Metamodel-Based Optimization Method for Traffic Network Signal Design under Stochastic Demand

Algorithm 1

Gradient-based metamodel algorithm.

	Step 1: initialization. Set the parameters of traffic assignment model . Set a set of initial signal settings .
	Step 2: apply the initial signal setting. Based on the initial signal settings , calculate the average equilibrium flow , and get the corresponding ; calculate the gradient of the traffic assignment model and the gradient of the initial average equilibrium flow, construct the combined metamodel as equation (24), and apply it into equations (25)–(28) to solve the signal control optimization problem, obtain the control , and update the iteration step .
	Step 3: calculate the average equilibrium flow. Implement to derive and update the set of signal settings and the corresponding average equilibrium flow, i.e., and .
	Step 4: update the gradient-based metamodel. Calculate the gradient of the metamodel according to equation (22); calculate the Jacobian matrix based on equation (23) to obtain ; update the combined metamodel at the current iteration, i.e., .
	Step 5: update the signal setting. Calculate by solving the control optimization (25)–(28) with the updated metamodel and update the signal setting .
	Step 6: check termination. Stop if the termination condition is satisfied; otherwise, set and go to Step 3.