Question 3 (30 marks) The following optimisation problem has two objectives f1 (maximise) and f2 (minimize): f1=(x0.5)2+2f2=(y0.5)2+2 subject to 0x1and0y1 where x and y are the decision variables. Assume an initial population with 4 individuals (0.2,0.2),(0.4,0.4),(0.6,0.6),(0.8, 0.8). Each individual represents a potential solution (x,y). (a) Using an appropriate encoding, generate 4 children by applying both crossover and mutation operators for each pair of parents randomly selected, with a mutation size of 0.1 . (10 marks) (b) Draw a scatter plot and show the Pareto front based on an intermediate child population generated in part (a) and its parent population. Select 4 solutions from the scatter plot for the next generation. (5 marks) (c) Continue to produce another subsequent generation of offspring and illustrate the final Pareto-optimal solution in a separate scatter plot. Keep the population size fixed at 4