## 1 Introduction  
The global express market has expanded significantly in recent years, with express business volume and revenue continuing to rise. Take China as an example: China's express business volume has increased nearly 40 times in ten years, with China's express business volume reaching 108.30 billion pieces in 2021 and a total annual express business revenue of RMB 1033.23 billion, representing significant gains. As the economy and technology drive the development of high-precision industries, the demand for high-value-added goods such as precision instruments, pharmaceuticals, and high-time efficiency goods such as fresh and cold chain products has increased, reflecting the demand for high quality in terms of transport efficiency and service quality. In 2012, China's Guangzhou Railway Group made its first attempt to launch a pilot high-speed rail freight service from Guangzhou to Changsha in conjunction with courier companies. In 2014, the China Railway Express launched four kinds of high-speed railway express products, including \"same-day delivery\", \"next-morning delivery\", \"next-day delivery\", etc. In 2017, the China Railway Express jointly launched the \"Double 11\" Beijing-Shanghai express service with the Shunfeng Express Company. In December 2020, the world's first freight trainset product with a speed of over 350 km per hour was released. The expansion of the scale of operation, the gradual standardization of operation, and the technical attack are all important thrusts in the development of high-speed rail express transport. However, the current high-speed rail express is basically based on direct transport, failing to reasonably allocate capacity, and the transport scheme is not flexible enough. In the face of huge transport demands and development prospects, it is necessary to carry out research on the theoretical system of high-speed rail express scheduling, to reasonably allocate transport resources, to improve the adaptability of product supply structure to changes in transport demand and freight structure, and to promote green and low-carbon development of logistics. Piggyback is a freight transportation organization mode in which small and high-value-added commodities are placed in the luggage storage area or the last row of seats on passenger trains. This mode does not need to modify the interior of the train car and set up a division of express loading and unloading operation areas in the station and platform, which indicates that the loading and unloading operation is very flexible. The high-speed confirmation train mode is namely to transport express products by a high-speed confirmation train, which runs before the official daily passenger loading to test the normal operation of railroad equipment and facilities and ensure the safety of train operation. This mode has no crossover with passenger transport, while passenger transport has no impact on cargo loading and unloading. This mode can use more space in the train. In this paper, the method of compiling the high-speed railway express train operation scheme is designed with comprehensive consideration of the time requirements of high-speed railway express freight. Based on the alternative set of HSR operating schemes, an optimization model for HSR express transport schemes in the cargo transportation process is constructed. We offer the following contributions to the research on high-speed rail express transportation plan optimization:  
1. We consider both piggyback transport mode and high-speed railway confirmation train mode in the research so that the optimization results have more practical significance. 2. We propose a transportation plan optimization model based on the space-time-state network for high-speed railway express (Section 3) to consider the time requirements of high-speed railway express products. 3. We illustrate the use of the optimization model and the improved adaptive genetic algorithm (Section 4) to solve the problem of a real high-speed railway system. The remainder of this paper is organized as follows.