End-to-end learning trains a machine-learning model to formulate solutions directly from an input problem instance, rather than separately engineering every intermediate optimization stage. section 11.5 section 11.10
Within machine learning for combinatorial optimization, distinguish three roles:
- End-to-end learning maps an input instance directly to a proposed solution. section 11.5
- Learning to configure algorithms predicts parameters such as learning rates, annealing schedules, mutation variation, or pheromone influences. section 11.5
- Machine learning combined with optimization repeatedly consults a model using the algorithm’s current state. section 11.5
Pointer networks for routing
A pointer network applies sequence-to-sequence learning with attention to variable-sized inputs. One example trains on m points and validates on n points for the Euclidean planar symmetric traveling-salesperson problem. section 11.5 section 11.10
Figure 11.14 Machine learning (ML) for combinatorial optimization (CO) problems
Use the comparison figure to distinguish direct solution formulation, learned algorithm configuration, and repeated model-guided optimization. section 11.5

