st RAN Slicing into its robust counterpart. Consequently, we obtain two types of constraints: constraints (10.27)-(10.29) represent the robust counterpart of those rows in (10.24) containing one stochastic variable; constraint (10.30) are those rows in (10.24) without stochastic variables. The robust counterpart of (10.23) (or called ROBUST) is formulated as follows: (10.26) hix+yi11, (10.27) (10.28) y01,jh>01,, (10.29) (10.30) X E X R C , (10.31) where Aj E B, and X ER otherwise}, in which C = {1,2, .cU1J B = , are sets of the subscripts of continuous and binary variables respectively. We use a IRC XJJC dimensional matrix, denoted by HRC, to represent the coefficients of (P), where can see that problem (P) is also an MIP. However, we need to introduce (2 new variables and new constraints to transform (10.23) into (P), which means that the robust counterpart transformation scales linearly with the number of substrate and virtual links. Consequently, utilizing Matlab solver as a black box for solving (P) may lead to a slow convergence and scalability problem [29]. With the aim of finding better solutions faster than the MIP solver alone, in Section 10.3.3, we propose a heuristic algorithm to solve problem (P). 10.3.3 Variable Neighborhood Search Based Heuristic for Robust RAN Slicing Problem (P) is a 0-1 mixed integer programming, which is proved to be NP-hard [19] and time-consuming when solved by some exact methods, such as branch-and-bound, branch-and-cut, and Lagrangian relaxation [30]. To address this problem, we develop a heuristic algorithm to solve problem (P), whose basic idea is as follows: First, we give an initial feasible solution utilizing Matlab solver as a black box SO that we can add an objective cut to (P). Then we solve the linear relaxation of P, denoted by LP(P), which is formulated by relaxing the integer variables of (P) from {0,1} to [0, 1]. The distance between the feasible solution and the solution of LP(P) is calculated. By 10.3 Robust RAN Slicing rounding the relaxed variables according