Matrix Encoding Networks for Neural Combinatorial Optimization
This addresses a gap for ML engineers working on complex combinatorial optimization problems with matrix parameters, offering a novel method for previously inaccessible domains.
The paper tackles the challenge of solving combinatorial optimization problems with matrix-style relationship data by introducing Matrix Encoding Networks (MatNet), which processes such inputs to guide solution searches. It demonstrates MatNet's effectiveness by achieving state-of-the-art performance on flexible flow shop problems and being the first neural approach for asymmetric traveling salesman problems.
Machine Learning (ML) can help solve combinatorial optimization (CO) problems better. A popular approach is to use a neural net to compute on the parameters of a given CO problem and extract useful information that guides the search for good solutions. Many CO problems of practical importance can be specified in a matrix form of parameters quantifying the relationship between two groups of items. There is currently no neural net model, however, that takes in such matrix-style relationship data as an input. Consequently, these types of CO problems have been out of reach for ML engineers. In this paper, we introduce Matrix Encoding Network (MatNet) and show how conveniently it takes in and processes parameters of such complex CO problems. Using an end-to-end model based on MatNet, we solve asymmetric traveling salesman (ATSP) and flexible flow shop (FFSP) problems as the earliest neural approach. In particular, for a class of FFSP we have tested MatNet on, we demonstrate a far superior empirical performance to any methods (neural or not) known to date.