David Bergman

Rahul Patel, Elias B. Khalil, David Bergman

In multicriteria decision-making, a user seeks a set of non-dominated solutions to a (constrained) multiobjective optimization problem, the so-called Pareto frontier. In this work, we seek to bring a state-of-the-art method for exact multiobjective integer linear programming into the heuristic realm. We focus on binary decision diagrams (BDDs) which first construct a graph that represents all feasible solutions to the problem and then traverse the graph to extract the Pareto frontier. Because the Pareto frontier may be exponentially large, enumerating it over the BDD can be time-consuming. We explore how restricted BDDs, which have already been shown to be effective as heuristics for single-objective problems, can be adapted to multiobjective optimization through the use of machine learning (ML). MORBDD, our ML-based BDD sparsifier, first trains a binary classifier to eliminate BDD nodes that are unlikely to contribute to Pareto solutions, then post-processes the sparse BDD to ensure its connectivity via optimization. Experimental results on multiobjective knapsack problems show that MORBDD is highly effective at producing very small restricted BDDs with excellent approximation quality, outperforming width-limited restricted BDDs and the well-known evolutionary algorithm NSGA-II.

David Bergman, Teng Huang, Philip Brooks et al.

Business research practice is witnessing a surge in the integration of predictive modeling and prescriptive analysis. We describe a modeling framework JANOS that seamlessly integrates the two streams of analytics, for the first time allowing researchers and practitioners to embed machine learning models in an optimization framework. JANOS allows for specifying a prescriptive model using standard optimization modeling elements such as constraints and variables. The key novelty lies in providing modeling constructs that allow for the specification of commonly used predictive models and their features as constraints and variables in the optimization model. The framework considers two sets of decision variables; regular and predicted. The relationship between the regular and the predicted variables are specified by the user as pre-trained predictive models. JANOS currently supports linear regression, logistic regression, and neural network with rectified linear activation functions, but we plan to expand on this set in the future. In this paper, we demonstrate the flexibility of the framework through an example on scholarship allocation in a student enrollment problem and provide a numeric performance evaluation.