#3. [14] Consider the function f(x) given in the following figure and define the optimization problem as Minimize f(x), x {{1, 2, 3, 4, 5, 6, 7, 8). luul. 2 3 4 5 6 a) [4] Suppose you solve the problem using Local Search Heuristics with xi = 2 as a starting solution and the neighborhood Ni(xx) = {xx -1, xx +1}, k >= 1. What is the local minimum with respect to this neighborhood Ni? 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(xx) = {xx -2, Xx -1, xx +1, Xxx +2}, k>= 1. What is the local minimum and the corresponding value, with respect to N2? Show the steps of the procedure roughly. c) [5] Suppose you solve the problem using Local Search with x = 2 as a starting solution and the neighborhood N3(xx) = {** -2, xk -1, xx +1, xx +2, Xx +3}, k >= 1. What is the local minimum and the corresponding value, with respect to N3? Show the steps of the procedure roughly. #3. [14] Consider the function f(x) given in the following figure and define the optimization problem as Minimize f(x), x {{1, 2, 3, 4, 5, 6, 7, 8). luul. 2 3 4 5 6 a) [4] Suppose you solve the problem using Local Search Heuristics with xi = 2 as a starting solution and the neighborhood Ni(xx) = {xx -1, xx +1}, k >= 1. What is the local minimum with respect to this neighborhood Ni? 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(xx) = {xx -2, Xx -1, xx +1, Xxx +2}, k>= 1. What is the local minimum and the corresponding value, with respect to N2? Show the steps of the procedure roughly. c) [5] Suppose you solve the problem using Local Search with x = 2 as a starting solution and the neighborhood N3(xx) = {** -2, xk -1, xx +1, xx +2, Xx +3}, k >= 1. What is the local minimum and the corresponding value, with respect to N3? Show the steps of the procedure roughly