This paper proposes a new population-based simplex method for continuous function optimization. The proposed method, called Adaptive Population-based Simplex (APS), is inspired by the Low-Dimensional Simplex Evolution (LDSE) method. LDSE is a recent optimization method, which uses the reflection and contraction steps of the Nelder-Mead Simplex method. Like LDSE, APS uses a population from which different simplexes are selected. In addition, a local search is performed using a hyper-sphere generated around the best individual in a simplex. APS is a tuning-free approach, it is easy to code and easy to understand. APS is compared with five state-of-the-art approaches on 23 functions where five of them are quasi-real-world problems. The experimental results show that APS generally performs better than the other methods on the test functions. In addition, a scalability study has been conducted and the results show that APS can work well with relatively high-dimensional problems.
Some modifications of low-dimensional simplex evolution and their convergence