BHAMSLE: A Breakpoint Heuristic Algorithm for Maximum Simulated Likelihood Estimation of Advanced Discrete Choice Models

Maximum simulated likelihood estimation (MSLE) is inherently complex due to the presence of multiple local maxima, which hinder standard optimization methods. One solution is to reformulate MSLE as a mixed-integer linear program (MILP), enabling the use of combinatorial techniques to obtain globally optimal solutions. However, this approach introduces two difficulties: (1) the reliance on simulation-based approximation, which is unavoidable when dealing with continuous mixtures and does not pose a fundamental limitation, and (2) the computational intractability of large-scale instances. To address the latter, we adapt the Breakpoint Heuristic Algorithm (BHA), originally developed for choice-based pricing, which has proven effective in solving similar MILPs with high accuracy and reduced computational time. The resulting method, the BHA for MSLE (or BHAMSLE for short), exploits the problem's combinatorial structure by identifying decision-making breakpoints in a coordinate descent framework. Numerical experiments show that BHAMSLE significantly outperforms state-of-the-art global optimization methods that do not exploit this structure. Our approach delivers strong initialization points for estimation, yielding higher log-likelihoods, more stable and interpretable estimates, and improved recovery of latent segments, even in models with mixed parameters and restricted choice sets.