Multistage adaptive optimization using hybrid scenario and decision rule formulation

Scenario-based stochastic programming and linear decision rule (LDR)-based robust optimization are prevalent methods for solving multistage adaptive optimization (MSAP) problems. In practical applications such as capacity expansion planning of chemical processes, often multiple sources of uncertainty affect the problem which introduces challenges to traditional stochastic optimization methods. While a large number of uncertain parameters exist in the problem, using scenario-based method results in very large problem size and the solution becomes computationally expensive. In addition, when the constraints include multiplication of uncertain parameters and adaptive variables, the constraints are not linear with respect to uncertain parameters when the LDR method is used. In order to address these challenges, we propose two different hybrid methods where scenario and decision rule methods are combined to solve the MSAP problem. The article demonstrates the computational performance of the proposed hybrid methods using two chemical process planning examples.