Research Article

Performance Comparison of Mode Choice Optimization Algorithm with Simulated Discrete Choice Modeling

Table 17

Log-likelihood values obtained from four algorithms responding to a new way of calculating the initial Hessian matrix adopted from BHHH and BHHH-2 algorithm (exp. 3) ().

Algorithms & log-likelihood valuesStep size ()
1/321/161/81/41/21

DFP-(BHHH)
 Starting-−869.0964727−869.0964727−869.0964727−869.0964727-
 Convergence-−705.5637886−705.5640275−705.5628106−705.563426-
 Iteration num.-74371911-
DFP-(BHHH-2)
 Starting-−869.0964727−869.0964727−869.0964727−869.0964727-
 Convergence-−705.5624724−705.5613663−705.5582318−705.5777822-
 Iteration num.-74371910-
BFGS-(BHHH)
 Starting−869.0964727−869.0964727−869.0964727−869.0964727−869.0964727−869.0964727
 Convergence−705.5653328−705.5632175−705.5626989−705.5594868−705.5738092−705.6029697
 Iteration num.147743719106
BFGS-(BHHH-2)
 Starting−869.0964727−869.0964727−869.0964727−869.0964727−869.0964727−869.0964727
 Convergence−705.5647226−705.5653491−705.560551−705.5562946−705.5684402−705.5903477
 Iteration num.147733719106

Algorithms & log-likelihood valuesInterval of uncertainty
LL, ULLL, ULLL, ULLL, ULLL, ULLL, ULLL, ULLL, UL

DFP-GSM-(BHHH)
 Starting−869.0964727−869.0964727−869.0964727−869.0964727−869.0964727−869.0964727−869.0964727−869.0964727
 Convergence−705.5780259−705.5800667−705.5793165−705.5793036−705.5793088−705.5793663−705.5792608−705.5792724
 Iteration num.76666666
DFP-GSM-(BHHH-2)
 Starting−869.0964727−869.0964727−869.0964727−869.0964727−869.0964727−869.0964727−869.0964727−869.0964727
 Convergence−705.5801332−705.5791271−705.5791655−705.5790698−705.5790891−705.579119−705.5791455−705.5790615
 Iteration num76666666
BFGS-GSM-(BHHH)
 Starting−869.0964727−869.0964727−869.0964727−869.0964727−869.0964727−869.0964727−869.0964727−869.0964727
 Convergence−705.7714975−705.5794055−705.5794037−705.579253−705.5792989−705.5793014−705.5793255−705.5793366
 Iteration num56666666
BFGS-GSM-(BHHH-2)
 Starting−869.0964727−869.0964727−869.0964727−869.0964727−869.0964727−869.0964727−869.0964727−869.0964727
 Convergence−705.5911918−705.5791171−705.5791203−705.5790991−705.5791241−705.5791221−705.579121−705.5791082
 Iteration num.66666666