Using genetic algorithms to optimize stopping patterns for passenger rail transportation

In a passenger railroad system, the stopping pattern optimization problem determines the train stopping strategy, taking into consideration multiple train classes, station types, and customer origin-destination (OD) demand, to maximize the profit made by a rail company. The stopping pattern is traditionally decided by rule of thumb, an approach that leaves much room for improvement. In this article, we propose an integer program for this problem and provide a systematic approach to determining the optimal train stopping pattern for a rail company. Commonly used commercial optimization packages cannot solve this complex problem efficiently, especially when problems of realistic size need to be solved. Therefore, we develop two genetic algorithms, namely binary-coded genetic algorithm (BGA) and integer-coded genetic algorithm (IGA). In many of the past evolutionary programming studies, the chromosome was coded using the binary alphabet as BGA. The encoding and genetic operators of BGA are straightforward and relatively easy to implement. However, we show that it is difficult for the BGA to converge to feasible solutions for the stopping pattern optimization problem due to the complex solution space. Therefore, we propose an IGA with new encoding mechanism and genetic operators. Numerical results show that the proposed IGA can solve real-world problems that are beyond the reach of commonly used optimization packages.