Computational Methods for Calculating Multimodal Multiclass Traffic Network Equilibrium: Simulation Benchmark on a Large-Scale Test Case
Algorithm 2
Simulated annealing algorithm.
Result: Inner loop path flow distribution of iteration
Initialization: Set , where denotes the initial temperature;
Set inner loop iteration index to one and ;
Whileanddo
ifthen
Gas Phase:
Generate a solution candidate by Randomization method.
Randomization: users choose their path randomly from the path set;
else ifthen
Liquid Phase:
Generate the first solution candidate by Randomization method; Generate the second and third solution candidates by applying MSA and Gap-based methods to ;
else
Solid Phase:
Generate the first and second solution candidates by applying MSA and Gap-based methods to ;
end
Execute traffic simulation in parallel for all candidates;
Identify the shortest path for all ODs based on the simulation results for each candidate;
Update based on updated shortest path(s) for all candidates;
Calculate the solution acceptance probability for each candidate by the following equation:
where denotes a candidate, denotes the binary decision variable and ;
Take decision about accepting each candidate to determine ;
Decrease the temperature by the following formula:
