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Optimization problems exists extensively in real life, especially in science and engineering. Over the past decades, various optimization techniques have been developed to solve complex optimization problems in different areas especially that are unable to be solved by traditional methods. QUasi-Affine TRansformation Evolutionary (QUATRE) algorithm is a new novel evolution structure for global optimization, which is a swarm based algorithm and use quasi-affine transformation approach for evolution. Nevertheless, there are still some weaknesses in these QUATRE variants. This paper presents a novel E-QUATRE algorithm in which an automatically generated evolution matrix with self-adaptive mechanism and an adaptive control parameter F are proposed for the enhancement of the QUATRE algorithm. Moreover, this paper also discusses the relationship between QUATRE algorithm, Particle Swarm Optimization (PSO) and Differential Evolution (DE) algorithm, all of which are also famous swarm based Stochastic Algorithms (SAs). Algorithm validation is conducted under CEC2013 test suite on single-objective numerical optimization, and E-QUATRE algorithm is compared with several famous Particle Swarm Optimization (PSO) variants, Differential Evolution (DE) variants and QUATRE variants. The experiment results indicate that the proposed E-QUATRE algorithm has a better performance than these swarm based algorithms with fixed population. [ABSTRACT FROM AUTHOR]