“…For symmetric instances, this number is halved, ⌈ n(n−1) 2 ρ⌉, since d j (x, y) = d j (y, x). Besides, the authors in [23] also suggest using the city replacement to generate dynamism into static TSPs [36], where a number of cities are replaced with new ones. Formally, given a graph G = (V, E) with v nodes and e edges, this benchmark generator replaces, every τ iterations, ⌈ρ × n 2 ⌉ random nodes (cities) in N in in the instance with the same number of random nodes in N out , where V is a set of nodes (cities), E is a set of arcs fully connecting the nodes, τ and ρ are the frequency and magnitude of changes, respectively, n is the size of the problem and N in ∩ N out = N are two sets containing n 2 nodes each.…”