Image-Based Decomposition for Fast Iterative Solve of Complex Linear Problems

A computer-implemented method of solving a supply chain planning problem modeled as linear programing problem, comprising:

• generating pixels, by an image rendering engine, of a supply chain problem image, the pixels representing links between constraints and variables of the linear programming problem;
• identifying, by an image processing engine, one or more contours of the supply chain problem image using a machine-learning model trained using a convolutional neural network and contour-labeled images received from the image rendering engine, wherein the one or more contours comprise at least a first contour and a second contour, wherein the first contour represents one or more first constraints and the second contour represents one or more second constraints;
• determining, by a decomposition module, a partition comprising the at least two components linked by the first contour is more balanced than a partition comprising the at least two components linked by the second contour;
• selecting, by the decomposition module, the at least one of the one or more first constraints as the one or more complicating constraints;
• formulating, by a solver, at least two decomposed subproblems sharing one or more complicating constraints associated with at least one of the one or more contours;
• and
• solving, by the solver, the decomposed subproblems to generate a solution to the supply chain planning problem.

A non-transitory computer-readable medium embodied with software providing solving of supply chain planning problems modeled as linear programing problems, the software when executed:

• generates, by an image rendering engine, pixels of a supply chain problem image, the pixels representing links between constraints and variables of the linear programming problem;
• identifies, by an image processing engine, one or more contours of the supply chain problem image using a machine-learning model trained using a convolutional neural network and contour-labeled images received from the image rendering engine, wherein the one or more contours comprise at least a first contour and a second contour, wherein the first contour represents one or more first constraints and the second contour represents one or more second constraints;
• determines, by a decomposition module, a partition comprising the at least two components linked by the first contour is more balanced than a partition comprising the at least two components linked by the second contour;
• selects, by the decomposition module, the at least one of the one or more first constraints as the one or more complicating constraints;
• formulates, by a solver, at least two decomposed subproblems sharing one or more complicating constraints associated with at least one of the one or more contours;
• and
• solves, by the solver, the decomposed subproblems to generate a solution to the supply chain planning problem.