A Lagrangian decomposition scheme for choice-based optimization

Choice-based optimization problems are the family of that incorporate stochasticity individual preferences according to discrete choice models make planning decisions. This integration brings non-convexity and nonlinearity associated mathematical formulations. Previously, authors have tackled these issues by introducing a simulation-based approximation model with aim linearizing it. Nevertheless, already existing exact methods state-of-the-art commercial solvers fail solve relevant instances. In this paper, we propose novel Lagrangian decomposition method inspired scenario grouping in stochastic programming framework choice-based problems. addition, develop tailored algorithm generate feasible solutions original problem from solution subproblem Hence, at each iteration subgradient method, which is used dual, provide both an upper lower bound problem. enables calculation duality gap assess quality generated solutions. Computational results show provides optimality gaps below 0.5% restricted within low computational times. We also leads high-quality gaps. • for general Decomposition groups improve obtained bound. Exploring via solves formulation.