Random derivative-free algorithm for solving unconstrained or bound constrained continuously differentiable non-linear problems

Abstract

Derivative-free optimization is an area of long history which has so many applications in different fields. It has lately received considerable attention within the engineering community. This paper describes a random derivative-free algorithm for solving unconstrained or bound constrained continuously differentiable non-linear problems. This method is a combination of particle swarm and directional direct search algorithms. The key difference in direct search methods is in the way of generating positive bases. At first glance, a simple way of generating positive bases has been introduced for solving continuously differentiable problems. Then, it has been shown that using the particle swarm algorithm with a direct search algorithm can solve non-linear optimization problems efficiently. Some standard examples have been presented to demonstrate the ability and effectiveness of this approach.