Virtual balise placement for GNSS-based train control using aquila optimization-enhanced multi-objective optimization

The Virtual Balise (VB) technology enables a specification-compatible application of Global Navigation Satellite System (GNSS) in existing train control systems. However, the effectiveness of VB functions highly depends on the GNSS positioning performance at VBs, but how to effectively determine the exact geospatial coordinates of VBs remains unexplored. This paper aims to introduce an advanced optimization method to determine the VB layout considering the GNSS positioning performance at candidate VB locations. Specifically, two classification methods of the target railway track areas are elaborately designed to classify and identify candidate track segments for VB placement, and a novel Nondominated Sorting Genetic Algorithm II (NSGA-II) optimization method is proposed based on the enhancement by the Aquila Optimization (AO) algorithm to determine the exact VB layout solution. The test results for a high-speed railway line demonstrate that the derived optimized VB layout solution achieves a high capture rate of 100%, leading to a 7.57% reduction in Horizontal Positioning Error (HPE). In conclusion, the proposed AO-enhanced NSGA-II method is capable of achieving the advanced optimization capability for the VB database design over the reference strategies, which illustrates the great potential in promoting the practical application of GNSS in future intelligent train control systems. © 2025 Elsevier Ltd