Incorporating scatter search and threshold accepting in finding maximum likelihood estimates for the multinomial probit model

This paper presents a procedure that incorporates scatter search and threshold accepting to find the maximum likelihood estimates for the multinomial probit (MNP) model. Scatter search, widely used in optimization-related studies, is a type of evolutionary algorithm that uses a small set of solutions as the selection pool for mating and generating new solutions to search for a globally optimal solution. Threshold accepting is applied to the scatter search to improve computational efficiency while maintaining the same level of solution quality. A set of numerical experiments, based on synthetic data sets with known model specifications and error structures, were conducted to test the effectiveness and efficiency of the proposed framework. The results indicated that the proposed procedure enhanced performance in terms of likelihood function value and computational efficiency for MNP model estimation as compared to the original scatter search framework.