A Preference Matrix based Genetic Algorithm (PMGA) was introduced for solving the Long-Term Car Pooling Problem (LTCPP), and a group of users with both vehicle and the same destination was assigned to the co-generation group to minimize the total travel cost. First, the objective function of calculating the cost of all users was set up, and a long-term car pooling model with constraints of user time window and car capacity was designed. Then based on the characteristics of the model and classic Genetic Algorithm (GA), a preference matrix mechanism was adapted into the crossover and mutation operators to memorize and update the preference information among different users, thus improving the quantity and the quality of feasible solutions. The experimental results show that in the same computing environment, the optimal solution value of 20 solutions obtained by PMGA is the same as that of the exact algorithm when the number of users is less than 200. Moreover, PMGA is remarkable in solution quality when dealing with large size of instances. The proposed algorithm can significantly improve the solution quality of the long-term car pooling problem, and play an important role in reducing vehicle emission and traffic congestion.

Focused on the topic that the ordinary full-text searching technology could not realize mathematical expression retrieval resulted from the complex two-dimensional structure characteristics of formulae, a method of LaTeX formulae analyzing and indexing was proposed. On the basis of the fully consideration of formulae' characteristics and the structure of LaTeX language, a parsing algorithm was designed for analyzing LaTeX expressions and extracting their retrieval features. Taking it as a foundation, a hierarchical index model was designed which employed the information of operands and operators extracted from mathematical expressions through the parsing algorithm. The index model has two layers, Treap data structure layer and inverted index layer, which laid the foundation of the retrieval and matching to formulae. The experiment was carried out under the mode of browser/server through taking 6234 formulae from mathematical textbooks as data set. The parsing algorithm gets 124960 expression nodes from resource formulae of which the highest baseline level is 11. The average time consumed of the index system is 33.8317 seconds. The experimental results show the proposed parsing algorithm and the index method are helpful for realizing mathematical expression retrieval with high efficiency and correctness.

A nonlinear image encryption algorithm based on random Fractional Mellin Fransform (FrMT) was proposed to get rid of the potential insecurity problem of the linear encryption system. The random FrMT was constructed by combining log-polar transformation with random Fractional Fourier Fransform (FrFT), and a real-valued symmetrical random matrix was generated by Linear Congruential Generator (LCG) in randomizing process. The real value input image was encrypted by random FrMT which made the encryption be nonlinear, and the output ciphertext of the FrMT was also real-valued, which was convenient for storage and transmission. The encryption algorithm had three keys that were the parameters of LCG. Compared with FrMT, the fractional order key of random FrMT was more sensitive. The numerical simulation results demonstrate that the encryption algorithm is against common attacks, and sensitive to keys with good security.

To reduce the heavy transmission burden of multichannel color image encryption algorithms, a single-channel color image encryption algorithm based on cutting spectrum and 2D Arnold transform was presented. In the proposed algorithm, the R, G, B components of the original color image were extracted, and their spectra were obtained separately by the Fractional Fourier Transform (FrFT) of different orders, followed by cutting their spectra to construct a new spectrum, then the combined spectrum was scrambled by the 2D Arnold transform to confuse and diffuse the spectrum information well enough. The encrypted image was a gray image, thus the transmission burden was reduced apparently while the main information of the original color image was kept. The simulation results and performance analyses verify the validity and the security of the encryption algorithm.