Both statistical and neural network methods may fail in forecasting time series even operating on a great amount of data. It is an open question of which amount fits best to make sufficiently accurate forecasts on it. This implies that the length or time series might be optimised. Hence, the objective is to improve the quality of forecasting by an assumption that parameters are set nearly at their optimal values. To achieve objective, the two types of the benchmark time series are considered: sine-shaped series and random-like series with repeatability. Trend, seasonality, and decay properties embedded into each type. Based on the benchmark of 24 time series models, it is ascertained that, for improving the forecasting, the time series should be smoothed and then downsampled. These operations can be fulfilled successively until the improvement fails. If preliminary smoothing worsens forecasts, the raw time series is straightforwardly downsampled until the forecasting accuracy starts dropping. However, if time series has a visible property of being noised, the preliminary smoothing is strongly recommended.

A fast-and-flexible method of ARIMA model optimal selection is suggested for univariate time series forecasting. The method allows obtaining as-highly-accurate-as-possible forecasts automatically. It is based on effectively finding lags by the autocorrelation function of a detrended time series, where the best-fitting polynomial trend is subtracted from the time series. The forecasting quality criteria are the root-mean-square error (RMSE) and the maximum absolute error (MaxAE) allowing to register information about the average inaccuracy and worst outlier. Thus, the ARIMA model optimal selection is performed by simultaneously minimizing RMSE and Max-AE, whereupon the minimum defines the best model. Otherwise, if the minimum does not exist, a combination of minimal-RMSE and minimal-MaxAE ARIMA models is used.

We consider a problem of minimizing the maritime cargo delivery route length to reduce the delivery cost. In our model, the cost is equivalent to the sum of tour lengths of feeders used for the delivery to cover the route. Formulated as a multiple tr...

Appropriate Number and Allocation of RELUS in Convolutional Neural Networks

The problem of minimizing the cost of maritime cargo delivery is considered. The cost is equivalent to the sum of the tour lengths of feeders used for the delivery. The problem is formulated as a multiple traveling salesman problem. In order to find its solution as the shortest route of the tours of feeders, a genetic algorithm is used where we present two inequalities constraining the tour length of every feeder to lie between the shortest and longest lengths. Apart from the constant tour constraint violation penalty in the genetic algorithm, we suggest a changeable penalty as an exponential function of the algorithm iteration, where we maintain the possibility of the penalty rate to be either increasing or decreasing, whose steepness is controlled by a positive parameter. Our tests show that the changeable penalty algorithm may return shorter routes, although the constant penalty algorithms cannot be neglected. As the longest possible tour of the feeder is shortened, the changeable penalty becomes more useful owing to a penalty discount required either at the beginning or at the end of the algorithm run to improve the selectivity of the best feeder tours. In optimizing maritime cargo delivery, we propose to run the genetic algorithm by the low and constant penalties along with the increasing and decreasing penalties. The solution is the minimal value of the four route lengths. In addition, we recommend that four algorithm versions be initialized by four different pseudorandom number generator states. The expected gain is a few percent, by which the route length is shortened, but it substantially reduces expenses for maritime cargo delivery.

A problem of appropriately allocating pooling layers in convolutional neural networks is considered. The consideration is based on CIFAR-10, NORB, and EEACL26 datasets for preventing “overfitting” in a solution of the problem. For highly accurate image recognition within these datasets, the networks are used with the max pooling operation. The most common form of such operation, which is a 2 × 2 pooling layer, is applied with a stride of 2 without padding after convolutional layers. Based on performance against a series of the network architectures, a rule for the best allocation of max pooling layers is formulated. The rule is to insert a few pooling layers after the starting convolutional layers and to insert a one pooling layer after the last but one convolutional layer (“11...100...010”). For much simpler datasets, the best allocation is “11...100...0”.