a) Suppose we have a distillation process where the objective is to separate components of a...

  

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a) Suppose we have a distillation process where the objective is to separate components of a mixture in the input stream. The relationship between the input variable, temperature, and the output variable, distillate fractions, is not precise but the human operator of this process has developed an intuitive understanding of this relationship. Now we define fuzzy sets A and B 0.0 0.7 1.0 0.4 A = steam temperature is hot = - + 175 180 190 185 0.0 0.5 0.8 1.0 = + + + 89 92 95 98 0.0 0.5 1.0 0.5 89 92 95 98 B2 = mixture separation is average = + + + We wish to determine the proposition, IF "temperature is hot" THEN "separation of mixture is good," or symbolically, A B. However, two operators have different prospections of "good", combining the two operators, we can get the following relation R = (AXB1) U (Ax B2) i) Determine R B1 = mixture separation is good [25%] ii) If the temperature is A', find B' using max-min composition, i.e., find 1.0 0.8 0.5 0.2 B' = A' R., where A' = + + + 175 180 185 190 [25%] Q4. a) Present the basic format of an Evolutionary Algorithm using a flow chart format. Briefly explain each component of the algorithm. [25%] b) Consider the neural network shown in Figure Q4. The network contains two inputs, a hidden layer with three neurons and an output layer with two neurons. The weights of the network are optimised with a Genetic Algorithm. Output Input Figure Q4 i) Propose a solution representation for this problem. [25%] ii) Propose two genetic operators for this algorithm. Explain how the genetic operators work. [25%] iii) Show the network architectures obtained through the application of the genetic operators you propose. [25%] a) Suppose we have a distillation process where the objective is to separate components of a mixture in the input stream. The relationship between the input variable, temperature, and the output variable, distillate fractions, is not precise but the human operator of this process has developed an intuitive understanding of this relationship. Now we define fuzzy sets A and B 0.0 0.7 1.0 0.4 A = steam temperature is hot = - + 175 180 190 185 0.0 0.5 0.8 1.0 = + + + 89 92 95 98 0.0 0.5 1.0 0.5 89 92 95 98 B2 = mixture separation is average = + + + We wish to determine the proposition, IF "temperature is hot" THEN "separation of mixture is good," or symbolically, A B. However, two operators have different prospections of "good", combining the two operators, we can get the following relation R = (AXB1) U (Ax B2) i) Determine R B1 = mixture separation is good [25%] ii) If the temperature is A', find B' using max-min composition, i.e., find 1.0 0.8 0.5 0.2 B' = A' R., where A' = + + + 175 180 185 190 [25%] Q4. a) Present the basic format of an Evolutionary Algorithm using a flow chart format. Briefly explain each component of the algorithm. [25%] b) Consider the neural network shown in Figure Q4. The network contains two inputs, a hidden layer with three neurons and an output layer with two neurons. The weights of the network are optimised with a Genetic Algorithm. Output Input Figure Q4 i) Propose a solution representation for this problem. [25%] ii) Propose two genetic operators for this algorithm. Explain how the genetic operators work. [25%] iii) Show the network architectures obtained through the application of the genetic operators you propose. [25%]

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