(577d) Novel Method for Global Optimization of Nonconvex Minlp Problems

Most of chemical engineering problems rely on the use of non-linear models, which are frequently non-convex. Global optimization methods are desired, especially because they are able to generate lower bounds that allow us to know how far we are from the global optimum solution. Although in some cases there is no strict need of finding the global optimum solution (gap zero), it is very important to have at least an idea of how much better a solution could be. Another important advantage of global optimization methods is that initial starting points for the problem are not required.

We present two global optimization methods. One of them relies on the discretization of a critical function, which is part of a non-linear non-convex constraints (or a variable for bilinear cases). This method requires the use of binary variables that increase in number as the model increases. In a second approach, the critical function is strategically rewritten as parameters and a set of equations based on lower and upper values of the function values, which replaces the non-convex non-linear constraints to generate lower bounds.

In both cases the lower bound model is also used to eliminate portions of the intervals of different variables when it is identified that these cannot be part of the global optimum solution. Based on this ability, an elimination procedure is built. The advantages of both methods will be discussed and examples will be presented to show and compare the efficiency of the methods.