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Customized buses (CBs) are a new mode of public transportation and an important part of diversified public transportation, providing advanced, attractive and user-led service. The operational activity of a CB is planned by aggregating space–time demand and similar passenger travel demands. Based on an analysis of domestic and international research and the current development of CBs in China and considering passenger travel data, this paper studies the problems associated with the operation of CBs, such as stop selection, line planning and timetables, and establishes a model for the stop planning and timetables of CBs. The improved immune genetic algorithm (IIGA) is used to solve the model with regard to the following: 1) multiple population design and transport operator design, 2) memory library design, 3) mutation probability design and crossover probability design, and 4) the fitness calculation of the gene segment. Finally, a real-world example in Beijing is calculated, and the model and solution results are verified and analyzed. The results illustrate that the IIGA solves the model and is superior to the basic genetic algorithm in terms of the number of passengers, travel time, average passenger travel time, average passenger arrival time ahead of schedule and total line revenue. This study covers the key issues involving operational systems of CBs, combines theoretical research and empirical analysis, and provides a theoretical foundation for the planning and operation of CBs.

Under the hypothesis that the first derivative satisfies some kind of weak Lipschitz conditions, a new semilocal convergence theorem for inexact Newton method is presented. Unified convergence criteria ensuring the convergence of inexact Newton method are also established. Applications to some special cases such as the Kantorovich type conditions andγ-Conditions are provided and some well-known convergence theorems for Newton's method are obtained as corollaries.

In order to improve the optimization accuracy and convergence rate for trajectory optimization of the air-to-air missile, a multi-interval mesh refinement Radau pseudospectral method was introduced. This method made the mesh endpoints converge to the practical nonsmooth points and decreased the overall collocation points to improve convergence rate and computational efficiency. The trajectory was divided into four phases according to the working time of engine and handover of midcourse and terminal guidance, and then the optimization model was built. The multi-interval mesh refinement Radau pseudospectral method with different collocation points in each mesh interval was used to solve the trajectory optimization model. Moreover, this method was compared with traditional h method. Simulation results show that this method can decrease the dimensionality of nonlinear programming (NLP) problem and therefore improve the efficiency of pseudospectral methods for solving trajectory optimization problems.

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