6.1 Consider the following bi-objective optimization problem. This is a stan- dard single-variable bi-objective problem often used to test multiobjective optimizers. (6.29) M1 = x2 M2 = (x - 2)2 -55x55 (6.30) (6.31) (a) Obtain several optimal points on the Pareto frontier using the weighted sum method. Use the MATLAB function fmincon for optimization. Plot each design objective as a function of x on the same figure (as shown in Fig. 6.2). Identify on this plot, the Pareto solutions that you just obtained. Turn in your M-files. (b) Plot the Pareto optimal points in the M1-42 space. Turn in your M-files and the plot. Objective 2 Objective Function value M1 B M2 C Pareto Figure 6.2. Multiobjective Optimization 6.1 Consider the following bi-objective optimization problem. This is a stan- dard single-variable bi-objective problem often used to test multiobjective optimizers. (6.29) M1 = x2 M2 = (x - 2)2 -55x55 (6.30) (6.31) (a) Obtain several optimal points on the Pareto frontier using the weighted sum method. Use the MATLAB function fmincon for optimization. Plot each design objective as a function of x on the same figure (as shown in Fig. 6.2). Identify on this plot, the Pareto solutions that you just obtained. Turn in your M-files. (b) Plot the Pareto optimal points in the M1-42 space. Turn in your M-files and the plot. Objective 2 Objective Function value M1 B M2 C Pareto Figure 6.2. Multiobjective Optimization