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

Learning-Augmented Combinatorial Solvers: A Solver-Architecture Taxonomy

Published: 2025/11/09, Updated: 2026/10/05

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 paper presents a solver-architecture taxonomy of machine-learning and reinforcement-learning interventions in combinatorial solving. Rather than treating learning-augmented solving as a collection of isolated applications, we organize existing methods according to the solver-level decisions they influence, including propagation, branching, conflict analysis, restart control, structural analysis, and formulation-level reasoning. The discussion focuses on SAT/CDCL, Lazy Clause … Read more