Optimization of Multimodal Public Transit Networks Considering Spatial Equity

Abstract

Public transport equity is usually assessed after a network has been designed rather than treated as a requirement that shapes the design itself. This study develops an equity-oriented optimization framework for hierarchical multimodal transit networks in which a fixed rail backbone, main-bus routes, and feeder-bus routes are designed jointly. The model minimizes an integrated objective combining total system cost and the modal accessibility gap between public transport and private cars, while spatial equity is imposed as a binding constraint through two alternative Gini-based standards: a demand-proportional (horizontal) index and a need-sensitive (vertical) index. The problem is solved by a genetic algorithm that embeds a strategy-based passenger assignment with crowding effects and tracks the best-so-far solution across generations. Experiments on Mandl’s benchmark network across eight scenarios, combining the two equity standards with four threshold levels, yield average travel times of 11.8–13.9 min. The two standards produce structurally different networks, and stricter equity does not necessarily degrade performance: the strictest need-sensitive scenario attains the lowest average travel time, although it also records the largest modal gap relative to cars. The framework thus supports scenario-based comparison, in which the equity formulation and threshold serve as explicit policy levers rather than fixed technical bounds.