A Mixed Neuro Graph Approach with Gradient Boosting to Hybrid Job-Shop Scheduling to Minimize a Regular Function of Job Completion Times and Numbers of Used Machines

The paper considers a multi-stage processing system including sets of identical (parallel) machines and a set of dedicated machines processing different operations of the given jobs in any sectors of economy. Based on the weighted Mixed Neuro graph model, the paper proposes adaptive algorithms for solving this problem via appropriate Mixed Neuro graph transformations. The main novelty is (1) low demands on the source data-unlike classical machine learning algorithms, the approach can offer stable interpretable results even with a short dataset size; (2) the number of new matrix multiplication operations that make up the main load when training models increases linearly with the number of new data from 0 to 999 time periods; (3) the results of the model are repeatable due to the stability of the coefficients of the model. These algorithms are able to solve (exactly or heuristically) the tested instances with N jobs and W types of parallel identical machines within on the personal computer. The gradient boosting result is in interval 5.9677410-3.4982093.