A non-anticipative learning-optimization framework for solving multi-stage stochastic programs

We present a non-anticipative learning- and scenario-based prediction-optimization (ScenPredOpt) framework that combines deep learning, heuristics, and mathematical solvers for solving combinatorial problems under uncertainty. Specifically, we transform neural machine translation frameworks to predict the optimal solutions of scenario-based multi-stage stochastic programs. The learning models are trained efficiently using the input and solution data of the multi-stage single-scenario deterministic problems. Then our ScenPredOpt framework creates a mapping from the inputs used in training into an output of predictions that are close to optimal solutions. We present a Non-anticipative Encoder-Decoder with Attention (NEDA) approach, which ensures the non-anticipativity property of multi-stage stochastic programs and, thus, time consistency by calibrating the learned information based on the problem's scenario tree and adjusting the hidden states of the neural network. In our ScenPredOpt framework, the percent predicted variables used for the solution are iteratively reduced through a relaxation of the problem to eliminate infeasibility. Then, a linear relaxation-based heuristic is performed to further reduce the solution time. Finally, a mathematical solver is used to generate the complete solution. We present the results on two NP-Hard sequential optimization problems under uncertainty: stochastic multi-item capacitated lot-sizing and stochastic multistage multidimensional knapsack. The results show that the solution time can be reduced by a factor of 599 with an optimality gap of only 0.08%. We compare the results of the ScenPredOpt framework with cutting-edge exact and heuristic solution algorithms for the problems studied and find that our framework is more effective. Additionally, the computational results demonstrate that ScenPredOpt can solve instances with a larger number of items and scenarios than the trained ones. Our non-anticipative learning-optimization approach can be beneficial for stochastic programming problems involving binary variables that are solved repeatedly with various types of dimensions and similar decisions at each period.