A Genetic Algorithm with cycle representation and contraction digraph model for Guideway Network design of Personal Rapid Transit

In this paper, we propose a steady-state genetic algorithm (GA) with cycle-based representation and a contraction digraph model to deal with the guideway network design problem of personal rapid transit (PRT). PRT is a novel transportation paradigm, where many computer-controlled vehicles running on an elevated guideway network (GN). A GN may contain hundreds of guideway links and how to design the minimum-cost feasible GN is a challenging problem. Given a set of stations, the proposed GA models a candidate GN as a union of one or more simple directed cycles visiting two or more stations. This cycle representation not only provides high solution locality but allows us to establish a contraction digraph model, where its feasibility can be efficiently evaluated. We also develop special genetic operators well suited for the cycle representation. Numerical experiments conducted for various problem instances show the proposed GA outperforms the conventional ones once the solution is represented by a moderate number of cycles.