optimize equation by put indexes of a set's elements

Question

suppose S is a set contains n elements and each element showed by S_i. S_i's are positive natural numbers.put indexes(1 to n) to elements of S so that y will be the lowest amount. y =∑_j=1ⁿ(∑_i=1^j s_i/ s_j) and s₀ = 0. for example if S={1,2,3} y will be y= 1/1 + (2+1)/2+(2+1+3)/3 = 4.5 or y= 1/1 + (1+3)/3+ (1+3+2)/2 = 16/3 and for now the minimum amount of y is 4.5 and until now indexes must select like s₁ = 1 and s₂ = 2 and s₃ = 3 which y could be minimum so that way to find indexes of S which y will be the lowest amount