Global maximum likelihood estimation procedure for multinomial probit (MNP) model parameters Yu-Hsin Liu a, * , Hani S. Mahmassani b,1 a Department of Civil Engineering, National Chi-Nan University, 1, Ta-Hsueh Rd. Puli, Nantou County 545, Taiwan, ROC b Department of Civil Engineering and Department of Management Science & Information Systems, The University of Texas at Austin, Austin, TX 78712, USA Accepted 2 June 1999 Abstract This paper presents a procedure, named GAMNP, incorporating genetic algorithms (GAs) and non- linear programming (NLP) techniques to ®nd the ``global'' maximum likelihood estimate (MLE) in mul- tinomial probit (MNP) model estimation. The GAMNP estimation procedure uses GAs to search for ``good'' starting points systematically and globally through the possible solution areas that satisfy the property of positive de®nite variance±covariance matrix; the NLP algorithm is then used to ®ne-tune the solutions obtained from the GAs procedure. A numerical experiment was conducted to test the perfor- mance of the GAMNP estimation procedure based on an arti®cial data set with known parameter values, model speci®cation, and error structure. The log-likelihood function value, parameter accuracy measures, and the CPU execution time were adopted as performance measures in this experiment. The experimental results indicated that the GAMNP estimation procedure is able to ®nd the global MLE in MNP model estimation when the analyst does not have a priori expectations of the magnitudes of the parameters. The highlight, the importance of using systematic starting solution search procedures, like those used in genetic algorithms, instead of selecting starting solutions arbitrarily. Ó 2000 Elsevier Science Ltd. All rights reserved. Transportation Research Part B 34 (2000) 419±449 www.elsevier.com/locate/trb * Corresponding author. Tel.: +011-886-49-910960 ext. 4959; fax: +011-886-49-918679. E-mail addresses: yuhsin@ncnu.edu.tw (Y.-H. Liu), masmah@mail.utexas.edu (H.S. Mahmassani). 1 Tel.: +512-471-4539; fax: +512-471-0592. 0191-2615/00/$ - see front matter Ó 2000 Elsevier Science Ltd. All rights reserved. PII:S0191-2615(99)00033-8