# Q-MeaMetaVC: An MVC Solver of a Large-Scale Graph Based on Membrane Evolutionary Algorithms
## 1 Introduction
The FastVC2 proposed in the article [8] combines the graph reduction strategy with the local search algorithm and performs well in solving the MVC of large-scale instances. FastVC2 outperforms FastVC [8] in 26 instances. FastVC2 combines EdgeGreedyVC with MatchVC+ and GreedyVC+ to obtain a higher-quality initial solution, using the Best from Multiple Selections (BMS) heuristic so that it can better strike a balance between time complexity and solution quality. The authors of [9] proposed a dynamic thresholding search for an MVC (DTS_MVC) algorithm, which uses a vertex-based fast search strategy and the operation-prohibiting mechanism in the threshold search stage to expand the search space without falling into local optimum. Experimental evaluation of 86 large real-world graphs shows that DTS_MVC performs very well. Based on warning propagation (WP), the authors of [10] have developed a new linear space-time algorithm called MVC-WP to solve the MVCP (Minimum Vertex Cover Problem) on large graphs. The authors of [11] proposed a dynamic feature selection algorithm based on the MVC of a large graph, which requires only a small amount of calculation. Based on MetaVC, MetaVC2 [12] introduces a neural network-based method to enhance automatic construction. During the automatic construction process, the neural network model identifies and terminates the target algorithm with unsatisfactory operation results. Intuitively, this saves a lot of time and explores many constructs within a given budget, outperforming the REAL-WORLD benchmark. The authors of [13] proposed an MVC algorithm framework PEAF (PEAF refers to the MVCP solution framework consisting of preprocessing, exact algorithm, and approximation algorithm) based on problem reduction and divide-and-conquer ideas, and designed a large sparse graph MVC solver PEAVC based on PEAF. PEAVC has slightly adjusted the execution order of the solution phase, first solving the connected components with a special structure and then solving the remaining connected components. It uses the PreP algorithm in the preprocessing stage. For bipartite graph-connected components, it uses the exact algorithm BGVC to solve. For the remaining connected components, the approximate algorithm FastVC2 is used to solve the running time according to the proportion of its vertices to the remaining vertices. The inverse processing stage uses the inverse processor Inv_PreP. It compares the reduction capabilities of multiple preprocessors, demonstrating the different strategy's effectiveness and the superiority of PEAVC on large-scale sparse graphs. Inspired by membrane computing, [PERSON] combined the membrane nested structure with other evolutionary algorithms in 2004 and proposed the membrane algorithm framework [14]. Since then, researchers have used various algorithms based on this framework to solve different problems. For example, the authors of [15] proposed a membrane clustering algorithm predicated on membrane algorithm (MA)-based automatic clustering, which can easily find the number of clusters under the control of an evolutionary communication mechanism. Combining particle swarm optimization (PSO) and MA, the authors of [16] proposed a modified membrane-inspired algorithm based on particle swarm optimization (mMPSO) to solve the path-planning problem of multi-objective robots in dynamic obstacles and dangerous environments. Furthermore, the authors of [17] proposed a new MA for numerical optimization, and the authors of [18] combined MA with Quantum Evolutionary Algorithm (QEA). ME [19] proposed in 2019 is an evolutionary algorithm framework inspired by the behavioral characteristics of biological cells. Currently, MEA has been used to solve various combinatorial optimization problems, such as the traveling salesman problem (TSP) [20], maximum clique problem (MCP) [21], bi-objective critical node detection problem (CNDP) [22] and minimum vertex cover problem (MVCP). In [19], the MEA for solving the MVCP, called MEAMVC, is introduced.