In this paper we study the Local Optimisation of Signal Settings (LOSS) problem that arises when signal control parameters of an urban road network are locally optimised and have to be consistent with equilibrium traffic flows. This problem can be formulated with an (asymmetric) equilibrium assignment model. In this paper we study the problem and the corresponding equilibrium model and compare several solution algorithms proposed in the literature. All algorithms were tested on a real-scale network with different demand levels and a different number of signalised intersections. Numerical results show that differences in computing times among algorithms are significant when the network is highly congested and there are many signalised inters...