A Raindrop Algorithm for Searching The Global Optimal Solution in Non-linear Programming

TL;DR

This paper introduces a raindrop algorithm based on a random walk model for efficiently finding global solutions in complex non-linear programming problems without derivative information.

Contribution

It presents a novel derivative-free optimization method and demonstrates its effectiveness on irregular non-linear problems with few iterations.

Findings

Successfully finds global optima in highly irregular functions

Does not require derivative information

Converges with a small number of iterations

Abstract

In this paper, we apply the random walk model in designing a raindrop algorithm to find the global optimal solution of a non-linear programming problem. The raindrop algorithm does not require the information of the first or second order derivatives of the object function. Hence it is a direct method. We investigate the properties of raindrop algorithm. Besides, we apply the raindrop algorithm to solve a non-linear optimization problem, where the object function is highly irregular (neither convex nor concave). And the global optimal solution can be found with small number of iterations.