Geometric Programming Problems with Triangular and Trapezoidal Two-fold Uncertainty Distributions

TL;DR

This paper extends geometric programming to handle parameters with triangular and trapezoidal two-fold uncertainties, proposing reduction methods and a chance-constrained framework to solve such problems effectively.

Contribution

It introduces a novel approach to model and solve GP problems with complex two-fold uncertainties using reduction techniques and chance constraints.

Findings

Reduction methods effectively convert two-fold uncertainties into single-fold.

The chance-constrained framework successfully solves uncertain GP problems.

Numerical example demonstrates the practicality of the proposed methods.

Abstract

Geometric programming (GP) is a well-known optimization tool for dealing with a wide range of nonlinear optimization and engineering problems. In general, it is assumed that the parameters of a GP problem are deterministic and accurate. However, in the real-world GP problem, the parameters are frequently inaccurate and ambiguous. This paper investigates the GP problem in an uncertain environment, with the coefficients as triangular and trapezoidal two-fold uncertain variables. In this paper, we introduce uncertain measures in a generalized version and focus on more complicated two-fold uncertainties to propose triangular and trapezoidal two-fold uncertain variables within the context of uncertainty theory. We develop three reduction methods to convert triangular and trapezoidal two-fold uncertain variables into single-fold uncertain variables using optimistic, pessimistic, and expected value criteria. Reduction methods are used to convert the GP problem with two-fold uncertainty into the GP problem with single-fold uncertainty. Furthermore, the chance-constrained uncertain-based framework is used to solve the reduced single-fold uncertain GP problem. Finally, a numerical example is provided to demonstrate the effectiveness of the procedures.