Surrogate functions are often employed to reduce the number of objective function evaluations in a continuous optimization. However, their effects have seldom been investigated theoretically. This paper analyzes effect surrogate information-geometric optimization (IGO) framework, which includes as an algorithm instance variant covariance matrix adaptation evolution strategy—a widely used solver...

This paper begins with a geometric statement of constraint optimization problems, which include both equality and inequality-type restrictions. The cost to optimize is curvilinear functional defined by given differential one-form, while the optimal state be determined curve connecting two points, among all curves satisfying some primal feasibility conditions. resulting outcome an invariant Frit...

Geometric branch-and-bound methods are popular solution algorithms in deterministic global optimization to solve problems in small dimensions. The aim of this paper is to formulate a geometric branch-and-bound method for constrained global optimization problems which allows the use of arbitrary bounding operations. In particular, our main goal is to prove the convergence of the suggested method...

Geometric programming problem is a powerful tool for solving some special type non-linear programming problems. It has a wide range of applications in optimization and engineering for solving some complex optimization problems. Many applications of geometric programming are on engineering design problems where parameters are estimated using geometric programming. When the parameters in the prob...

An efficient method for scattering Genetic Algorithm (GA) individuals in the design space is proposed to accelerate airfoil shape optimization. The method used here is based on the variation of the mutation rate for each gene of the chromosomes by taking feedback from the current population. An adaptive method for airfoil shape parameterization is also applied and its impact on the optimum desi...