# A Novel Binary QUasi-Affine TRansformation Evolutionary (QUATRE) Algorithm
## 1 Introduction  
The optimization problem refers to determine the value of decision variables under special constraints so that the objective functions can reach the optimal values. Traditional methods to solve the optimization problems include simplex method, steepest descent method, trust region method, penalty function method, etc. However, traditional optimization algorithms usually need to satisfy some specific conditions. For example, some algorithms require that the objective function must be continuous or differentiable, some require the problem to be solved is a convex optimization problem, and others require the constraint conditions to meet linear conditions. However, it is sometimes difficult to satisfy these conditions in practical applications. Therefore, in the 1940s, heuristic algorithms emerged, which constructed a model highly similar to the problem to be solved based on intuition or experience, and gave a feasible solution to the optimization problem at an acceptable cost. Furthermore, the deviation degree from the obtained feasible solution to the optimal solution could not be predicted. Heuristic algorithms reduce computational complexity at the expense of computational accuracy. In the 1960s, under the inspiration of bionics, meta-heuristic algorithms appeared, which obtained inspiration from random phenomena in nature. Meta-heuristic algorithms combined random algorithms with localalgorithms in order to jump out of the local optimal solution with a probability. Meta-heuristic algorithms have become one of the hottest spots in the optimization problems, for there is not any special condition that constrains the objective functions, whereas satisfactory solutions can often be obtained. According to the mechanisms to be based on, meta-heuristic algorithms can be coarsely divided into two categories: one is inspired by biological processes, and the other is inspired by physical or mathematical models. Among them, meta-heuristic algorithms inspired by biological processes can be finely separated into swarm intelligence algorithms, which are based on animal social behaviors, and evolutionary algorithms, which are based on the theory of evolution. In the meta-heuristic algorithms inspired by physical or mathematical models, Simulated Annealing (SA) [1; 2; 3] was inspired by the internal molecular state and internal energy of solids in the process of changing from high temperature to low temperature. It is easy to compute but is hard to converge; Gravitational Search Algorithm (GSA) [4; 5; 6] was proposed based on Newtonian gravity and the laws of motion, and it has strong exploitation ability but weak exploration ability; Sine Cosine Algorithm (SCA) [7; 8; 9] created multiple initial random candidate solutions and then used a mathematical model based on sine and cosine functions to make these solutions fluctuate in the direction of the optimal solution or in the opposite direction. In Swarm intelligence algorithms, Particle Swarm Optimization (PSO) [10; 11; 12; 13] simulated the foraging behaviour of birds to obtain the optimal solution. In particular, it was the first swarm intelligence algorithm; Ant Colony Optimization (ACO) [14; 15; 16] was inspired by the foraging behavior of ant colony. The parameter setting of ACO is complicated. If the parameter setting is improper, it is easy to deviate from the high-quality solution; Cat Swarm Optimization (CSO) [17; 18] mimicked cats hunting behaviour to obtain the optimal solution; Bat Algorithm (BA) [19; 20; 21] was proposed based on the echolocation behavior of bats; Pigeon Inspired Optimization (PIO) [22; 23] was designed by mimicking the homing behavior of the pigeon.