D version
16.8
S3
(ppm) 5
34
(%)
20 T2
100 12500 9500
54.8
15
T1
T3 100 12500 9500 0
S2
(t/h) C1 C2 C3
95
C1 C2 C3
15 400 35
T10
100 50
(ppm) C1 C2 C3
110 12500 160
98
T310
100 45 9500
100 12500 9500 T2
(ppm)
S1
C1 C2 C3
99
20
Non-Linear Optimization
It is necessary to obtain a final effluent with a concentration lower than the maximum allowed by law:
And the objective is to minimize the total flow to be treated, ie min
Evaluation criteria: i) Answer to questions (mini report, maximum 4 pages); (ii)
.
It is intended to design the optimal network for the treatment of effluents from aqueous streams from
an industrial process. There are 3 currents (S1-S3) with the following characterization for the 3 relevant
contaminants (C1-C3):
There are 3 treatment processes (T1-T3) that can be used with the following technical characteristics
for the different contaminants (removal ratio and maximum inlet concentration):
Problem
March 2022Final work
Note: The network superstructure is on slide 89 and the NLP model is on slide 90.
Functionality and presentation of the spreadsheet in Excel submitted in Moodle, which must include a
worksheet for each item. In case of obvious similarities between the submitted files, the authors will
be called for discussion.
,
,
,
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1) Consider the linear relaxation of the NLP formulation shown on slide 101.
a) Solve it with the Excel solver, using as initialization the solution of 1a). If no
3) The global optimal solution presents partial bypass of the currents to the treatment system.
Questions
2) Implement the nonlinear programming model from slide 90.
2b) is it in fact the global optimum?
What is the estimate of the flow to be addressed for the nonlinear problem?
b) Represent the network corresponding to the optimal solution of a), showing only the
total to treat.
no slide 92.
a) Implement the linear programming model and solve it using Excel Solver.
find a workable solution, try a serial boot as suggested
Determine the minimum value of bypass that can be obtained and the penalty on the flow
c) Is the solution of a) an admissible solution of the nonlinear problem? If you don't think so,
initialization values of the variables and represent the optimal solution of the problem
Non-Linear Optimization
active links and non-zero variable value.
Experiment with other initialization values until you find the global optimum. Indicate the
b) It is possible that the solution of 2a) is not the global optimum of the problem (< 251 t/h).
March 2022
of a)?
c) Theoretical question: What procedure(s) could you use to prove that the solution of
(active links and variable value different from zero).
indicate a set of constraints of the nonlinear model that is violated by the solution
Final work
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