An efficient uncertain chance constrained geometric programming model based on value-at-risk for truss structure optimization problems

Uncertain geometric programming is a type of geometric programming involving uncertain variables. As described in the literature, the uncertain geometric programming model based on expected value cannot reflect the risk preference of decision-makers. It motivates us to establish an uncertain geometric programming model based on value-at-risk to describe the risk level that managers can tolerate. Firstly, we propose the uncertain geometric programming model based on value-at-risk. Then, according to the operational law in uncertainty theory, this model is transformed into a crisp and equivalent form. Three numerical examples are used to verify the model's efficacy, and the paper emphasizes the influence of confidence level in the objective function and the constraints. In addition, the paper discusses the expected value model under an uncertain environment and presents the difference between expected value and value-at-risk. Finally, we apply the model to the problem of a two-bar truss, and the optimal solution can be obtained within the risk level that the structural designer can accept.