Non-convex chance-constrained optimization for blending recipe design under uncertainties

Abstract

A global optimization algorithm is proposed to design blending recipes for gasoline production with nonlinear mixing law and parameter uncertainty. Important fuels, such as gasoline, are produced by mixing several intermediate feedstocks in such a way that all quality specifications are met, and total profit is maximized. Conventional blending design approaches that rely on linear models and deterministic optimization may generate a suboptimal or infeasible solution due to model inaccuracy and failure to account for parameter uncertainty. The proposed work designs the blending recipe subject to chance constraints with normally distributed uncertain parameters and nonlinear mixing rule. The resulting non-convex joint chance-constrained program is solved to a near-global optimum through second-order cone relaxation, branch-and-bound, optimality-based bound tightening, and reformulate-linearization techniques. A case study involving nine feedstocks and two grades of gasoline is presented to demonstrate the effectiveness of the proposed method.