Transformer Models – Optimization Online

Inverse Optimization Without Inverse Optimization: Direct Solution Prediction with Transformer Models

Published: 2026/02/01

Combinatorial Optimization, Integer Programming Constrained Learning, Generative Neural Networks, inverse optimization, Structured Prediction, Transformer Models

We present an end-to-end framework for generating solutions to combinatorial optimization problems with unknown components using transformer-based sequence-to-sequence neural networks. Our framework learns directly from past solutions and incorporates the known components, such as hard constraints, via a constraint reasoning module, yielding a constrained learning scheme. The trained model generates new solutions that are structurally … Read more

Machine Learning Algorithms for Assisting Solvers for Constraint Satisfaction Problems

Published: 2025/11/09

Morteza Kimiaei

Vyacheslav Kungurtsev

Applications - OR and Management Sciences, Combinatorial Optimization, Optimization in Data Science Boolean Satisfiability, Conflict-Driven Clause Learning, Constraint Satisfaction Problem, Graph Neural Networks, Hybrid Solvers, Lazy Clause Generation, Learned Heuristics, machine learning, Neuro-Symbolic Optimization, reinforcement learning, Transformer Models

This survey proposes a unifying conceptual framework and taxonomy that systematically integrates Machine Learning (ML) and Reinforcement Learning (RL) with classical paradigms for Constraint Satisfaction and Boolean Satisfiability solving. Unlike prior reviews that focus on individual applications, we organize the literature around solver architecture, linking each major phase—constraint propagation, heuristic decision-making, conflict analysis, and meta-level … Read more