(b) Consider the case whereby you are given a population-based, iterative algorithm used for stochastic search in an optimization (minimization) setting. In every iterate, a population or collection of solutions p = {x1,x2,..., xPopsize}, x' E s is found. The quality or objective value of each solution x' is f(x'), whereby the minimization function is of the form f:S R. In this minimization setting, the algorithm generates a sequence of populations (p.) = Po.PvP2, ...,Ptmax Prove the correctness of this program (algorithm). You can make some simplifying assumption: (i) Able to compute or is given the objective value for any solution x E s, that is, f(x). (ii) tmax is the number of iterates and is known. (iii) There is only one minimum solution x* that is known with f(x*) = 0. (iv) The minimum solution is guaranteed to be found within tmax iterates. Hint: one can always choose the best solution of the population in each iterate to keep track of progress of the algorithm. Full marks for further arguments for proving total correctness. [30 marks]