A Hybrid Simplex Search for Global Optimization with Representation Formula and Genetic Algorithm

Abstract

We consider the problem of minimizing a given function \(f:\mathbb {R}^n\longrightarrow \mathbb {R}\) on a regular not empty closed set S. When f attains a global minimum at exactly one point \(x^* \in S\), for a convenient random variable X and a convenient function \(g:\mathbb {R}^2\longrightarrow \mathbb {R}\). In this paper, we propose to use this Representation Formula (RF) to numerically generate an initial population. In order to obtain a more accurate results, the Representation Formula has been coupled with other algorithms: Classical Genetic Algorithm (GA). We obtain a new algorithm called (RFGA), Genetic Algorithm using Nelder Mead algorithm at the mutation stage (GANM). We obtain a new algorithm called (RFGANM), Nelder Mead Algorithm. We obtain a new algorithm called (RFNM).