Ant colony optimization (ACO) is a very suitable path search algorithm, whose typical application is traveling salesman problem. However, as one heuristic algorithm, it has many shortcomings, such as slow convergent speed and low searching efficiency. To overcome these shortcomings, the premium-penalty strategy has been introduced, and the pheromone diversity of the good paths and the ordinary ones is increased to polarize pheromone density of all paths. Thus, premium-penalty ant colony optimization (PPACO) is proposed. And its good performance is verified by the applications to some typical traveling salesman problems. Its two important parameters are discussed too. Because location critical slip surface in slope stability analysis is a path search problem, it can be solved by the ACO very suitably. Therefore, based on PPACO and typical mature limit equilibrium analysis (Spencer method), a new method to analyze the slope stability is proposed. Through two typical examples, one simple slope and one complicated slope, the efficiency and effectiveness of the new algorithm are verified. The results show that, the new algorithm can always find the less safety factor and its critical slip surface in shorter time than many previous algorithms, and the new algorithm can be used in real engineering very well. 
Premium-penalty ant colony optimization and its application in slope stability analysis