CONCLUSIONS 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; supplyGA 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 (F w total = ton/hr) B TEST CASE STUDY B 10 Units with 6 pollutants, contaminated supply water (same order as in table, ppm : 160, 30, 150, 10, 10, 240) a)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 b)For multiple contaminated sources, eliminate, first, the over polluted sources; then, apply the free graph algorithm b) Optimal solution with Genetic Algorithm (F w total = ton/hr) Original optimal solution from Savelski et al. TEST CASE STUDY A 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 Florianópolis - Santa Catarina - Brasil APPLICATION’S INTERFACE Input data file for a network of 10 units and 6 contaminants. Fresh water from Source-1, contaminated When active, propagate the best individual thru generations; after cross- over, randomly generate individuals from a shrinking vicinity of the best individual 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 GENETIC ALGORITHM PROCEDURE 1.Choose the elements of the upper triangular matrix X as genes; 2.Form a chromosome, defining an individual, from all de genes of the matrix X; 3.Choose the alleles a gene can have (in our case, a continuous domain, bounded by some convenient chosen values); population 4.Choose the magnitude of the population formed of individuals; generations 5.Choose the appropriate number of generations a population should have; 6.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 population pool 7. Generate the initial population pool 8. 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 THE MATHEMATICAL MODEL Total mass balance kPartial mass balance, for k pollutant species The first set of constraints The second set of constraints The objective function Observations From first set of constraints - for any k species, the equal sign is valid for some minimum fresh water flow, dependent of m ki 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 f i should be picked-up The objective function, in order to minimize the total amount of fresh water 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 , Bucharest, Romania, X ji - water flow from j to i operation (likewise X ij ); - k pollutant concentration coming from j operation; - k pollutant concentration going to i operation; W i - exit flow from unit operation i; L i - possible flow loss; m ki - k pollutant released in water in unit operation i; f i - fresh water flow to i operation; SCHEMATIC MODEL OF UNIT OPERATION I 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 (m=1, 2 … i-1), and sending streams to probably all next n (j & N-1) knots (n=i+1,i+2 … N). THE ORIENTED GRAPH ABSTRACT Genetic Algorithm 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" (j=1, 2, … j  i, … N), and sending streams to probably (but not necessarily) all the other operations "j" (j=1, 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.. generation 9.Make a new generation, interbreeding individuals according to one-point crossover 10. their frequency of selection, using one-point crossover method; mutation 11. Apply mutation to randomly selected individuals; 12. If the minimum objective function is attained, stop the algorithm; otherwise, restart from 8.