动态凸包引导的偏优规划蚁群算法求解TSP问题

Ant colony algorithm of partially optimal programming based on dynamic convex hull guidance for solving TSP problem

针对蚁群算法搜索空间大、收敛速度慢、容易陷入局部最优等缺陷,提出一种基于动态凸包引导的偏优规划蚁群算法。改进后的算法动态控制蚂蚁的待选城市范围,有助于在跳出局部最优并向全局最优逼近的基础上减少蚂蚁搜索空间;同时,引入延陷漂流因子和基于待选城市构建的凸包来干预当前蚂蚁的城市选择,增加算法前期解的多样性并提高蚂蚁的偏优规划能力;再利用局部与整体相结合的完整路径信息、凸包的构建信息来协调信息素的更新,引导后继蚂蚁路径偏优规划,提高算法的求解精度;设计具有收敛性的信息素最大最小值限制策略,既加快算法的求解速度又避免算法过早停滞;最后在4种经典TSP模型上应用改进后的算法。仿真结果表明,所提算法在求解精度和收敛速度等方面均有显著提高,且具有较好的适用性。

To solve basic ant colony algorithm’s drawbacks of large search space,low convergence rate and easiness of trapping in local optimal solution,an ant colony algorithm of partially optimal programming based on dynamic convex hull guidance was proposed.The improved algorithm dynamically controlled the urban selection range of the ants,which could reduce the search space of ants on basis of helping the algorithm to jump out of local optimal solution to global optimal solution.Meanwhile,the delayed drift factor and the convex hull constructed by the cities to be chosen were introduced to intervene the current ants’urban choice,it could increase the diversity of the early solution of the algorithm and improve the ability of ants’partially optimal programming.Then the pheromone updating was coordinated by using construction information of convex hull and the complete path information that combined local with whole,it could improve the accuracy of the algorithm by guiding the subsequent ants to partially optimal programming.The pheromone maximum and minimum limit strategy with convergence was designed to avoid the algorithm’s premature stagnation and accelerate the solving speed of the algorithm.Finally,the proposed algorithm was applied to four classic TSP models.Simulation results show that the algorithm has better optimal solution,higher convergence rate and better applicability.