## 1 Introduction  
In recent years, China's HSR system has been developing rapidly. With the increase in the railway's running mileage, the scale of passenger transport is also enlarging. By 2021, China's Railway running mileage was 150,000 km, including 40,000 km of high-speed railway, accounting for 26.7% of the total. With the COVID-19 pandemic under effective control, China's Railway passenger traffic volume rebounded to 2.533 billion in 2021, an increase of 16.9% year-on-year, among which the number of passengers sent by the high-speed Electric Multiple Units (EMU) accounted for more than 70% of the total passenger volume. According to the Medium and Long Term Railway Network Plan (2020-2035), China's Railway network will extend to 200,000 km by 2035, including 70,000 km of high-speed railway, and cities with a population of 500,000 or more will be accessible by a high-speed railway [1]. With the further expansion of the railway network, railway transport enterprises are gradually moving towards marketization. In 2013, China Railway implemented a separation of the enterprise from administration, which officially opened the prelude to the market-oriented reform of the railway transport market [2]. In 2016, the ticket-pricing power of the high-speed railway was handed over to transport enterprises, signaling that the enterprises had gained the power to adjust ticket prices according to market supply, demand, and competition. At the end of 2020, to solve the contradiction between supply and demand and promote the market-oriented development of the Beijing-Shanghai HSR, it was decided to adjust the ticket price, with the actual ticket price implemented as the base price. Although the market-oriented reform of railway transport has begun to bear fruit, it still faces the following severe challenges [3]. (1) The imbalance between revenue and expenditure. The railway has the characteristics of a high construction cost and a long payback period, especially the HSR. Although the transport revenue has increased year by year in recent years, it is still far below the investment. (2) The supply and demand mismatch. Due to the insufficient grasp of passengers' demand, the uneven allocation seriously hinders the further increase in transport revenue. (3) It is difficult to consider both ticket revenue and the train seat capacity utilization. In the context of the market-oriented reform of the HSR, due to the differences in passengers' ability to accept ticket prices, if transport companies adjust ticket prices by more than the acceptable level of passengers, it may affect passengers' demand for tickets, thus affecting the train seat capacity. According to the law of passenger flow fluctuation, the method by which to jointly optimize the existing ticket pricing and allocation and make full use of the train seat capacity while increasing transport revenue is a difficult problem that needs to be solved urgently in the current market-oriented reform of railway transport enterprises. In the final analysis, the lack of an accurate grasp of passenger dynamic demand in ticket pricing and allocation is the main reason that causes the waste of train seat capacity and lower revenue. Although China Railway has gradually liberalized the independent pricing power of China's high-speed railway and tested it in some respects, it is still in the exploratory period. The current ticketing organization work still adopts the fixed ticket price and pre-allocation scheme during the pre-sale period. This scheme not only lacks the consideration of the dynamic demand characteristics of passengers during the pre-sale period, but also ignores that ticket pricing and allocation is an interconnected and inseparable whole. In conclusion, to improve the competitiveness and efficiency for HSRs' passenger transport, it is necessary to study the joint optimization of ticket pricing and allocation on the HSR based on dynamic passenger demand during the pre-sale period. The remainder of this paper is organized as follows.