An Ant-Based Algorithm for the Minimum Vertex Cover Problem

3 Ant-Based MVC Algorithm 18begin// construction stageC ← ∅for each vertex vcoverFactor[v] ← α ∗ τ[v] + β ∗ currDeg[v]end-forcandSet ← vertex set V sorted in non-increasing order of coverFactorwhile E is not emptyadd the vertex v with highest coverFactor in candSet to Cremove the vertex v from candSetremove all edges incident with v from Efor each vertex u where u is a neighbor of vcurrDeg[u] ← currDeg[u] − 1coverFactor[u] ← τ[u]∗ currDeg[u]end-forcandSet ← candSet sorted in non-increasing order of coverFactorend-whilereturn CendFigure 3.5. Construction Stage.two techniques are explained in detail in the following sections.The entire local optimization stage runs in cycles, where the two techniquesare applied sequentially. Initially, C is copied into bestLocalC. At the beginning ofeach cycle, the rebuild vertex cover technique operates on the cover C, returned bythe construction algorithm. The new solution, localC, generated by this techniqueis then passed to the redundant vertex removal technique, where the redundantvertices are removed. If the size of this new localC is smaller than bestLocalC, thenwe copy localC into bestLocalC; otherwise it is discarded. The entire procedure isthen repeated in the next cycle. Finally, after all the cycles have been completed,the bestLocalC is returned. Figure 3.6 provides an overview of the steps involvedin the local optimization stage.