Raunak Sarbajna, Md$.$ Mahin and Christoph F$.$ Eick

COSC $4368$: Fundamentals of Artificial Intelligence Spring $2024$

Problem Set $1($Individ$..$n$1$ male $1$ Centering on Search$)$

Fig. $1$: Finding a Needle in a Large Haystack with Intelligent Search

Submission Deadlines: Task$1$: Mo$.,$ Feb. $12,11$:$59$p; Task$2$: Fr$.,$ Feb. $23,11$:$59$p

Last Updated: February $5,9$a

Weight: Task weight: $T1=35$ points, $T2=40$ points.

On Probabilistic Search Algorithms: Implementing and Experimenting with Randomized Hill Climbing with Resampling Raunak Third Draft

Implement a randomized hill climbing algorithm with resampling, called RHCR$2$ in the following, and conduct a set of experiments, minimizing the following function $f$ :

$f_{\text{F}\text{r}\text{o}\text{g}}(x,y)=x**cos(\sqrt[\phantom{2}]{|x+y+1|})**sin(\sqrt[\phantom{2}]{|y-x+1|})+$

$(1+y)**sin(\sqrt[\phantom{2}]{|x+y+1|})**cos(\sqrt[\phantom{2}]{|y-x+1|})$

with $x,$yin$[-512,512]$

Your procedure should be called RHCR$2$ and have the following input parameters:

$sp$ : is the starting point ${?}^2$ of the Randomized Hill Climbing Resampling$2($RHCR$2)$ run

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

$z$ : neighborhood size: for example, if $z$ is set to $z=10,p$ neighbors for the current solution $s$ are generated by adding vectors $v=(z_1,z_2)$ with $z_1$ and $z_2$ being random numbers in $-10,+10$ uniformly distributed

seed: which is an integer that will be used as the seed ${?}^3$ for the random generator you employ in your implementation.

Collaboration with other students is not allowed!

${?}^2$ A vector $(x_1,x_2)in[-512,+512][-512,+512]$; sample code to visualize $f$ can be found in MS Teams! $\text{'}$If you run RHCR $2$ with the same values for $sp,p,z$ and seed, it will always return the same solution; if you run if with the same values for $sp,p,z$ and a different seed, it likely will return a different solution and the number of solutions searched is almost always different.