Page 61 - Sustainability in the Process Industry Integration and Optimization

38 Cha p te r T h r ee

and (5) minimizing the system’s total environmental footprint or the
footprint per unit of product.
It is frequently necessary to optimize more than one criteria.
There are three main approaches to this task (Ehrgott, 2005):

1. Choose one criterion for formulating the objective function;
then add the other criteria as constraints to the problem.
2. Combine all the criteria into one objective function by
summing them up, where each criterion is weighted with a
given coefficient.
3. Perform a multicriteria optimization, accounting explicitly
for the conflicts between the chosen objectives (criteria).

3.10.4 Handling Process Complexity
Process synthesis and process design tasks—when performed on
real-life, industrial-scale problems—tend to involve substantial
number of operating units. Examples can be found in many areas:
• Synthesizing Heat Exchanger Networks involves a large
number of possible combinations of potential heat exchangers.
Thermodynamic and process-related constraints usually
reduce this number, but even then the complexity remains
significant.
• Water subsystem design is no exception, and problems with
20 or more water-using operations are common (Bagajewicz,
2000; Thevendiraraj et al., 2003). This number leads to high
levels of combinatorial complexity. In a superstructure, each
water-using operation (and each intermediate water main)
defines at least one mixer. If the number of water-using
operations is denoted by N , then there can be no fewer than
op
N corresponding binary variables in the network super-
op
structure, and the number of combinations of binary variable
values to be examined by the corresponding MIP solver
would equal 2 . Thus, for 20 operations there would be more
Nop
6
than a million (10 = 1,000,000) possible combinations.
When using MPR superstructure models directly, the number of
binary variables is dictated by the number of the candidate operating
units. In the worst case, the solution algorithm will have to examine
the entire search space, which depends exponentially on the number
of the binary variables. One modeling strategy that reduces the
search space by several orders of magnitude is to use the Maximal
Structure Generation (MSG) and Solution Structures Generation
(SSG) algorithms of the P-graph framework (Friedler et al., 1993).
These algorithms effectively discard all infeasible combinations of
the binary selection variables and retain only the feasible ones.