# Heuristic Multiobjective Discrete Optimization using Restricted Decision Diagrams

arXiv: https://arxiv.org/abs/2403.02482 · HTML: https://mlsanity.com/paper/2403.02482/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 40 references that are in the map.
- First posted on arXiv 4 Mar 2024.

## Builds on (most cited first, 12 of 12)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [pymoo: Multi-objective Optimization in Python](https://mlsanity.com/paper/2002.04504/) (2020)
- [Learning the Pareto Front with Hypernetworks](https://mlsanity.com/paper/2010.04104/) (2020)
- [Global Self-Attention as a Replacement for Graph Convolution](https://mlsanity.com/paper/2108.03348/) (2021)
- [Multi-Objective GFlowNets](https://mlsanity.com/paper/2210.12765/) (2022)
- [Pareto Set Learning for Expensive Multi-Objective Optimization](https://mlsanity.com/paper/2210.08495/) (2022)
- [Improving Optimization Bounds using Machine Learning: Decision Diagrams meet Deep Reinforcement Learning](https://mlsanity.com/paper/1809.03359/) (2018)
- [Network Models for Multiobjective Discrete Optimization](https://mlsanity.com/paper/1802.08637/) (2018)
- [Branch-and-bound for biobjective mixed-integer linear programming](https://mlsanity.com/paper/1709.03668/) (2017)
- [LEO: Learning Efficient Orderings for Multiobjective Binary Decision Diagrams](https://mlsanity.com/paper/2307.03171/) (2023)

## Abstract (arXiv)

Decision diagrams (DDs) have emerged as a state-of-the-art method for exact multiobjective integer linear programming. When the DD is too large to fit into memory or the decision-maker prefers a fast approximation to the Pareto frontier, the complete DD must be restricted to a subset of its states (or nodes). We introduce new node-selection heuristics for constructing restricted DDs that produce a high-quality approximation of the Pareto frontier. Depending on the structure of the problem, our heuristics are based on either simple rules, machine learning with feature engineering, or end-to-end deep learning. Experiments on multiobjective knapsack, set packing, and traveling salesperson problems show that our approach is highly effective, recovering over 85% of the Pareto frontier while achieving 2.5x speedups over exact DD enumeration on average, with very few non-Pareto solutions. The code is available at https://github.com/rahulptel/HMORDD.