We propose a method for accelerating chaotic evolution (CE) search using the triple and quadruple comparison mechanisms. We utilize some performance measurements to analyse and verify our proposed algorithm with benchmark functions. The CE is one of evolutionary computation (EC) algorithms that fuses the iteration of evolution and the ergodicity of a chaos system for optimization. We apply the opposition-based learning (OBL) mechanism to CE algorithm to obtain opposite vectors in its search process. Besides the target vectors and chaotic vectors in the conventional CE algorithm, the opposite vectors are also examined during determining the offspring individual for the next generation. Generally, one of drawbacks for the conventional EC algorithm is that premature convergence towards a local optimum instead of a global optimum. The advantage of our proposed algorithm is that it has a higher possibility to avoid being trapped in a premature convergence so that it can reduce a lot of unnecessary computational costs. We also evaluate these algorithms using 12 benchmark functions and some performance measurements. The experiments found that applying OBL mechanism to the CE algorithm can obtain a better optimization performance than the conventional one, especially in the high dimensional optimization tasks.