Page 48 - Sustainability in the process industry

Pro c ess O p timization 25

and then finally implementing the model computationally. In the
course of formulating the mathematical and implementation
components, it may be necessary to make some corrections to the
conceptual and/or mathematical components.

3.3 Optimization: Definition and Mathematical
Formulation

3.3.1 What Is Optimization?
Optimization can be applied to different tasks: new system design,
the synthesis of a new processing network, and the retrofit design
and operational improvements in heat exchanger, reactor, and
separation networks. Optimization is employed to find the best
available option. An objective function consists of a performance
criterion to be maximized or minimized. The system properties that
determine this function are of two types:
1. Parameters—a set of characteristics that do not vary with
respect to the choice to be made
2. Variables—a set of characteristics that are allowed to vary

Some of the variables are specified by the decision maker or are
manipulated by the optimization tools; these are referred to as
specifications or decision variables. The remaining variables are termed
dependent variables, and their values are determined by the
specifications and the system’s internal relationships. The objective
function can be formulated in terms of a single variable or a
combination of dependent and decision variables. The value of the
objective function can be changed by manipulating the decision
variables.

3.3.2 Mathematical Formulation of Optimization Problems
Optimization tasks in industry include increasing heat recovery,
maximizing the efficiency of site utility systems, minimizing water
use and wastewater discharge, and other tasks. The formulations
that are used to solve such optimization problems are known as
mixed integer nonlinear programs (MINLPs). However, they are
frequently linearized to yield the more tractable mixed integer linear
programs (MILPs), and some can be further simplified and solved
via linear programming (LPR). In general, optimization problems
can be formulated as summarized in Table 3.1.
The continuous and discrete domains, together with the
constraints, define the feasible region for the optimization. This
region contains the set of options from which to choose. The value of
the function F depends on the values of the decision variables.