CONCLUSIONS

1
Fresh-water minimization through constrained
topoly design with Genetic Algorithm Dr. Vasile
LAVRIC, Drd. Petrica IANCU, Prof. Valentin PLESU
UNIVERSITY POLITEHNICA OF BUCHAREST, CENTRE FOR
TECHNOLOGY TRANSFER IN THE PROCESS INDUSTRIES 1,
Polizu Street, Building A, Room A056, Sector 1,
RO-011061, Bucharest, Romania, email
cttip_at_chim.upb.ro
SCHEMATIC MODEL OF UNIT OPERATION I
THE ORIENTED GRAPH
ABSTRACT
The water network is an oriented graph, with
multiple starting knots (unit operations 1,2 3)
with no contaminant at entrance, each knot i of
the graph receiving streams from possibly all
previous m (1 2) knots only (m1, 2 i-1), and
sending streams to probably all next n (j N-1)
knots (ni1,i2 N).
The present paper deals with the design of a
water usage network using Genetic Algorithm as
optimization approach subject to the above
mentioned restrictions. This approach generates
the best water network topology with a minimum
fresh water usage, complying, in the same time,
with all restrictions. An optimal water network
could be viewed as a graph, starting from unit
operations with the lowest contaminant
concentrations at entrance, each unit operation
"i" receiving streams from possibly (but not
inevitably) all the other operations "j" (j1, 2,
j?i, N), and sending streams to probably
(but not necessarily) all the other operations
"j" (j1, 2, j?i, N), except those which have
the imposed level of contaminants at entrance
close or equal to the fresh water level. The
mathematical model describing the unit "i" is
based upon total and contaminant species mass
balances, together with the input and output
constraints. Solving this optimization problem is
not trivial, since the unknowns' number outcomes
the equations' number. The GA optimization uses
each internal flow as a gene, defining a
chromosome from all these flows. The restrictions
are cope with naturally, during the population
generation, simply eliminating those individuals
outside the feasible domain. The individuals
interbreed according to their frequency of
selection, using one-point crossover method, and
then mutation is applied to randomly selected
individuals. The objective function is the total
fresh water consumption, which should be
minimized. Comparison with the results of water
pinch and mathematical programming methods is
made. .

• Xji - water flow from j to i operation
  (likewise Xij)
• - k pollutant concentration coming from j
  operation
• - k pollutant concentration going to i
  operation
• Wi - exit flow from unit operation i
• Li - possible flow loss
• mki - k pollutant released in water in unit
  operation i
• fi- fresh water flow to i operation

THE MATHEMATICAL MODEL

• Total mass balance
• Partial mass balance, for k pollutant species
• The first set of constraints
• The second set of constraints
• The objective function

GENETIC ALGORITHM PROCEDURE

• Choose the elements of the upper triangular
  matrix X as genes
• Form a chromosome, defining an individual, from
  all de genes of the matrix X
• Choose the alleles a gene can have (in our case,
  a continuous domain, bounded by some convenient
  chosen values)
• Choose the magnitude of the population formed of
  individuals
• Choose the appropriate number of generations a
  population should have
• Impose the main parameters of the genetic
  algorithm
• 6.1 favoring the best factor
• 6.2 fitness factor
• 6.3 crossover probability
• 6.4 mutation probability
• Generate the initial population pool
• With each individual
• 8.1 solve the mathematical model
• 8.2 compute the objective function
• 8.3 convert the objective function to a scaled
  fitness
• 8.4 convert the scaled fitness to an expected
  frequency of
• selection as parent

Observations

• From first set of constraints - for any k
  species, the equal sign is valid for some minimum
  fresh water flow, dependent of mki
• In order for the inequality to hold for the worst
  case of k pollutant, the maximum value for fi
  should be picked-up
• From second set of constraints - for any k
  species, the equal sign is valid for some minimum
  fresh water flow
• In order for the inequality to hold, the maximum
  value for fi should be picked-up
• The objective function, in order to minimize the
  total amount of fresh water

• Make a new generation, interbreeding individuals
  according to
• their frequency of selection, using one-point
  crossover method
• Apply mutation to randomly selected individuals
• If the minimum objective function is attained,
  stop the algorithm
• otherwise, restart from 8.

Input data file for a network of 10 units and 6
contaminants. Fresh water from Source-1,
contaminated
APPLICATIONS INTERFACE
TEST CASE STUDY A
When active, propagate the best individual thru
generations after cross-over, randomly generate
individuals from a shrinking vicinity of the best
individual
10 units with 3 contaminants (A, B and C), as
published in Efficient Use And Reuse of Water
in Refineries and Process Plants M. J. Savelski,
M. Rivas and M. J. Bagajewicz ENPROMER'99 Floria
nópolis - Santa Catarina - Brasil
When active, neglect internal flows under a
specified value (1 t/h, customary)
When active, reorder units in the network
descending, according to the maximum contaminant
load per unit
When active, reorder units in the network
descending, according to the maximum fresh water
needed per unit
Inspect/change input data buttons maximum
input/output unit concentrations, contaminants
load per unit, regeneration unit input/output
concentrations, contaminants load in fresh water
b) Optimal solution with Genetic Algorithm
(Fwtotal 389.87 ton/hr)
Original optimal solution from Savelski et al.
TEST CASE STUDY B
CONCLUSIONS

• 10 Units with 6 pollutants, contaminated supply
  water (same order as in table, ppm 160, 30,
  150, 10, 10, 240)
• For a single contaminated source, the level of
  contamination, for all pollutants, is subtracted
  from the maximum allowable input/output then,
  the oriented graph methodology is applied
• For multiple contaminated sources, eliminate,
  first, the over polluted sources then, apply the
  free graph algorithm

• GA technique was implemented to find the optimal
  water network topology together with the minimum
  fresh water consumption, observing for each unit
  operation
• The maximum allowable pollutant input
  concentration
• The maximum allowable pollutant output
  concentration
• GA performs better than other current techniques
  (mathematical programming, tree search
  methodology with branch cutting, water pinch)
• GA can handle an indefinite number of pollutants
• GA can handle contaminated sources of supply
  water
• GA could be generalized to non-oriented graphs,
  if all knots have non-zero input pollutant
  concentrations

Optimal solution (Fwtotal 910.778 ton/hr)