Implement Particle Swarm Optimization algorithm and use it to find the global solution of

$f(x)={\displaystyle \underset{j=1}{\overset{?}{}}}\{{\displaystyle \underset{i=1}{\overset{n}{}}}(i^j+)[(\frac{x_i}{i}{)}^j-1]\},-n{x}_{i}n,$

where $>0.$ Does the optimal solution depend on $?$