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Approaches based on Binary decision diagrams (BDDs) have recently achievedstate-of-the-art results for multiobjective integer programming problems. Thevariable ordering used in constructing BDDs can have a significant impact ontheir size and on the quality of bounds derived from relaxed or restricted BDDsfor single-objective optimization problems. We first showcase a similar impactof variable ordering on the Pareto frontier (PF) enumeration time for themultiobjective knapsack problem, suggesting the need for deriving variableordering methods that improve the scalability of the multiobjective BDDapproach. To that end, we derive a novel parameter configuration space based onvariable scoring functions which are linear in a small set of interpretable andeasy-to-compute variable features. We show how the configuration space can beefficiently explored using black-box optimization, circumventing the curse ofdimensionality (in the number of variables and objectives), and finding goodorderings that reduce the PF enumeration time. However, black-box optimizationapproaches incur a computational overhead that outweighs the reduction in timedue to good variable ordering. To alleviate this issue, we propose LEO, asupervised learning approach for finding efficient variable orderings thatreduce the enumeration time. Experiments on benchmark sets from the knapsackproblem with 3-7 objectives and up to 80 variables show that LEO is ~30-300%and ~10-200% faster at PF enumeration than common ordering strategies andalgorithm configuration. Our code and instances are available athttps://github.com/khalil-research/leo.

LEO: Learning Efficient Orderings for Multiobjective Binary Decision Diagrams