For shortcomings of poor exploaration and parameter complexities of the butterfly optimization algorithm, an improved butterfly optimization algorithm based the self-adaption method (SABOA) was proposed to extremely enhance the searching accuracy and the iteration capability. SABOA has advantages of having fewer parameters, the simple algorithm structure, and the strong precision. First, a new fragrance coefficient was added to the basic butterfly optimization algorithm. Then, new iteration and updating strategies were introduced in global searching and local searching phases. Finally, this paper tested different optimization problems including low-high functions and constrained problems, and the obtained results were compared with other well-known algorithms, this paper also drew various mathematical statistics figures to comprehensively analyze searching performances of the proposed algorithms. The experimental results show that SABOA can get less number of function evaluations compared to other considered algorithms, which illustrates that SABOA has great searching balance, large exploration, and high iterative speed. INDEX TERMS Butterfly optimization algorithm, global optimization, constrained problem. I. INTRODUCTION In applied mathematics and engineering fields, there are numerous optimization problems whose calculated solutions are in a large and complex searching space. Traditional optimization methods, including the steepest descent method, the conjugate gradient method, the variable scale method, and Newton method, can only deal with objective functions that are simple, continuously differentiable, and high order differentiable [1]-[3]. With the increasing of problem diversities and problem complexities, traditional optimization methods can not meet different requirements of higher calculation speed and lower average percentage error, so it is crucial to find for new optimization methods that have fast calculation speed and perfect convergence abilities [4], [5]. With the development of artificial intelligence, digitization, and computer technologies, numerous meta-heuristic optimization algorithms have been increasingly proposed and applied in science and engineering fields [6]-[8]. Meta-heuristic algorithms own characteristics of selforganizing, mutual compatibility, simplicity, parallelism, wholeness and harmony. Meta-heuristic algorithms work The associate editor coordinating the review of this manuscript and approving it for publication was Jagdish Chand Bansal.