optimization algorithm

Color mixing is used in dental practice to produce a wide variety of colors. Mathematical methods can be used to reproduce colors.

We employed a mathematical algorithm to identify the basic essential three Vita Classical colors (VCC) that can be used to produce, through controlled mixing, all other colors of the VCC array in dental practice with the least possible errors. These were found to be: B1, B3, and C4. Another algorithm was constructed to find out mixing ratios of B1, B3, and C4 that would produce the remaining colors of VCC array with least errors. However, there were differences in colors and these were calculated as ΔE.

B1, B3, and C4 produced all other colors through direct mixing with the least average error (AE). Errors were found to range from 0.3985% to 1.5675% (average = 0.7473788%). The highest color errors were noticed during the production of A3.5 (1.5675%) and C3 (1.42%).

B1, B3, and C4 are the colors most likely to produce all other colors through direct mixing having the least AE.

The principle of passive sound control is based on the phenomenon of sound absorption by absorbers. The factors affecting sound absorption include porosity, pore size, pore opening size, thickness, and air flow resistance.

In this study, the authors compared the optimization results of the effective parameters on sound absorption coefficient (AC) using the three optimization methods Guided Local Search (GLS), Genetic Algorithm (GA) and Particle Swarm Optimization (PSO). The programming was done in MATLAB software. Thicknesses of 5, 10, 20, 30 and 40 mm were chosen for optimization at frequencies of 500 to 3000 Hz.

In frequencies above 2 kHz (thickness 5 to 40 mm), the three optimal methods had the same performance and estimated AC of 1. At low frequencies of 2 kHz and thicknesses of 30 and 40 mm, GA and PSO methods obtained an AC of 1.

It seems that the GA and PSO optimization algorithm are suitable methods to optimize the AC of metal foam in low and high frequencies.

Extensive studies have so far been carried out on developing safety models. Despite the extensive efforts made in identifying independent variables and methods for developing models, little research has been carried out in providing amendatory solutions for enhancing the level of safety. Thus, the present study first developed separate accident frequency prediction models by transportation modes, and then in the second phase, a development of safety improvement method (DSIM) was proposed.

To this end, the data related to 14,903 accidents in 96 traffic analysis zones in Tehran, Iran, were collected. To evaluate the effect of intra‑zone correlation, a multilevel model and a negative binomial (NB) model were developed based on both micro‑ and macro‑level independent variables. Next, the DSIM was provided, aiming at causing the least change in the area under study and with attention to the defined constraints and ideal gas molecular movement algorithm.

Based on a comparison of the goodness‑of‑fit measures for the multilevel model with those of the NB model, the multilevel models showed a better performance in explaining the factors affecting accidents. This is due to considering the multilevel structure of the data in such models. The final results were obtained after 200 iterations of the optimization algorithm. Thus, to decrease accidents by 30% and cause the least change in the area under study, the independent variable of “vehicle kilometer traveled per road segment” underwent a considerable change, while little change was observed for the other variables.

The final results of the DSIM showed that the ultimate solutions derived from this method can be different from the final solutions derived from the analysis of the results from the safety models. Hence, it is necessary to develop new methods to propose solutions for increasing safety.