Uncertain random geometric programming problems

TL;DR

This paper introduces a new deterministic framework for uncertain random geometric programming problems using linear-normal uncertain random variables and transformation techniques.

Contribution

It develops novel transformation methods to convert uncertain random variables into manageable forms, enabling deterministic solutions for complex geometric programming problems.

Findings

Transformation techniques successfully convert uncertain random variables to stochastic variables.

The deterministic representation simplifies solving uncertain random geometric programming problems.

Numerical example demonstrates the practical effectiveness of the proposed methods.

Abstract

In this paper, we introduce a deterministic formulation for the geometric programming problem, wherein the coefficients are represented as independent linear-normal uncertain random variables. To address the challenges posed by this combination of uncertainty and randomness, we introduce the concept of an uncertain random variable and present a novel framework known as the linear-normal uncertain random variable. Our main focus in this work is the development of three distinct transformation techniques: the optimistic value criteria, pessimistic value criteria, and expected value criteria. These approaches allow us to convert a linear-normal uncertain random variable into a more manageable random variable. This transition facilitates the transformation from an uncertain random geometric programming problem to a stochastic geometric programming problem. Furthermore, we provide insights into an equivalent deterministic representation of the transformed geometric programming problem, enhancing the clarity and practicality of the optimization process. To demonstrate the effectiveness of our proposed approach, we present a numerical example.