P1: This problem is adapted from Messac 2015 []. Consider the following multiobjective optimiza- tion problem: minx {f1(x) = x1, f2(x) = x2} subject to: x21 + x22 9 1 x41 +x42 16 x31 27 +x32 1 0 x1 2.9 0 x2 2.9 Note that this is a uniquely contrived problem where the objective functions are the optimization variables. This means that the optimization variable space is also the objective function space, and the constraints on design variables directly constrain the Pareto frontier. Perform the following tasks:

a) Solve this problem using the weighted sum method1 to generate the Pareto frontier. Does the weighted sum method provide a good representation of the Pareto frontier? Explain your answer.

b) Solve this problem using the epsilon-constraint method2 to generate the Pareto frontier. Does the epsilon-constraint method provide a good representation of the Pareto frontier? Explain your answer.

P1: This problem is adapted from Messac 2015 []. Consider the following multiobjective optimization problem: minxsubjectto:{f1(x)=x1,f2(x)=x2}x12+9x221x14+x241627x13+x2310x12.90x22.9 Note that this is a uniquely contrived problem where the objective functions are the optimization variables. This means that the optimization variable space is also the objective function space, and the constraints on design variables directly constrain the Pareto frontier. Perform the following tasks: a) Solve this problem using the weighted sum method 1 to generate the Pareto frontier. Does the weighted sum method provide a good representation of the Pareto frontier? Explain your answer. b) Solve this problem using the epsilon-constraint method 2 to generate the Pareto frontier. Does the epsilon-constraint method provide a good representation of the Pareto frontier? Explain your answer. c) [OPTIONAL] If you would like, check your result by comparing against the solution produced using the MATLAB implementation of Multiobjective Genetic Algorithm (MOGA) 3