Uncertain random geometric programming problems
Tapas Mondal, Akshay Kumar Ojha, Sabyasachi Pani
TLDR
This paper develops a novel framework to handle geometric programming problems with coefficients modeled as linear-normal uncertain random variables by transforming them into deterministic equivalents.
Key contributions
- Introduces the concept of linear-normal uncertain random variables to model combined uncertainty and randomness in coefficients.
- Proposes three transformation criteria—optimistic, pessimistic, and expected value—to convert uncertain random variables into random variables.
- Derives an equivalent deterministic formulation of the transformed stochastic geometric programming problem for practical optimization.
Why it matters
By bridging uncertain and random variables within geometric programming, this work enables more realistic modeling of uncertainty in optimization problems and provides practical deterministic formulations that facilitate solution methods, thereby advancing robust decision-making in engineering and applied sciences.
Original 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.
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