Multi-objective graph partitioning for the MFD-based perimeter control of an urban network

The Macroscopic Fundamental Diagrams (MFDs) can be applied to guide perimeter control strategies where the network is divided into several manageable regions. Although there has been a large body of literature on the MFD theory, more research is needed on how the network should be best partitioned to suit this purpose. We argue that multiple objectives should be considered, which are (i) each region should have a well-defined MFD so its behaviour can be modelled with reasonable accuracy; (ii) the MFDs should show a clear indication of where the critical density lies; (iii) neighbouring regions should have low time correlation of traffic density to avoid peaking at the same time; (iv) the regions should have a similar size so they have enough capacity to act as the buffer for their neighbours. We developed metrics to quantify these properties and proposed a greedy multi-objective k-way spectral graph partitioning algorithm, in combination with a local search agglomerative process, to search for partitions that optimize these metrics. Pareto-efficiency based criteria were adopted in candidate selection. The case study using the real traffic data from Perth (Western Australia) showed that our method consistently outperforms the benchmarks generated by random partitioning and the traffic density similarity spectral clustering algorithm.