*Article* **Success History-Based Adaptive Di**ff**erential Evolution Using Turning-Based Mutation**

#### **Xingping Sun, Linsheng Jiang, Yong Shen \*, Hongwei Kang \* and Qingyi Chen**

School of Software, Yunnan University, Kunming 650000, China; sunxp@ynu.edu.cn (X.S.); jls@mail.ynu.edu.cn (L.J.); devas9@ynu.edu.cn (Q.C.)

**\*** Correspondence: sheny@ynu.edu.cn (Y.S.); hwkang@ynu.edu.cn (H.K.)

Received: 24 August 2020; Accepted: 7 September 2020; Published: 11 September 2020

**Abstract:** Single objective optimization algorithms are the foundation of establishing more complex methods, like constrained optimization, niching andmulti-objective algorithms. Therefore, improvements to single objective optimization algorithms are important because they can impact other domains as well. This paper proposes a method using turning-based mutation that is aimed to solve the problem of premature convergence of algorithms based on SHADE (Success-History based Adaptive Differential Evolution) in high dimensional search space. The proposed method is tested on the Single Objective Bound Constrained Numerical Optimization (CEC2020) benchmark sets in 5, 10, 15, and 20 dimensions for all SHADE, L-SHADE, and jSO algorithms. The effectiveness of the method is verified by population diversity measure and population clustering analysis. In addition, the new versions (Tb-SHADE, TbL-SHADE and Tb-jSO) using the proposed turning-based mutation ge<sup>t</sup> apparently better optimization results than the original algorithms (SHADE, L-SHADE, and jSO) as well as the advanced DISH and the jDE100 algorithms in 10, 15, and 20 dimensional functions, but only have advantages compared with the advanced j2020 algorithm in 5 dimensional functions.

**Keywords:** single objective optimization; differential evolution; success-history; premature convergence; turning-based mutation
