Let h be the objective function that takes as input a real vector from $[0,10]3$ and returns a real number to be maximized, defined as follows:

def h$($x$)$:

if x$[0]==$x$[1]==$x$[2]==0$: return $31$

else: return x$[0]+$x$[1]+$x$[2]$

Also consider the well$-$known Particle Swarm Optimization $($PSO$)$ algorithm and a very trivial algorithm, called Random Search $($RS$),$ which iteratively generates random solutions, evaluates them, and returns the best one. Do you expect to observe a difference between RS and PSO in the time $($e$.$g$.,$ number of fitness evaluations$)$ required to reach the global optimum of h$?$ Also explain why and discuss whether one algorithm has some advantage over the other.