A Systematic Survey of Slice-Resource Optimization in the 5G Core with New Insights from 2-Edge-Connected Subgraph Models

Network slicing now delivers enhanced mobile broadband (eMBB), ultra-reliable low-latency communications (URLLC), and massive machine-type communications (mMTC) over a common 5G core, yet deciding which slice requests to admit, where to place each virtual network function (VNF), and how to route and protect traffic forms an NP-hard mixed-integer problem. We first cast those decisions in a compact 0–1/mixed-integer programme whose feasible set Ω unifies admission, placement, latency, and capacity constraints. That formulation provides a common yardstick for four solution lines reviewed here: (i) exact models solved by integer linear programming (ILP); (ii) fast constructive heuristics; (iii) evolutionary and neighbourhood-search meta-heuristics; and (iv) learning-driven approaches built on deep- and graph-reinforcement learning (RL). Evidence from more than thirty benchmark studies reveals a clear pattern: ILP remains optimal up to roughly fifty nodes but scales poorly; greedy or multi-stage heuristics retain 85–95% of ILP revenue while running in near-linear time; well-tuned meta-heuristics cut the gap to under eight per cent on thousand-node cores; and trained RL agents issue millisecond decisions only a few points shy of meta-heuristic quality. Two recent two-edge-connected embedding schemes are included as illustrative case studies. Open challenges—hybrid matheuristic workflows, energy-aware objectives, reproducible failure-rich benchmarks, and sub-millisecond control-plane inference—are outlined as priorities for dependable slice management in 5G and beyond. 5G Core Network, Network Slicing, Integer-Linear Programming, Evolutionary Meta-Heuristics, Deep-Reinforcement Learning, Two-Edge-Connected Protection