The approximation expression about error accumulation of a long-term prediction is derived. By analyzing this formula, we find that the factors that can affect the long-term predictability include the model parameters, prediction errors and the derivates of the used basis functions. To enlarge the maximum attempting time, we present that more suitable basis functions should be those with smaller derivative functions and a fast attenuation where out of the time series range. We compare the long-term predictability of a non-polynomial based algorithm and a polynomial one to prove the success of our method.

It is very difficult to know evolution state of ACO in its working. To solve the problem, we propose using colony entropy and mean colony entropy to monitor the algorithm. The two functions show fluctuation and declining trends depended on time t in a tour and iteration number. According to the principle, that each updated edge will get the same increment is improper. Then a weighted algorithm is proposed to calculate each arc's increment based on its selected probability. The strategy can provide more exploration to help to find the global optimum value, and experiments show its improved performance.