Preparing a class timetable or routine is a difficult task because it requires an iterative trial and error method to handle all the constraints. Moreover, it has to be beneficial both for the students and teachers. Therefore, the problem becomes a multi-objective optimization problem with a good number of constraints. There are two types of constraints: hard and soft constraint. As the problem is an NP-hard problem, population based multi-objective optimization algorithms (multi-objective evolutionary algorithm) is a good choice for solving the problem. There are well established hard constraints handling techniques for multi-objective evolutionary algorithms, however, the technique is not enough to solve the problem efficiently. In the paper, a smart initialization technique is proposed to generate fewer constraints violated solutions in the initial phase of the algorithm so that it can find feasible solutions quickly. An experimental analysis supports the assumption. Moreover, there are no well-known techniques available for handling soft constraints. A new soft constraints handing technique is proposed. Experimental results show a significant improvement can be achieved. Finally, proposed combined approach integrates smart initialization and soft constraints handling techniques. Better results are reported when comparing with a standard algorithm.

Given that divorce has become a recurring challenge with increasing intensity in our world today accompanying broken families, economy and social contagion, as well as the existence of difference in happiness between the couple and their children. Thus, a mathematical model for predicting the rate of divorce tendencies in the Nigerian society is hereby developed. Factors influencing the rate of divorce were outlined and mathematical relationships between these factors were established. Afterwards, the developed model was validated and the real life data collected were contrasted with the model data predictions using suitable statistical tools. The findings from the comparison showed that the real life data and the model data predictions have a higher degree of correlation; consequently, recommending the model as a benchmark measure for predicting rate of divorce/marital instability in Nigeria. In the same vein, recommendations were made at the end of the model analysis which when adhered to would yield.

Bogie is an emblematic complex mechanical as well as electronic part of the current high speed rail system. A small failure of components may lead to a loss of production, casualties and damage of the system. Therefore, security and reliability analysis of bogie system is a predominant task. This paper proposes a stochastic network flow model of bogie system based on the forces applied on the components of the bogie, simultaneously considering the deterioration level and functional correlation of components. At first, a detailed description of structure and functions of the CRH3 bogie is introduced. Then a stochastic network flow model is constructed by analysing the direction of various forces applied on bogie. In the proposed model, edges represent the bogie components and vertices are the transmission channels. The flow over each edge is analysed by the forces it withstands. Finally, a combination method using minimal cut sets is proposed to evaluate the reliability of high speed train bogie system. This paper provides a supportive guidance and practical approach to bogie system designers for efficient operation and maintenance of the bogie.

When forecasting time series, It was found that simple linear time series models usually leave facets of economic and financial unknown in the forecasting time series due to linearity behavior, which remains the focus of empirical and applied study. The study suggested the Nonlinear Autoregressive Neural Network model and a comparison was made using the ARIMA model for forecasting natural gas prices, as obtained from the analysis, NAR models were better than the completed ARIMA model, measured against three performance indicators. The decision criterion for the selection of the best suited model depends on MSE, RMSE and R2. From the results of the criterion it has found that both the models are providing almost closed results but NAR is the best suited model for the forecasting of natural gas prices.

Picture fuzzy set is an extension of fuzzy sets and intuitionistic sets. It is demonstrated have a wide application in the fact and theoretical. In this paper, we propose some novel similarity measures between picture fuzzy sets. The novel similarity measure is constructed by combining negative functions of each degree membership of picture fuzzy set. This similarity is shown that is better other similarity measures of picture fuzzy sets in some cases. Next, we apply them in several pattern recognition problems. Finally, we apply them to find the fault diagnosis of the steam turbine.