Gromov-Wasserstein Distance Optimization Based On Ant Colony Algorithm

The algorithm is an inevitable difficult problem for many researchers,which solves the optimization model of the minimum difference between two manifold surfaces constructed under the Gromov-Wasserstein(GW)distance.The mainstream numerical iterative optimization algorithms rely on initial solutions to cause local optimization.Besides,it is complicated and time consumingthe in calculation.Therefore,this paper proposes GW distance optimization based on ant colony algorithm.First,establishing a GW distance optimization model on the basis of ant colony algorithm.During that,the hypothesis of the model is proposed to convert the quaternary relationship in the definition of GW distance into the binary relationship in the ant colony algorithm.Second,considering the amount of calculation and the actual physical meaning of the elements of GW distance optimization,new constraint conditions are proposed.Then,in order to improve the robustness of the algorithm,the distance accumulation method-exponential distance accumulation strategy was redefined in the ant colony algorithm.Finally,the algorithm is practiced in the 3D non-rigid graph matching problem under the TOSCA database.It has the advantages of faster convergence speed,higher convergence accuracy,good noise resistance and stability.In addition,the solution algorithm also has good applications in the fields of graphics,computer vision and intelligent robots.