A Hybrid STA Based on Nelder–Mead Simplex Search and Quadratic Interpolation

Abstract

State transition algorithm (STA) is a metaheuristic method for global optimization. However, due to the insufficient utilization of historical information, it still suffers from slow convergence speed and low solution accuracy on specific problems in the later stages. This paper proposes a hybrid STA based on Nelder–Mead (NM) simplex search and quadratic interpolation (QI). In the exploration stage, NM simplex search utilizes the historical information of STA to generate promising solutions. In the exploitation stage, QI utilizes the historical information to enhance the local search capacity. The proposed method uses an eagle strategy to maximize the efficiency and stability. The proposed method successfully combines the merits of the three distinct approaches: the powerful exploration capacity of STA, the fast convergence speed of NM simplex search and the strong exploitation capacity of QI. The hybrid STA is evaluated using 15 benchmark functions with dimensions of 20, 30, 50 and 100. Moreover, the results are statistically analyzed using the Wilcoxon signed-rank sum test. In addition, the applicability of the hybrid STA to solve real-world problems is assessed using the wireless sensor network localization problem. Compared with six state-of-the-art metaheuristic methods, the experimental results demonstrate the superiority and effectiveness of the proposed method.