scenario-based hybrid robust-stochastic programming for coordinated scheduling of electricity & natural gas supply systems

Stochastic and robust optimizations have been considered as two different views of stochastic problems. while robust optimization takes optimization in the worst case, stochastic optimization regards no conservative view and merely focuses on expected value. however, a unilateral view of stochastic problems does not apply to most real problems. in this article, a hybrid robust and stochastic approach is proposed for optimization problems under uncertainty. our major contribution is presenting different conservative levels in solving an optimization problem using a hybrid robust and stochastic optimization approach. to this end, we cluster uncertain parameters into different clusters using latin hypercube sampling and k-means clustering tools; having established various numbers of clusters of uncertain parameters, different clustering criteria and a multi-criteria decision making (mcdm) tool is employed to determine the optimal number of clusters of uncertain parameters. then, a hybrid energy optimization model under uncertainty is applied to coordinate the scheduling of natural gas-fired electricity generation units and gas supply units (gas refinery) under natural gas and electricity demand uncertainty, with known probability distribution and uncertain parameters having different levels of conservatism. the results indicate that while no special trend is evident in the execution time as the number of clusters increases, the optimal value is decreased.