The minimum vertex cover (MVC) is a well-known combinatorial optimization problem. A game-based memetic algorithm (GMA-MVC) is provided, in which the local search is an asynchronous updating snowdrift game and the global search is an evolutionary algorithm (EA). The game-based local search can implement (k,l)-exchanges for various numbers of ${k}$ and ${l}$ to remove ${k}$ vertices from and add ${l}$ vertices into the solution set, thus is much better than the previous (1,0)-exchange. Beyond that, the proposed local search is able to deal with the constraint, such that the crossover operator can be very simple and efficient. Degree-based initialization method is also provided which is much better than the previous uniform random initialization. Each individual of the GMA-MVC is designed as a snowdrift game state of the network. Each vertex is treated as an intelligent agent playing the snowdrift game with its neighbors, which is the local refinement process. The game is designed such that its strict Nash equilibrium (SNE) is always a vertex cover of the network. Most of the SNEs are only local optima of the problem. Then an EA is employed to guide the game to escape from those local optimal Nash equilibriums to reach a better Nash equilibrium. From comparison with the state of the art algorithms in experiments on various networks, the proposed algorithm always obtains the best solutions.

中文翻译：

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网络顶点覆盖的基于游戏的模因算法

最小顶点覆盖（MVC）是众所周知的组合优化问题。提供了一种基于游戏的模因算法（GMA-MVC），其中本地搜索是异步更新的雪堆游戏，而全局搜索是进化算法（EA）。基于游戏的本地搜索可以实现（则）-各种数量的交换 $ {k} $ 和 $ {l} $ 去除 $ {k} $ 顶点并添加 $ {l} $ 顶点进入解集，因此比以前的（1,0）交换要好得多。除此之外，所提出的局部搜索能够处理约束，从而使得交叉算子可以非常简单和有效。还提供了基于度的初始化方法，该方法比以前的统一随机初始化要好得多。GMA-MVC的每个人都被设计为网络的随风飘飞的游戏状态。每个顶点都被视为与它的邻居一起玩雪堆游戏的智能代理，这是本地优化过程。游戏的设计使其严格的纳什均衡（SNE）始终是网络的顶点覆盖。大多数SNE只是问题的局部最优。然后，使用EA来指导游戏摆脱那些局部的最佳Nash平衡，从而达到更好的Nash平衡。