一类新型改进的广义蚁群优化算法

A New Improved Generalized Ant Colony Optimization Algorithm

提出了一类新型蚁群优化算法。该算法改进了概率选择函数,将概率选择函数由严格单调增函数推广为有界函数,给出了蚂蚁在某一源节点选择下一个节点的更一般的表达式。证明了算法收敛的重要定理:即对足够大的迭代次数,改进的广义蚁群优化算法至少找到最优解一次的概率趋近于1。提出了信息素渐近平衡原理。在信息素更新规则中,引入了信息素残留率函数、信息素增量函数。证明了渐近信息素在最优路径上将会趋于一个正数,而在非最优路径上将会趋于0。最后,计算机仿真实验结果表明,无论是获得的最优解的质量还是算法的收敛速度,文中提出的改进的广义蚁群优化算法都优于传统的蚁群优化算法。

A new improved generalized ant colony optimization algorithm （ IGACO ） is proposed in this paper. The selected probability functions are generalized from strictly increasing continuous functions to bounded functions, which gives a more general form of expression for the probability of selecting the next node. An important theorem is proved for describing the convergence of IGACO algorithm, i.e. for a sufficiently large number of algorithm iterations, the probability of finding the globally optimal solution at least once tends to 1. A principle of pheromone asymptotic balance is proposed. In the pheromone update rule,the residual rate function of pheromone and the global increasing function of pheromone are presented. Prove that the residual pheromone tends to a positive number on the edges that are globally optimal solution, and tends to 0 on the edges that are not globally optimal solution. Finally, the computational simulation shows that,compared with traditional ant colony optimization algorithm,the IGACO algorithm has good performance both on globally optimal solution and convergent speed.