#3. [14] Consider the function x) given in the following gure and dene the optimization problem as Minimizex))x E{1) 2) 3) 4) 5) 6) 7) 8}\" 8 5 q. 3 2 _ _ _ _ _ _ _ 1 I g I 1 2 3 4 5 6 T 8 a) [4] Suppose you solve the problem using Local Search Heuristics with x1 = 2 as a starting solution and the neighborhood N1(xk) = {chc -1, xk +1}, k >= 1. What is the local minimum with respect to this neighborhood N1? What is the local minimum value? Show the steps of the procedure roughly. b) [5] Suppose you solve the problem using Local Search with x1 = 2 as a starting solution and the neighborhood N2(xk) = {xk -2, I]: -1, 16k +1, 16k +2} , 1': >= 1. What is the local minimum and the corresponding value, with respect to N2? Show the steps of the procedure roughly. 0) [5] Suppose you solve the problem using Local Search with x1 = 2 as a starting solution and the neighborth N3(Ik) = {xx -2, xk -1, xk +1, .17}; +2, xk +3}, 1: >= 1. What is the local minimum and the corresponding value, with respect to N3? Show the steps of the procedure roughly