An Efficient Benders Decomposition Approach for Optimal Large-Scale Network Slicing

TL;DR

The paper tackles large-scale network slicing optimization by formulating NS as a mixed-binary linear program and solving it via a customized Benders decomposition that decouples function placement (FP) from traffic routing (TR). It introduces iterative information feedback between FP and TR, enabled by Farkas' Lemma to generate cuts, and enhances convergence with two families of valid inequalities that exploit connectivity and link capacity structure. The CBD framework guarantees global optimality with enough iterations and significantly improves solution quality and speed over state-of-the-art approaches on large networks. Numerical results on a sizeable test network demonstrate substantial convergence acceleration and superior performance relative to exact and heuristic methods. The approach offers a practical path to scalable, NFV-enabled NS in 5G/6G contexts and suggests future extensions to related problems like virtual network embedding.

Abstract

This paper considers the network slicing (NS) problem which attempts to map multiple customized virtual network requests to a common shared network infrastructure and allocate network resources to meet diverse service requirements. This paper proposes an efficient customized Benders decomposition algorithm for globally solving the large-scale NP-hard NS problem. The proposed algorithm decomposes the hard NS problem into two relatively easy function placement (FP) and traffic routing (TR) subproblems and iteratively solves them enabling the information feedback between each other, which makes it particularly suitable to solve large-scale problems. Specifically, the FP subproblem is to place service functions into cloud nodes in the network, and solving it can return a function placement strategy based on which the TR subproblem is defined; and the TR subproblem is to find paths connecting two nodes hosting two adjacent functions in the network, and solving it can either verify that the solution of the FP subproblem is an optimal solution of the original problem, or return a valid inequality to the FP subproblem that cuts off the current infeasible solution. The proposed algorithm is guaranteed to find the globally optimal solution of the NS problem. By taking the special structure of the NS problem into consideration, we successfully develop two families of valid inequalities that render the proposed algorithm converge much more quickly and thus much more efficient. Numerical results demonstrate that the proposed valid inequalities effectively accelerate the convergence of the decomposition algorithm, and the proposed algorithm significantly outperforms the existing algorithms in terms of both solution efficiency and quality.

Figures (10)

• Figure 1: The information feedback between the FP and TR subproblems in the decomposition algorithm.
• Figure 2: A toy example for illustrating that (i) there does not exist a path from any node in $\mathcal{V}\backslash\mathcal{V}(v_0)$ to any node in $\mathcal{V}(v_0)$; and (ii) for all $v \in \mathcal{V}\backslash(\mathcal{V}(v_0)\cup\{v_0\})$, there exists a path from node $v_0$ to node $v$. The red dot line is drawn for the contradiction proof of \ref{['fact']}.
• Figure 3: A toy network example where the rectangular nodes are cloud nodes and the circular nodes are the source and destination of a service.
• Figure 4: A toy network example where the rectangular nodes are cloud nodes and the circular nodes are the source and destination of the services. $(a)$ and $(b)$ over each cloud node and each link denote that the node and link capacities are $a$ and $b$, respectively.
• Figure 5: The average relative optimality gap improvement of relaxation \ref{['vnf1']} and \ref{['vnf2']}.

Theorems & Definitions (9)

• Lemma 1: Farkas' Lemma
• Proposition 2
• proof
• Theorem 3
• proof
• Example 1
• Theorem 4
• proof
• Example 2