# Real-Time Path Planning of Driverless Mining Trains with Time-Dependent Physical Constraints
## 1 Introduction  
Open pit mines have a large, complex system, and the optimisation of their railroad transportation system is an important part of it. The optimisation of the railroad transportation system can play a crucial role in reducing production and operation costs, as well as in improving the production and organisational efficiency of mines. In recent years, the mining industry has been continuously improving its production and operation equipment, leading to increased automation levels and improved productivity. However, despite these advancements, the bottleneck problems of the mine transport system have started to emerge, particularly with regard to the traditional routing optimisation planning models and algorithms that rely on a static road network analysis method.  
Much research work, including mixed integer programming and dynamic programming, has been conducted to solve urban railroad transportation optimisation problems in the literature [1; 2; 3; 4; 5; 6]. Compared with urban railway networks, mine railway networks have a limited amount of tracks, most of which are bidirectional single tracks. This leads to some particular problems, as follows.  
* Track allocation: Given most tracks are bidirectional single tracks, the transportation capacity is limited by the number of receiving and departure tracks, the number of siding/meetpoints, and the length of single tracks. Moreover, the capacity is also restricted by track maintenance.
* Train conflict: For a bidirectional single-track, there are mainly two conflicts between trains. First, a predefined time difference is necessary to ensure safe operation when trains running in the same direction. Secondly, trains in opposite directions cannot be in the same segment at any time.  
Given the problems stated above, the mine railroad scheduling problem is a complex optimisation problem, and the results under different decisions are far from each other. With the purpose of the less running time for all trains and maximizing the total amount ofrolling stock, this paper proposes an integrated model by which to optimize train timetable and track allocation. The main contributions of this paper are listed as follows.  
* We first formulate a multiobjective optimisation problem for mine railway scheduling by introducing a set of mathematical constraints.
* As the problem is NP-hard, we then devise a MIP-based solution to solve this problem in a real-time manner.
* We finally conduct test cases to demonstrate the validity and effectiveness of the solution.  
In the following sections, Section 2 presents a review on the railway scheduling and train timetabling problems. Section 3 introduces the system model and describes the mining railroad optimisation problem. Section 4 provides the mathematical formulation for the objective and the set of constraints. Section 5 presents a description of all the modules that constitute the developed solution, in order for all the readers to get an understanding of the entire process. Section 6 presents a summary of the result for the tests carried out to evaluate the proposed solution. Section 7 is dedicated to the conclusions.