Approximate termination condition analysis for ant colony optimization algorithm

Ant colony optimization (ACO) has become quite popular in recent years. It has been successfully applied to many combinatorial optimization problems. In contrast to many successful applications, the theoretical foundation of this randomized search heuristic is rather weak. One of problem is embodied in the termination condition of ACO. The few kinds of possible termination condition are used in experiment, but they are often difficult and uneconomic way for practical problem. On the other hand, using the numerous feasible solutions in each iteration is also a difficult question for ACO. So, difference rate ε_a and difference rate ε_b are introduced in this paper to analyze the approximate termination condition. The feasible solutions which constructed in each iteration are employed in difference rate. Convergence factor c_f is also introduced in termination condition. Simulation results show that using the difference rate and convergence factor as termination condition of ACO is feasible.