A Simple Novel Global Optimization Algorithm and Its Performance on Some Benchmark Functions

TL;DR

This paper introduces a simple, derivative-free global optimization framework called optimization by cut, which efficiently finds global minima of black-box functions through iterative region reduction, demonstrated on benchmark functions.

Contribution

The paper presents a novel, simple global optimization algorithm that does not require derivatives and effectively finds minima on benchmark functions.

Findings

Efficiently finds global minima in benchmark tests.

Does not require derivative information or special structure.

Operates effectively on black-box functions.

Abstract

This paper propose a new frame work for finding global minima which we call optimization by cut. In each iteration, it takes some samples from the feasible region and evaluates the objective function at these points. Based on the observations it cuts off from the feasible region a subregion that is unlikely to contain a global minimum. The procedure is then repeated with the feasible region replaced by the remaining region until the remaining region is ``small'' enough. If a global minimum is kept in the remaining region of each iteration, then it can be located with an arbitrary precision. The frame work is surprisingly efficient in view of its simple form and can be applied to black-box functions since neither special structure nor derivative information is required. The performance of the proposed frame work is evaluated on some benchmark functions and the results show that it can find a global minimum rather quickly.