An MILP-MINLP decomposition method for the global optimization of a source based model of the multiperiod blending problem

• The multiperiod blending problem gives rise to a nonconvex MINLP model.
• An alternative formulation is proposed to improve its relaxation.
• A two-level decomposition algorithm is proposed for global optimization.
• Computational results show significant improvements over general purpose solvers.

The multiperiod blending problem involves binary variables and bilinear terms, yielding a nonconvex MINLP. In this work we present two major contributions for the global solution of the problem. The first one is an alternative formulation of the problem. This formulation makes use of redundant constraints that improve the MILP relaxation of the MINLP. The second contribution is an algorithm that decomposes the MINLP model into two levels. The first level, or master problem, is an MILP relaxation of the original MINLP. The second level, or subproblem, is a smaller MINLP in which some of the binary variables of the original problem are fixed. The results show that the new formulation can be solved faster than alternative models, and that the decomposition method can solve the problems faster than state of the art general purpose solvers.