Signal optimisation using the cross entropy method

The problem of the optimisation of traffic signals in a network comes in a variety of forms, depending on whether the traffic model used to evaluate any proposed set timings is deterministic or Monte Carlo, whether the drivers' routes are fixed or dependent on the signal timings, and whether the control is fixed-time or responsive. The paper deals with fixed-time control, and investigates the application of the cross-entropy method (CEM) to find the global optimum solution. It is shown that the CEM can be applied both to deterministic and Monte Carlo problems and to fixed-route or variable-route problems. Such combinatorial problems typically have a large number of local optima and therefore simple hill-climbing methods are ineffective.The paper demonstrates firstly how the cross-entropy method provides an efficient and robust approach when the traffic model that provides, for any solution x, the value of the performance index (PI) z(x) is deterministic. It then goes onto discuss the effect of noise in the evaluation process, such as arises when a Monte Carlo simulation model is used, so that the PI can be expressed as z(x)=z₀(x)+e(x) where e is a random error, whose variance s² depends inversely either on T, the length of the simulation run, or on M the number of simulation runs carried out for any solution. A second example illustrates the application of the CEM to a noisy problem, in which a Monte Carlo traffic assignment model is used to estimate drivers' route choices in response to any proposed signal timings, and shows the principles by which the values of either T or M must be adapted through the iterative process.