Solving Geometric Programming Problems with Normal, Linear and Zigzag Uncertainty Distributions
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- Khanjani Shiraz, R., Tavana, M., Di Caprio, D. et al. J Optim Theory Appl (2016) 170: 243. doi:10.1007/s10957-015-0857-y
Geometric programming is a powerful optimization technique widely used for solving a variety of nonlinear optimization problems and engineering problems. Conventional geometric programming models assume deterministic and precise parameters. However, the values observed for the parameters in real-world geometric programming problems often are imprecise and vague. We use geometric programming within an uncertainty-based framework proposing a chance-constrained geometric programming model whose coefficients are uncertain variables. We assume the uncertain variables to have normal, linear and zigzag uncertainty distributions and show that the corresponding uncertain chance-constrained geometric programming problems can be transformed into conventional geometric programming problems to calculate the objective values. The efficacy of the procedures and algorithms is demonstrated through numerical examples.