| Generalized Ant Colony Optimization is the improvement and enhancement based on AntColony Optimization, but there is still a lot of missing on convergence rate theoretical analysis andoptimization performance. Lack of theoretical research has become a bottleneck constraint thefurther development and application of the algorithm.This article establishes a universal process model based on absorbing Markov process toanalyze the convergence rate of Generalized Ant Colony Optimization. When come to the detailedanalysis of convergence speed, use expected convergence time as the main indicator. Throughanalysis on the mathematical model and program, this article gets the fomula of time complexityand space complexity of Generalized Ant Colony Optimization.From the theoretical analysis on convergence rate, for large scale TSP, appropriately increasethe number of ants can reduce the number of iterations to converge to the optimal solution; if theprobability function of the choice of the optimal path is large enough, Generalized Ant ColonyOptimization can convergence to the optimal solution in polynomial time. Experiments show thatGeneralized Ant Colony Optimization is better than Ant Colony Optimization both on the quality ofthe solution obtained and the convergence speed, the advantage will be more obvious with theexpansion of the scale of the problem. What’s more, by choosing bounded probability selectedfunction according to specific issues, Generalized Ant Colony Optimization can converge in ashorter period of time and get a better solution.Applying Generalized Ant Colony Optimization to image segmentation proves theapplicability of the algorithm and the convergence time is less than Ant Colony Optimization. In theend of article proposes polymorphic Generalized Ant Colony Optimization algorithm and get aconclusion that the convergence speed of polymorphic Generalized Ant Colony Optimization issuperior to Generalized Ant Colony Optimization in image segmentation. |
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