Low Dimensional Simplex Evolution--A Hybrid Heuristic for Global Optimization

In this paper, a new real-coded evolutionary algorithm - low dimensional simplex evolution (LDSE) for global optimization is proposed. It is a hybridization of two well known heuristics, the differential evolution (DE) and the Nelder-Mead method. LDSE takes the idea of DE to randomly select parents from the population and perform some operations with them to generate new individuals. Instead of using the evolutionary operators of DE such as mutation and cross-over, we introduce operators based on the simplex method, which makes the algorithm more systematic and parameter-free. The proposed algorithm is very easy to implement, and its efficiency has been studied on an extensive testbed of 50 test problems from M.M. Ali et al. Numerical results show that the new algorithm outperforms DE in terms of number of function evaluations (nfe) and percentage of success (ps).