanism for the QUATRE algorithm was shown by [PERSON] [PERSON] and [PERSON] [46]. The reason why the exploration bias still exists in the binomial crossover was discussed [47]; then, a novel QUATRE structure with some novel standards and adaptation schemes was proposed. In addition, a novel bi-population QUasi-Affine TRansformation Evolution algorithm (BP-QUATRE) algorithm was proposed, which divided the populations into two subpopulations with different sorting and mutation strategies in each subpopulation [48] and a multi-group multi-choice communication strategy was proposed to solve the disadvantage that the original QUATRE was always easy to fall into local optimization and apply the proposed algorithm in wireless sensor network node localization [49]. A novel algorithm that combined QUATRE with PIO was proposed to avoid falling into local optimum by [PERSON] [50]. Practical optimization problems are various, some are high dimensional, some are many-objective optimization problems and others require minimal memory. Consequently, many excellent algorithms were proposed to apply the meta-heuristic algorithms for solving practical problems. Furthermore, a new surrogate-assisted model on PSO to deal with the high dimensional problem is used [12]; [PERSON]. [PERSON] et al. proposed a modified PSO based on a decomposition framework with different ideal points on each reference vector to solve many-objective optimization problems [13]; [PERSON]. [PERSON] et al. developed a compact scheme on CSO to effectively save the memory of the unmanned robot [30]. There are some other practical problems that are binary optimization problems, such as feature extraction and 0-1 knapsack problems, but most meta-heuristic algorithms are designed for a continuous search space. Therefore, it is essential to convert meta-heuristic algorithms in a binary version. The continuous PSO was converted into binary version for the first time by [PERSON], [PERSON] [51].