2) On Probabilistic Search Algorithms: Implementing and Experimenting with Randomized Hill Climbing Theodoros Implement Randomized Hill Climbing and apply it to a minimization problem involving the following function f:

f(x,y) = [1 + (x + y +1)2(19 - 14x + 3x2 -14y + 6xy +3y2)][30 + (2x - 3y)2(18 -32x + 12x2 + 4y - 36xy + 27y2)], where -2 x,y 2

Your procedure should be called RHC and have the following input parameters:

sp: is the starting point of the Randomized Hill Climbing run

p the number of neighbors of the current solution that will be generated

z neighborhood size; for example if z is set to z=0.5 p neighbors for the current solution s are generated by adding vectors v=(z1,z2) with z1 and z2 being random numbers in [-0.5,+0.5] uniformly distributed

seed which is an integer that will be used as the seed for the random generator you employ in your implementation.

RHC returns a vector (x,y) the value of f(x,y) and the number solutions that were generated during the run of RHC.

Run your randomized hill climbing procedure RHC twice for the following parameters:

sp = (0.4, -0.5), (-0.5, 0.3), (1, -2) and (0,0) p = 30 and 120 z = 0.03 and 0.1

For each of the 32 runs report:

a. the best solution (x,y) found and its value for f

b. number of solutions generated during the run .

Summarize your results in 4 tables; one for each p and z combination . Interpret the obtained results evaluating solution quality, algorithm speed, impact of sp, p, and z on solution quality and algorithm speed. Do you believe with other values for p and r better results could be accomplished? At last, assess if RHC did a good, medium or bad job in computing a (local) minimum for f.

Submission Guidelines:

p=30 & z=0.03	#sol searched 1	Sols 1	f(sol) 1	#sol searched2	Sol 2	f(sol) 2
(0.4, -0.5)
( (-0.5, 0.3)
(1, -2)
(0,0)

You should summarize your results in 4 tables formatted as the above, for each of the 4 combination of p & z. Dont forget to summarize the results of the 33^th run and to provide the other information asked for in the project specification!